%!PS-Adobe-2.0 %%Creator: dvips(k) 5.996 Copyright 2016 Radical Eye Software %%Title: arXiv:1609.03818v5 [math-ph] 5 Jun 2018 %%CreationDate: Wed Jun 6 23:01:39 2018 %%Pages: 11 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -R2 -P pk -z FSS_Festschrift_v6-Mai18.dvi -o %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2018.06.06:2301 %%BeginProcSet: texc.pro 0 0 %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /dir 0 def/dyy{/dir 0 def}B/dyt{/dir 1 def}B/dty{/dir 2 def}B/dtt{/dir 3 def}B/p{dir 2 eq{-90 rotate show 90 rotate}{dir 3 eq{-90 rotate show 90 rotate}{show}ifelse}ifelse}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)(LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse} forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{ BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat {BDot}imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B /M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M} B/g{0 M}B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{ 0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: FSS_Festschrift_v6-Mai18.out.ps 0 0 %! /pdfmark where{pop} {/globaldict where{pop globaldict}{userdict}ifelse/pdfmark/cleartomark load put} ifelse [ /Title(1. 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Fk(z)2470 3413 y Fh(i)2496 3403 y Fj(j)2516 3379 y Fg(2)2550 3403 y Fk(=)p Fm(2)3499 3440 y Fq(\(1.1\))86 3686 y(where)27 b(the)h Fo(z)542 3700 y Fk(i)596 3686 y Fn(2)d Ff(C)51 b Fq(are)28 b(the)g(p)s(ositions)e(of)h Fo(N)38 b Fq(particles)27 b(mo)m(ving)g(in)g Ff(R)2509 3653 y Fm(2)2555 3686 y Fq(,)h(iden)m(ti\014ed)e(with)g(the)i(complex) 86 3794 y(plane,)23 b(and)f(the)g(constan)m(t)h Fo(c)1061 3808 y Fm(Lau)1207 3794 y Fq(is)e(a)h(normalization)f(factor)i(\(dep)s (ending)d(on)i Fo(N)32 b Fq(and)22 b Fo(`)p Fq(\).)38 b(F)-8 b(or)23 b(fermions,)86 3902 y Fo(`)31 b Fq(is)e(o)s(dd)h(and)h Fn(\025)25 b Fq(3)32 b(\(the)f(case)h Fo(`)26 b Fq(=)g(1)31 b(corresp)s(onds)e(to)j(nonin)m(teracting)e(fermions\),)g(while)f(for)i (b)s(osons)86 4010 y Fo(`)25 b Fn(\025)g Fq(2)31 b(is)f(ev)m(en.)41 b(Bosonic)31 b(w)m(a)m(v)m(e)h(functions)d(of)i(this)e(t)m(yp)s(e)i (are)g(p)s(oten)m(tially)e(relev)-5 b(an)m(t)31 b(for)f(atomic)h(gases) 86 4118 y(in)36 b(arti\014cial)f(magnetic)j(\014elds)d([)1224 4118 y SDict begin H.S end 1224 4118 a Black Fq(8)p Black 1270 4059 a SDict begin H.R end 1270 4059 a 1270 4118 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Cooper-08) cvn H.B /ANN pdfmark end 1270 4118 a Fq(,)1332 4118 y SDict begin H.S end 1332 4118 a Black Fq(6)p Black 1378 4059 a SDict begin H.R end 1378 4059 a 1378 4118 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.BloDalZwe-08) cvn H.B /ANN pdfmark end 1378 4118 a Fq(,)1440 4118 y SDict begin H.S end 1440 4118 a Black Fq(21)p Black 1531 4059 a SDict begin H.R end 1531 4059 a 1531 4118 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.LewSei-09) cvn H.B /ANN pdfmark end 1531 4118 a Fq(,)1593 4118 y SDict begin H.S end 1593 4118 a Black Fq(30)p Black 1684 4059 a SDict begin H.R end 1684 4059 a 1684 4118 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 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Fh(i)2612 4688 y Fj(j)2632 4665 y Fg(2)2666 4688 y Fk(=)p Fm(2)3499 4726 y Fq(\(1.2\))86 4883 y(with)23 b Fo(A)h Fq(analytic,)i(an)m(tisymmetric)e(for)g (fermions)f(and)g(symmetric)h(for)g(b)s(osons.)38 b(Also)24 b(square)g(in)m(tegra-)86 4991 y(bilit)m(y)19 b(is)h(required,)i(but)e Fo(A)i Fq(is)e(not)h(restricted)g(to)h(p)s(olynomials.)35 b(If)20 b(there)i(is)e(strong)h(repulsiv)m(e)f(t)m(w)m(o-b)s(o)s(dy)86 5099 y(in)m(teraction)29 b(b)s(et)m(w)m(een)h(the)g(particles,)f(the)g (Laughlin)f(function)g(\()2362 5099 y SDict begin H.S end 2362 5099 a Black Fq(1.1)p Black 2478 5041 a SDict begin H.R end 2478 5041 a 2478 5099 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.1.1) cvn H.B /ANN pdfmark end 2478 5099 a Fq(\))i(is)e(a)i(natural)f(trial)f(function)g(for)86 5209 y(lo)m(w)k(energy)g(states.)48 b(The)31 b(factors)i(\()p Fo(z)1407 5223 y Fk(i)1458 5209 y Fn(\000)21 b Fo(z)1592 5223 y Fk(j)1628 5209 y Fq(\))1663 5176 y 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(page.2) cvn /DEST pdfmark end -222 785 a Black 86 559 a Fm(2)624 b(ELLIOTT)24 b(H.)f(LIEB,)h (NICOLAS)g(R)n(OUGERIE,)f(AND)g(JAK)n(OB)h(YNGV)-8 b(ASON)p Black 186 759 a Fq(The)39 b(success)h(of)g(Laughlin's)d(theory)j(of)g (the)g(F)m(QHE)g(fractions)g(1)p Fo(=`)p Fq(,)j(based)c(on)h(\()3146 759 y SDict begin H.S end 3146 759 a Black Fq(1.1)p Black 3262 700 a SDict begin H.R end 3262 700 a 3262 759 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.1.1) cvn H.B /ANN pdfmark end 3262 759 a Fq(\),)j(dep)s(ends)86 867 y(crucially)32 b(on)h(the)h(fact)g(that)g(the)g(Laughlin)d(w)m(a)m(v)m (e)36 b(function)c(b)s(eha)m(v)m(es)i(as)g(an)f Fr(inc)-5 b(ompr)g(essible)38 b(liquid)p Fq(,)86 975 y(whose)28 b(resp)s(onse)f(to)h(p)s(erturbations)e(and)i(external)g(\014elds)e(is) h(extremely)h(rigid.)38 b(This)26 b(in)h(fact)i(has)f(t)m(w)m(o)86 1083 y(distinct)h(asp)s(ects:)86 1268 y Fv(1.)k Fq(The)e(Laughlin)f(w)m (a)m(v)m(e)35 b(function)c(is)g(an)h(appro)m(ximate)h(ground)e(state)j (for)e(the)g(man)m(y-b)s(o)s(dy)g(Hamil-)86 1376 y(tonian,)e(and)g(its) g(energy)g(is)g(separated)g(from)g(the)h(rest)f(of)h(the)g(sp)s(ectrum) e(b)m(y)h(a)h(gap.)86 1561 y Fv(2.)j Fq(Mo)s(di\014cations)f(of)h(the)h (Laughlin)c(w)m(a)m(v)m(e)36 b(function)d(that)i(sta)m(y)g(within)d (the)i(ground)f(eigenspace)i(of)86 1669 y(the)f(man)m(y-b)s(o)s(dy)f (Hamiltonian)g(cannot)h(increase)g(the)g(lo)s(cal)g(one-particle)f (densit)m(y)h(b)s(ey)m(ond)f(a)i(\014xed)86 1777 y(v)-5 b(alue.)186 1963 y(The)31 b(main)g(evidence)i(for)f(these)g(facts)h(is) f(exp)s(erimen)m(tal)f(and)g(n)m(umerical.)45 b(F)-8 b(or)33 b(mo)s(del)e(zero-range)86 2071 y(in)m(teractions,)g(the)g (justi\014cation)f(of)h(Prop)s(ert)m(y)h Fv(1)f Fq(w)m(ould)f(amoun)m (t)h(to)h(a)g(pro)s(of)e(of)h(an)g Fo(N)10 b Fq(-indep)s(enden)m(t)86 2179 y(sp)s(ectral)35 b(gap,)j(see)e(e.g.)h([)986 2179 y SDict begin H.S end 986 2179 a Black Fq(21)p Black 1078 2120 a SDict begin H.R end 1078 2120 a 1078 2179 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.LewSei-09) cvn H.B /ANN pdfmark end 1078 2179 a Fq(,)g(Section)f(2.2])h(or)f([)1783 2179 y SDict begin H.S end 1783 2179 a Black Fq(36)p Black 1874 2120 a SDict begin H.R end 1874 2120 a 1874 2179 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouSerYng-13b) cvn H.B /ANN pdfmark end 1874 2179 a Fq(,)h(Section)f(2.1])h(and)e (references)h(therein.)56 b(W)-8 b(e)37 b(are)86 2287 y(not)30 b(a)m(w)m(are)h(of)f(a)g(solution)e(to)j(this)d(imp)s(ortan)m (t)h(problem,)g(but)g(some)h(exact)h(results)e(for)g(lo)m(w)h(v)-5 b(alues)29 b(of)86 2395 y Fo(N)40 b Fq(can)31 b(b)s(e)f(found)f(in)g([) 876 2395 y SDict begin H.S end 876 2395 a Black Fq(28)p Black 967 2336 a SDict begin H.R end 967 2336 a 967 2395 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.MasMatOuv-07) cvn H.B /ANN pdfmark end 967 2395 a Fq(,)1022 2395 y SDict begin H.S end 1022 2395 a Black Fq(29)p Black 1113 2336 a SDict begin H.R end 1113 2336 a 1113 2395 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.MasMatOuv-13) cvn H.B /ANN pdfmark end 1113 2395 a Fq(].)186 2502 y(Prop)s(ert)m(y)g Fv(2)g Fq(is)e(not)i(alw)m(a)m(ys)g(recognized)f(as)h(a)g(separate)g (issue,)f(but)g(is)f(also)i(crucial)e(for)h(Laughlin's)86 2610 y(original)i(argumen)m(t)h(supp)s(orting)e(quan)m(tization)j(of)f (the)h(Hall)e(conductivit)m(y)h([)2815 2610 y SDict begin H.S end 2815 2610 a Black Fq(15)p Black 2906 2552 a SDict begin H.R end 2906 2552 a 2906 2610 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Laughlin-81) cvn H.B /ANN pdfmark end 2906 2610 a Fq(,)2963 2610 y SDict begin H.S end 2963 2610 a Black Fq(18)p Black 3054 2552 a SDict begin H.R end 3054 2552 a 3054 2610 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Laughlin-99) cvn H.B /ANN pdfmark end 3054 2610 a Fq(])g(and)g(for)g(F)m(QHE)86 2718 y(ph)m(ysics)g(in)g(general.)46 b(Its)33 b(imp)s(ortance)e(lies)g(in)g(understanding)e(the)k(e\013ect)h (of)e(an)g(external)g(p)s(oten)m(tial)86 2826 y(that)40 b(w)m(ould)e(try)i(to)g(concen)m(trate)i(the)e(densit)m(y)e(as)i(m)m (uc)m(h)g(as)g(p)s(ossible)d(in)h(energetically)h(fa)m(v)m(orable)86 2934 y(places.)186 3042 y(If)i(the)h(energy)g(gap)g(in)e(Prop)s(ert)m (y)j Fv(1)f Fq(is)f(su\016cien)m(tly)f(large)i(w)m(e)g(can)g(exclude)g (a)g(jump)e(across)i(it)86 3150 y(and)32 b(restrict)h(atten)m(tion)h (to)g(w)m(a)m(v)m(e)h(functions)d(with)f(the)j(same)f(in)m(teraction)g (energy)h(as)f(the)g(Laughlin)86 3258 y(function.)39 b(W)-8 b(e)32 b(are)f(th)m(us)f(led)f(to)i(study)f(the)g(set)h(of)g (all)e(normalized)g(w)m(a)m(v)m(e)j(functions)d(of)i(the)f(form)932 3521 y SDict begin H.S end 932 3521 a 932 3521 a SDict begin 13 H.A end 932 3521 a 932 3521 a SDict begin [/View [/XYZ H.V]/Dest (equation.1.3) cvn /DEST pdfmark end 932 3521 a Fq(\011)1003 3535 y Fk(F)1062 3521 y Fq(\()p Fo(z)1139 3535 y Fm(1)1179 3521 y Fo(;)15 b(:)g(:)g(:)h(;)f(z)1422 3535 y Fk(N)1490 3521 y Fq(\))26 b(=)f Fo(F)13 b Fq(\()p Fo(z)1795 3535 y Fm(1)1835 3521 y Fo(;)i(:)g(:)g(:)i(;)e(z)2079 3535 y Fk(N)2147 3521 y Fq(\)\011)2253 3535 y Fm(Lau)2375 3521 y Fq(\()p Fo(z)2452 3535 y Fm(1)2492 3521 y Fo(;)g(:)g(:)g(:)i(;)e (z)2736 3535 y Fk(N)2804 3521 y Fq(\))660 b(\(1.3\))86 3784 y(with)32 b Fo(F)46 b Fq(analytic)32 b(and)h(symmetric)f(under)g (exc)m(hange)i(of)f(the)h Fo(z)2333 3798 y Fk(i)2361 3784 y Fq(.)49 b(This)31 b(form)i(exhausts)g(the)g(class)g(of)86 3892 y(functions)e(that)h(minimize)e(the)i(magnetic)h(kinetic)e(energy) h(and)g(at)h(the)f(same)g(time)g(a)m(v)m(oid)h(repulsiv)m(e)86 4000 y(in)m(teractions)g(b)m(y)h(v)-5 b(anishing)31 b(at)j(least)g(as)g (\()p Fo(z)1639 4014 y Fk(i)1690 4000 y Fn(\000)22 b Fo(z)1825 4014 y Fk(j)1862 4000 y Fq(\))1897 3967 y Fk(`)1963 4000 y Fq(as)34 b Fo(z)2120 4014 y Fk(i)2182 4000 y Fq(and)f Fo(z)2404 4014 y Fk(j)2474 4000 y Fq(come)i(together.)51 b(In)33 b(the)h(b)s(osonic)86 4108 y(case)42 b(and)f(with)f Fo(`)j Fq(=)g(2)f(these)f(are)h(exactly)g(the)f(ground)g(states)h(of)f (the)h(con)m(tact)h(in)m(teraction)f([)3570 4108 y SDict begin H.S end 3570 4108 a Black Fq(36)p Black 3661 4049 a SDict begin H.R end 3661 4049 a 3661 4108 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouSerYng-13b) cvn H.B /ANN pdfmark end 3661 4108 a Fq(,)86 4216 y(Section)29 b(2.1].)42 b(W)-8 b(e)30 b(shall)e(refer)h(to)h(the)f(class)g(of)h(states)g(of)g (the)f(form)g(\()2530 4216 y SDict begin H.S end 2530 4216 a Black Fq(1.3)p Black 2647 4157 a SDict begin H.R end 2647 4157 a 2647 4216 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.1.3) cvn H.B /ANN pdfmark end 2647 4216 a Fq(\))g(as)h Fr(ful)5 b(ly)31 b(c)-5 b(orr)g(elate)g(d)35 b(states)p Fq(.)186 4324 y(Ph)m(ysically)-8 b(,)39 b(\()682 4324 y SDict begin H.S end 682 4324 a Black Fq(1.3)p Black 799 4265 a SDict begin H.R end 799 4265 a 799 4324 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.1.3) cvn H.B /ANN pdfmark end 799 4324 a Fq(\))i(includes)e(the)i(addition)f(of)h (`quasi-holes')55 b(\(zeros)42 b(of)g(the)f(w)m(a)m(v)m(e-function\))h (to)86 4432 y(the)27 b(Laughlin)e(state,)30 b(essen)m(tially)c (arbitrary)g(correlations)h(b)s(et)m(w)m(een)h(the)g(particles')e(and)h (quasi-holes')86 4540 y(lo)s(cations)35 b(b)s(eing)g(allo)m(w)m(ed.)58 b(It)36 b(is)f(in)m(tuitiv)m(e)g(that)h(this)f(leads)h(to)g(a)h (decrease)g(of)f(the)g Fr(glob)-5 b(al)47 b Fq(densit)m(y)-8 b(.)86 4648 y(It)35 b(is)e(far)h(from)g(ob)m(vious,)i(ho)m(w)m(ev)m (er,)h(that)e(no)f Fr(lo)-5 b(c)g(al)46 b Fq(increase)34 b(of)h(the)g(densit)m(y)f(can)g(o)s(ccur)h(an)m(ywhere.)86 4756 y(Sev)m(eral)e(quasi-holes)f(arranged)h(tigh)m(tly)g(on)g(a)g (circle)g(could,)g(p)s(erhaps,)f(increase)h(the)h(densit)m(y)e(inside) 86 4863 y(the)40 b(circle.)67 b(Moreo)m(v)m(er,)44 b Fo(F)52 b Fq(need)40 b(not)f(con)m(tain)h(an)m(y)g(zeros)g(at)g(all)f (lik)m(e,)i(e.g.,)i(exp\()p Fo(c)3128 4795 y Fl(P)3225 4890 y Fk(i)3268 4863 y Fo(z)3314 4830 y Fm(2)3310 4889 y Fk(i)3354 4863 y Fq(\),)f(whic)m(h)86 4971 y(stretc)m(hes)31 b(the)g(supp)s(ort)e(of)h(the)h(densit)m(y)e(in)g(one)i(direction)e (and)h(shrinks)e(it)i(in)f(another.)186 5079 y(In)e(this)h(pap)s(er,)g (w)m(e)h(rep)s(ort)e(on)i(recen)m(t)g(densit)m(y)f(b)s(ounds)e(for)i (fully)e(correlated)j(states)h(that)f(demon-)86 5187 y(strate)39 b(the)f(v)-5 b(alidit)m(y)37 b(of)h(Prop)s(ert)m(y)h Fv(2)g Fq(without)e(in)m(v)m(oking)g(Prop)s(ert)m(y)i Fv(1)p Fq(.)64 b(They)38 b(hold)f(essen)m(tially)g(on)86 5296 y(length)g(scales)h Fo(O)s Fq(\()p Fo(N)822 5263 y Fm(1)p Fk(=)p Fm(4)932 5296 y Fq(\),)i(m)m(uc)m(h)e(smaller)e(than)h (the)h(full)d(exten)m(t)k(of)f(the)g(liquid,)e(whic)m(h)h(is)g(of)g (order)86 5410 y Fo(N)169 5377 y Fm(1)p Fk(=)p Fm(2)279 5410 y Fq(,)30 b(and)f(are)i(related)f(to)g(earlier)f(partial)g (results)g(pro)m(v)m(ed)h(in)f([)2361 5410 y SDict begin H.S end 2361 5410 a Black Fq(37)p Black 2452 5351 a SDict begin H.R end 2452 5351 a 2452 5410 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouYng-14) cvn H.B /ANN pdfmark end 2452 5410 a Fq(,)2507 5410 y SDict begin H.S end 2507 5410 a Black Fq(38)p Black 2598 5351 a SDict begin H.R end 2598 5351 a 2598 5410 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouYng-15) cvn H.B /ANN pdfmark end 2598 5410 a Fq(].)41 b(The)29 b(full)f(pro)s(ofs)h(are)h(some-)86 5518 y(what)i(in)m(v)m(olv)m(ed)g(and)f(presen)m(ted)i(elsewhere)e([) 1692 5518 y SDict begin H.S end 1692 5518 a Black Fq(25)p Black 1783 5459 a SDict begin H.R end 1783 5459 a 1783 5518 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.LieRouYng-17) cvn H.B /ANN pdfmark end 1783 5518 a Fq(],)i(but)f(w)m(e)h(sk)m(etc)m (h)g(the)f(main)g(argumen)m(ts)g(b)s(elo)m(w)f(and)86 5626 y(discuss)d(ph)m(ysical)h(applications.)p Black Black eop end end %%Page: 3 3 TeXDict begin HPSdict begin 3 2 bop -300 300 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end -300 300 a -222 785 a SDict begin H.S end -222 785 a -222 785 a SDict begin H.R end -222 785 a -222 785 a SDict begin [/View [/XYZ H.V]/Dest (page.3) cvn /DEST pdfmark end -222 785 a Black 1210 559 a Fm(RIGIDITY)32 b(OF)f(THE)f(LA)n(UGHLIN)h (LIQUID)1090 b(3)p Black 86 676 a SDict begin H.S end 86 676 a 86 676 a SDict begin 13 H.A end 86 676 a 86 676 a SDict begin [/View [/XYZ H.V]/Dest (section.2) cvn /DEST pdfmark end 86 676 a 1191 759 a Fq(2.)46 b Fp(Incompressibility)32 b(estima)-6 b(tes)186 921 y Fq(In)26 b(his)g(pioneering)g(pap)s(er)g([) 1149 921 y SDict begin H.S end 1149 921 a Black Fq(16)p Black 1240 862 a SDict begin H.R end 1240 862 a 1240 921 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Laughlin-83) cvn H.B /ANN pdfmark end 1240 921 a Fq(],)j(Laughlin)c(already)i(argued)g (that)h(the)f(one-particle)h(densit)m(y)e(of)i(the)86 1036 y(state)38 b(\()350 1036 y SDict begin H.S end 350 1036 a Black Fq(1.1)p Black 467 978 a SDict begin H.R end 467 978 a 467 1036 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.1.1) cvn H.B /ANN pdfmark end 467 1036 a Fq(\))f(has)g(the)h (form)e(of)i(a)f(circular)f(droplet)g(of)i(radius)2333 959 y Fn(p)p 2409 959 121 4 v 77 x Fo(`N)47 b Fq(where)36 b(the)i(densit)m(y)e(tak)m(es)j(the)86 1144 y(constan)m(t)28 b(v)-5 b(alue)27 b(\()p Fo(\031)s(`)p Fq(\))844 1111 y Fj(\000)p Fm(1)939 1144 y Fq(.)39 b(The)27 b(argumen)m(t)h(w)m(as)f (based)g(on)g(the)g(plasma)f(analogy)-8 b(,)29 b(where)e(the)g (absolute)86 1252 y(square)k(of)g(the)g(w)m(a)m(v)m(e)h(function)e(is)g (written)g(as)h(the)g(Gibbs)f(distribution)d(of)k(a)g(classical)f(2D)i (Coulom)m(b)86 1360 y(gas,)f(and)f(subsequen)m(tly)f(treated)i(b)m(y)g (a)f(mean-\014eld)g(appro)m(ximation.)186 1468 y(Recen)m(t)23 b(mathematical)f(analysis)f([)1400 1468 y SDict begin H.S end 1400 1468 a Black Fq(35)p Black 1491 1410 a SDict begin H.R end 1491 1410 a 1491 1468 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouSerYng-13a) cvn H.B /ANN pdfmark end 1491 1468 a Fq(,)1539 1468 y SDict begin H.S end 1539 1468 a Black Fq(36)p Black 1629 1410 a SDict begin H.R end 1629 1410 a 1629 1468 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouSerYng-13b) cvn H.B /ANN pdfmark end 1629 1468 a Fq(,)1677 1468 y SDict begin H.S end 1677 1468 a Black Fq(39)p Black 1768 1410 a SDict begin H.R end 1768 1410 a 1768 1468 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouYng-17) cvn H.B /ANN pdfmark end 1768 1468 a Fq(])h(has)g(con\014rmed)f (the)h(v)-5 b(alidit)m(y)21 b(of)h(this)f(appro)m(ximation)86 1576 y(for)28 b(the)h(Laughlin)e(states)i(and)g(Laughlin's)d (quasi-hole)i(states)h(where)g(the)f(prefactor)i Fo(F)41 b Fq(is)28 b(a)h(pro)s(duct)86 1684 y(in)g(whic)m(h)g(eac)m(h)j(factor) f(dep)s(ends)d(on)j(a)g Fr(single)f Fq(v)-5 b(ariable,)29 b(i.e.,)i(w)m(a)m(v)m(e)h(functions)d(of)i(the)f(sp)s(ecial)f(form)983 1851 y SDict begin H.S end 983 1851 a 983 1851 a SDict begin 13 H.A end 983 1851 a 983 1851 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.1) cvn /DEST pdfmark end 983 1851 a Fq(\011)1054 1873 y Fk(f)1095 1854 y Fd(\012)p Fh(N)1205 1851 y Fq(\()p Fo(z)1282 1865 y Fm(1)1322 1851 y Fo(;)15 b(:)g(:)g(:)h(;)f(z)1565 1865 y Fk(N)1633 1851 y Fq(\))26 b(=)1793 1765 y Fl(Y)1790 1961 y Fk(j)t Fm(=1)1928 1851 y Fo(f)10 b Fq(\()p Fo(z)2060 1865 y Fk(j)2096 1851 y Fq(\)\011)2202 1865 y Fm(Lau)2325 1851 y Fq(\()p Fo(z)2402 1865 y Fm(1)2442 1851 y Fo(;)15 b(:)g(:)g(:)i(;)e(z)2686 1865 y Fk(N)2753 1851 y Fq(\))711 b(\(2.1\))86 2100 y(with)38 b Fo(f)49 b Fq(b)s(eing)37 b(a)j(p)s(olynomial.)65 b(These)39 b(results)f(ho)m(w)m(ev)m(er)j(do)e(not)h(imply)d(densit)m(y)h(b)s (ounds)g(for)h(the)86 2208 y Fr(gener)-5 b(al)29 b Fq(state)i(\()651 2208 y SDict begin H.S end 651 2208 a Black Fq(1.3)p Black 767 2149 a SDict begin H.R end 767 2149 a 767 2208 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.1.3) cvn H.B /ANN pdfmark end 767 2208 a Fq(\).)41 b(The)28 b(latter)h(could,)f(in) g(particular,)f(b)s(e)h(a)h(linear)e(sup)s(erp)s(osition)f(of)i (functions)g(of)86 2316 y(the)j(form)f(\()493 2316 y SDict begin H.S end 493 2316 a Black Fq(2.1)p Black 609 2257 a SDict begin H.R end 609 2257 a 609 2316 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.2.1) cvn H.B /ANN pdfmark end 609 2316 a Fq(\),)h(and)f(the)g(densit)m(y)g(of)h(a)g (linear)d(sup)s(erp)s(osition)f(needs)j(not)h(coincide)f(with)f(the)h (linear)86 2424 y(sup)s(erp)s(osition)d(of)j(the)h(densities,)e(b)s (ecause)h(of)h(quan)m(tum-mec)m(hanical)f(in)m(terferences.)186 2532 y(The)j(analysis)g(of)i([)855 2532 y SDict begin H.S end 855 2532 a Black Fq(35)p Black 946 2473 a SDict begin H.R end 946 2473 a 946 2532 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouSerYng-13a) cvn H.B /ANN pdfmark end 946 2532 a Fq(,)1006 2532 y SDict begin H.S end 1006 2532 a Black Fq(36)p Black 1097 2473 a SDict begin H.R end 1097 2473 a 1097 2532 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouSerYng-13b) cvn H.B /ANN pdfmark end 1097 2532 a Fq(])f(w)m(as)h(generalized)f(to)h(other)g(prefactors)g(of)f(a)h(sp)s (ecial)e(kind)f(in)i([)3424 2532 y SDict begin H.S end 3424 2532 a Black Fq(37)p Black 3515 2473 a SDict begin H.R end 3515 2473 a 3515 2532 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouYng-14) cvn H.B /ANN pdfmark end 3515 2532 a Fq(].)53 b(A)86 2640 y(common)36 b(feature)f(that)h(emerged)g(w) m(as)g(an)f(upp)s(er)f(b)s(ound)f(on)i(the)h(one-particle)f(densit)m(y) g(of)g(magni-)86 2748 y(tude)k(\()p Fo(\031)s(`)p Fq(\))465 2715 y Fj(\000)p Fm(1)560 2748 y Fq(,)k(whic)m(h)38 b(is)h(the)h (densit)m(y)f(of)h(the)g(Laughlin)d(state)k(itself.)68 b(Suc)m(h)39 b(a)h(b)s(ound)e(w)m(as)i(called)86 2856 y(an)35 b Fr(inc)-5 b(ompr)g(essibility)40 b(estimate)j Fq(in)34 b([)1419 2856 y SDict begin H.S end 1419 2856 a Black Fq(37)p Black 1510 2797 a SDict begin H.R end 1510 2797 a 1510 2856 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouYng-14) cvn H.B /ANN pdfmark end 1510 2856 a Fq(])i(b)s(ecause)g(it) f(is)f(a)i(manifestation)f(of)h(the)f(resistance)h(of)g(the)86 2963 y(Laughlin)30 b(state)k(against)f(attempts)g(to)g(compress)g(its)f (densit)m(y)-8 b(.)46 b(It)33 b(relies)e(essen)m(tially)h(on)g(the)h (strong)86 3071 y(correlations)e(of)g(the)h(Laughlin)d(function)h(and)g (the)i(analyticit)m(y)f(of)g Fo(F)44 b Fq(in)30 b(\()2714 3071 y SDict begin H.S end 2714 3071 a Black Fq(1.3)p Black 2831 3013 a SDict begin H.R end 2831 3013 a 2831 3071 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.1.3) cvn H.B /ANN pdfmark end 2831 3071 a Fq(\))h(whic)m(h,)g(ph)m(ysically)-8 b(,)30 b(is)86 3179 y(due)35 b(to)h(the)g(strong)g(magnetic)g(\014eld)e (con\014ning)g(the)i(particles)f(to)h(the)g(LLL.)f(Without)h(suc)m(h)f (a)h(\014eld)86 3287 y(and)28 b(with)f(w)m(eak)j(correlations,)e(the)h (electron)g(densit)m(y)f(in)f(a)i(crystal)g(can)g(b)s(e)f(arbitrarily)d (high)j(lo)s(cally)-8 b(,)86 3395 y(due)30 b(to)h(constructiv)m(e)g(in) m(terference)f(of)h(Blo)s(c)m(h)f(w)m(a)m(v)m(es.)186 3503 y(The)j(mean-\014eld)g(metho)s(ds)g(of)h([)1321 3503 y SDict begin H.S end 1321 3503 a Black Fq(35)p Black 1412 3444 a SDict begin H.R end 1412 3444 a 1412 3503 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouSerYng-13a) cvn H.B /ANN pdfmark end 1412 3503 a Fq(,)1471 3503 y SDict begin H.S end 1471 3503 a Black Fq(36)p Black 1562 3444 a SDict begin H.R end 1562 3444 a 1562 3503 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouSerYng-13b) cvn H.B /ANN pdfmark end 1562 3503 a Fq(,)1621 3503 y SDict begin H.S end 1621 3503 a Black Fq(37)p Black 1712 3444 a SDict begin H.R end 1712 3444 a 1712 3503 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouYng-14) cvn H.B /ANN pdfmark end 1712 3503 a Fq(])g(are)g(not)h(applicable)c(to)k(general)f(prefactors)g Fo(F)13 b Fq(.)51 b(The)86 3611 y(question)29 b(of)g(a)h(b)s(ound)d(on) i(the)h(densit)m(y)f(for)g(the)g(general)h(case)g(w)m(as)g(treated)g (in)f([)2911 3611 y SDict begin H.S end 2911 3611 a Black Fq(38)p Black 3002 3552 a SDict begin H.R end 3002 3552 a 3002 3611 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouYng-15) cvn H.B /ANN pdfmark end 3002 3611 a Fq(])g(with)f(an)i(en)m (tirely)86 3719 y(di\013eren)m(t)g(tec)m(hnique,)g(ro)s(oted)g(in)f(2D) i(p)s(oten)m(tial)f(theory)-8 b(.)41 b(The)30 b(b)s(ound)e(obtained)i (w)m(as)g(four)g(times)g(the)86 3827 y(exp)s(ected)g(optimal)e(v)-5 b(alue)29 b(\()p Fo(\031)s(`)p Fq(\))1193 3794 y Fj(\000)p Fm(1)1317 3827 y Fq(ho)m(w)m(ev)m(er.)42 b(In)28 b(this)g(pap)s(er)g(w) m(e)i(explain)e(that)i(an)f(impro)m(v)m(ed)f(v)m(ersion)86 3935 y(of)i(the)h(p)s(oten)m(tial)f(theoretic)h(metho)s(d)f(leads)f(to) j(the)e(correct)i(optimal)d(b)s(ound)f(for)i Fr(arbitr)-5 b(ary)41 b Fo(F)13 b Fq(.)186 4043 y(As)27 b(indicated)e(b)m(y)i(n)m (umerical)f(studies)g([)1570 4043 y SDict begin H.S end 1570 4043 a Black Fq(7)p Black 1615 3984 a SDict begin H.R end 1615 3984 a 1615 4043 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Ciftja-06) cvn H.B /ANN pdfmark end 1615 4043 a Fq(],)j(the)e(incompressibilit)m(y)c(b)s(ound)i(for)i(the)g (densit)m(y)f(cannot)86 4151 y(b)s(e)42 b(exp)s(ected)h(to)g(hold)e(p)s (oin)m(t)m(wise)g(for)h(\014nite)g Fo(N)10 b Fq(.)77 b(W)-8 b(e)43 b(pro)m(v)m(e,)k(ho)m(w)m(ev)m(er,)g(that)c(it)f(holds)f (for)i(lo)s(cal)86 4259 y(a)m(v)m(erages.)g(Denote)888 4454 y SDict begin H.S end 888 4454 a 888 4454 a SDict begin 13 H.A end 888 4454 a 888 4454 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.2) cvn /DEST pdfmark end 888 4454 a Fo(\032)935 4468 y Fk(F)993 4454 y Fq(\()p Fo(z)t Fq(\))26 b(=)f Fo(N)1330 4331 y Fl(Z)1380 4537 y Fc(R)1427 4517 y Fg(2\()p Fh(N)5 b Fd(\000)p Fg(1\))1662 4454 y Fn(j)p Fq(\011)1758 4468 y Fk(F)1832 4454 y Fq(\()p Fo(z)t(;)15 b(z)1995 4468 y Fm(2)2035 4454 y Fo(;)g(:)g(:)g(:)i(;)e(z)2279 4468 y Fk(N)2347 4454 y Fq(\))p Fn(j)2407 4412 y Fm(2)2462 4454 y Fo(dz)2551 4468 y Fm(2)2606 4454 y Fo(:)g(:)g(:)h(dz)2816 4468 y Fk(N)3499 4454 y Fq(\(2.2\))86 4659 y(the)30 b(particle)g (densit)m(y)g(of)g(the)h(state)g(\()1402 4659 y SDict begin H.S end 1402 4659 a Black Fq(1.3)p Black 1519 4601 a SDict begin H.R end 1519 4601 a 1519 4659 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.1.3) cvn H.B /ANN pdfmark end 1519 4659 a Fq(\).)41 b(Our)29 b(main)g(result)h(is)86 4826 y SDict begin H.S end 86 4826 a 86 4826 a SDict begin 13 H.A end 86 4826 a 86 4826 a SDict begin [/View [/XYZ H.V]/Dest (teo.1) cvn /DEST pdfmark end 86 4826 a Black Fv(Theorem)k(1)h Fq(\()p Fv(Densit)m(y)h(b)s(ound)p Fq(\))p Fv(.)p Black 86 4934 a Fr(F)-7 b(or)34 b(any)f Fo(\013)26 b(>)f Fq(1)p Fo(=)p Fq(4)33 b Fr(and)h(any)f(disk)g Fo(D)i Fr(of)e(r)-5 b(adius)34 b Fo(N)1888 4901 y Fk(\013)1970 4934 y Fr(we)f(have,)g(uniformly)h(in)e(the)h(choic)-5 b(e)33 b(of)g Fo(F)13 b Fr(,)1386 5135 y SDict begin H.S end 1386 5135 a 1386 5135 a SDict begin 13 H.A end 1386 5135 a 1386 5135 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.3) cvn /DEST pdfmark end 1386 5135 a 1401 5011 a Fl(Z)1451 5217 y Fk(D)1531 5135 y Fo(\032)1578 5149 y Fk(F)1661 5135 y Fn(\024)1791 5073 y Fq(1)p 1767 5114 93 4 v 1767 5197 a Fo(\031)s(`)1870 5135 y Fn(j)p Fo(D)s Fn(j)p Fq(\(1)22 b(+)d Fo(o)p Fq(\(1\)\))1115 b(\(2.3\))86 5340 y Fr(wher)-5 b(e)34 b Fn(j)p Fo(D)s Fn(j)e Fr(is)h(the)g(ar)-5 b(e)g(a)34 b(of)f(the)g(disk)g(and)h Fo(o)p Fq(\(1\))f Fr(tends)h(to)f(zer)-5 b(o)34 b(as)f Fo(N)i Fn(!)25 b(1)p Fr(.)186 5512 y Fq(Recall)j(that)h(the)g(magnetic) h(length)e(is)g(1)p Fo(=)1652 5437 y Fn(p)p 1728 5437 46 4 v 75 x Fq(2)q(.)40 b(The)28 b(a)m(v)m(erage)k(can)d(th)m(us)f(b)s (e)g(tak)m(en)i(on)f(\\mesoscopic)86 5626 y(scales",)j Fo(O)s Fq(\()p Fo(N)601 5593 y Fm(1)p Fk(=)p Fm(4+)p Fk(")799 5626 y Fq(\),)f(m)m(uc)m(h)g(smaller)f(than)g(the)h(full)e (exten)m(t)j(of)f(the)h(state,)g Fo(O)s Fq(\()p Fo(N)2955 5593 y Fm(1)p Fk(=)p Fm(2)3065 5626 y Fq(\),)g(but)e(not)h(quite)p Black Black eop end end %%Page: 4 4 TeXDict begin HPSdict begin 4 3 bop -300 300 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end -300 300 a -222 785 a SDict begin H.S end -222 785 a -222 785 a SDict begin H.R end -222 785 a -222 785 a SDict begin [/View [/XYZ H.V]/Dest (page.4) cvn /DEST pdfmark end -222 785 a Black 86 559 a Fm(4)624 b(ELLIOTT)24 b(H.)f(LIEB,)h (NICOLAS)g(R)n(OUGERIE,)f(AND)g(JAK)n(OB)h(YNGV)-8 b(ASON)p Black 86 759 a Fq(do)m(wn)31 b(to)h(the)f(exp)s(ected)h(\014nest)f (scale,)h Fo(O)s Fq(\(1\).)44 b(F)-8 b(or)32 b(realistic)e(n)m(um)m(b)s (ers)g([)2617 759 y SDict begin H.S end 2617 759 a Black Fq(40)p Black 2708 700 a SDict begin H.R end 2708 700 a 2708 759 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.StoTsuGos-99) cvn H.B /ANN pdfmark end 2708 759 a Fq(])h(one)h(can)f(ha)m(v)m(e)i (Quan)m(tum)86 867 y(Hall)d(systems)i(with)e Fo(N)42 b Fq(of)31 b(the)h(order)f(of)h(10)1639 834 y Fm(9)1679 867 y Fq(,)g(in)e(whic)m(h)g(case)j(the)e(ratio)h(b)s(et)m(w)m(een)g (the)g(length)f(scales)86 975 y Fo(N)169 942 y Fm(1)p Fk(=)p Fm(4)321 975 y Fq(and)42 b Fo(N)593 942 y Fm(1)p Fk(=)p Fm(2)745 975 y Fq(is)g(ab)s(out)g(10)1211 942 y Fj(\000)p Fm(2)1306 975 y Fq(.)77 b(A)42 b(simple)f(co)m(v)m(ering)i (argumen)m(t)g(\(reminiscen)m(t)e(of)i(the)f(`c)m(heese)86 1083 y(theorem',)29 b(see)f([)657 1083 y SDict begin H.S end 657 1083 a Black Fq(26)p Black 748 1025 a SDict begin H.R end 748 1025 a 748 1083 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.LieSei-09) cvn H.B /ANN pdfmark end 748 1083 a Fq(,)h(Section)e(14.4])j(or)d([)1465 1083 y SDict begin H.S end 1465 1083 a Black Fq(22)p Black 1556 1025 a SDict begin H.R end 1556 1025 a 1556 1083 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Lieb-76) cvn H.B /ANN pdfmark end 1556 1083 a Fq(,)i(Theorem)e(14]\))i(sho)m(ws)e(that)i(\()2658 1083 y SDict begin H.S end 2658 1083 a Black Fq(2.3)p Black 2774 1025 a SDict begin H.R end 2774 1025 a 2774 1083 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.2.3) cvn H.B /ANN pdfmark end 2774 1083 a Fq(\))f(implies)d(the)j(analogous)86 1191 y(result)h(for)h(an)m(y)h(op)s(en)f(set,)h(not)g(just)e(a)i(disk.) 186 1299 y(It)43 b(follo)m(ws)f(that,)47 b(for)c(a)h(con)m(tin)m(uous)e (con\014ning)g(p)s(oten)m(tial)h Fo(V)20 b Fq(,)46 b(the)e(smallest)e (p)s(oten)m(tial)h(energy)86 1407 y(obtainable)29 b(with)g(a)i(fully)d (correlated)j(state,)h(i.e.,)852 1621 y SDict begin H.S end 852 1621 a 852 1621 a SDict begin 13 H.A end 852 1621 a 852 1621 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.4) cvn /DEST pdfmark end 852 1621 a Fo(E)919 1635 y Fk(V)980 1621 y Fq(\()p Fo(`;)15 b(N)10 b Fq(\))26 b(:=)f(min)1525 1493 y Fl(\032)1593 1497 y(Z)1644 1703 y Fc(R)1691 1685 y Fg(2)1745 1621 y Fo(V)c(\032)1866 1635 y Fk(F)1924 1621 y Fo(;)41 b Fq(\011)2061 1635 y Fk(F)2150 1621 y Fq(of)30 b(the)h(form)f(\()2660 1621 y SDict begin H.S end 2660 1621 a Black Fq(1.3)p Black 2776 1562 a SDict begin H.R end 2776 1562 a 2776 1621 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.1.3) cvn H.B /ANN pdfmark end 2776 1621 a Fq(\))2811 1493 y Fl(\033)2895 1621 y Fo(;)579 b Fq(\(2.4\))86 1840 y(is)29 b(b)s(ounded)g(b)s(elo)m (w)g(b)m(y)h(the)h(\\bath)m(tub)f(energy")h([)1841 1840 y SDict begin H.S end 1841 1840 a Black Fq(24)p Black 1933 1781 a SDict begin H.R end 1933 1781 a 1933 1840 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.LieLos-01) cvn H.B /ANN pdfmark end 1933 1840 a Fq(,)f(Theorem)g(1.14])882 2059 y SDict begin H.S end 882 2059 a 882 2059 a SDict begin 13 H.A end 882 2059 a 882 2059 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.5) cvn /DEST pdfmark end 882 2059 a Fo(E)954 2021 y Fm(bt)949 2081 y Fk(V)1026 2059 y Fq(\()p Fo(`)p Fq(\))25 b(:=)h(min)1447 1931 y Fl(\032)1515 1935 y(Z)1566 2141 y Fc(R)1613 2122 y Fg(2)1668 2059 y Fo(V)20 b(\032)1808 1954 y Fl(\014)1808 2009 y(\014)1808 2063 y(\014)1859 2059 y Fq(0)26 b Fn(\024)e Fo(\032)i Fn(\024)2227 1997 y Fq(1)p 2204 2038 93 4 v 2204 2121 a Fo(\031)s(`)2307 2059 y(;)2377 1935 y Fl(Z)2428 2141 y Fc(R)2475 2122 y Fg(2)2530 2059 y Fo(\032)f Fq(=)g Fo(N)2781 1931 y Fl(\033)2864 2059 y Fo(;)610 b Fq(\(2.5\))86 2285 y(i.e.)39 b(the)26 b(minim)m(um)e(of)i(the)g(p)s(oten)m(tial)g (energy)g(o)m(v)m(er)i(all)d(densities)f Fo(\032)i Fq(b)s(ounded)e(b)m (y)i(\()p Fo(\031)s(`)p Fq(\))3116 2252 y Fj(\000)p Fm(1)3211 2285 y Fq(.)39 b(This)25 b(lo)m(w)m(er)86 2393 y(b)s(ound)1519 2520 y SDict begin H.S end 1519 2520 a 1519 2520 a SDict begin 13 H.A end 1519 2520 a 1519 2520 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.6) cvn /DEST pdfmark end 1519 2520 a Fo(E)1586 2534 y Fk(V)1647 2520 y Fq(\()p Fo(`;)15 b(N)10 b Fq(\))27 b Fb(')e Fo(E)2073 2482 y Fm(bt)2068 2542 y Fk(V)2144 2520 y Fq(\()p Fo(`)p Fq(\))1247 b(\(2.6\))86 2671 y(holds)29 b(for)h(large)g Fo(N)41 b Fq(pro)m(vided)29 b Fo(V)50 b Fq(v)-5 b(aries)30 b(only)g(on)g (scales)g(m)m(uc)m(h)h(larger)f(than)g Fo(N)2907 2638 y Fm(1)p Fk(=)p Fm(4)3017 2671 y Fq(.)186 2779 y(The)k(b)s(ound)f(\() 697 2779 y SDict begin H.S end 697 2779 a Black Fq(2.3)p Black 814 2720 a SDict begin H.R end 814 2720 a 814 2779 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.2.3) cvn H.B /ANN pdfmark end 814 2779 a Fq(\))j(means)f(that)h(an)m(y)f (compression)f(of)i(the)f(particle)g(densit)m(y)f(ab)s(o)m(v)m(e)j(the) e(\\magic)86 2887 y(v)-5 b(alue")22 b(\()p Fo(\031)s(`)p Fq(\))521 2854 y Fj(\000)p Fm(1)638 2887 y Fq(that)h(one)g(could)e (imagine)g(to)i(accommo)s(date)h(the)f(v)-5 b(ariations)21 b(of)h(an)g(external)g(p)s(oten)m(tial)86 2995 y(w)m(ould)g(mak)m(e)i (us)e(lea)m(v)m(e)i(the)f(class)g(of)g(fully)e(correlated)i(states,)j (with)c(corresp)s(onding)f(increase)i(in)e(either)86 3103 y(the)j(magnetic)g(kinetic)f(energy)h(or)g(the)g(in)m(teraction)g (energy)-8 b(.)39 b(Assuming)22 b(the)i(sp)s(ectral)f(gap)h(men)m (tioned)86 3211 y(in)29 b(Prop)s(ert)m(y)i Fv(1)p Fq(,)g(no)f(suc)m(h)g (densit)m(y)g(bump)f(is)g(allo)m(w)m(ed.)41 b(This)28 b(justi\014es)h(t)m(w)m(o)j(things)d Fr(a)k(p)-5 b(osteriori)9 b Fq(:)86 3347 y Fn(\017)25 b Fq(That)h(it)e(is)g(legitimate)i(to)f (neglect)h(disorder)e(in)f(the)j(sample)e(and/or)h(small)f(external)h (electric)g(\014elds,)86 3455 y(as)31 b(is)e(done)h(as)h(a)f(\014rst)g (appro)m(ximation)f(in)g(the)i(deriv)-5 b(ation)29 b(of)i(F)m(QHE)f(w)m (a)m(v)m(e-functions.)86 3591 y Fn(\017)35 b Fq(Laughlin's)e(argumen)m (t)i([)1048 3591 y SDict begin H.S end 1048 3591 a Black Fq(15)p Black 1140 3532 a SDict begin H.R end 1140 3532 a 1140 3591 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Laughlin-81) cvn H.B /ANN pdfmark end 1140 3591 a Fq(,)1200 3591 y SDict begin H.S end 1200 3591 a Black Fq(17)p Black 1291 3532 a SDict begin H.R end 1291 3532 a 1291 3591 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Laughlin-87) cvn H.B /ANN pdfmark end 1291 3591 a Fq(])g(\(see)h(also)e([)1749 3591 y SDict begin H.S end 1749 3591 a Black Fq(14)p Black 1841 3532 a SDict begin H.R end 1841 3532 a 1841 3591 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Jain-07) cvn H.B /ANN pdfmark end 1841 3591 a Fq(,)i(Sections)e(4.4,)k(9.3)e(and)e (9.5]\))j(that)e(switc)m(hing)f(on)86 3698 y(an)26 b(electric)h(curren) m(t)f(mo)m(v)m(es)i(electrons)f(transv)m(ersally)f(without)f(creating)i (an)m(y)g(c)m(harge)h(accum)m(ulation,)86 3806 y(and)i(generates)h(a)g (Hall)f(conductivit)m(y)f(of)i(v)-5 b(alue)30 b(1)p Fo(=`)p Fq(.)186 3942 y(It)k(has)g(b)s(een)g(prop)s(osed)f(\(see)i([)1275 3942 y SDict begin H.S end 1275 3942 a Black Fq(8)p Black 1321 3884 a SDict begin H.R end 1321 3884 a 1321 3942 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Cooper-08) cvn H.B /ANN pdfmark end 1321 3942 a Fq(,)1380 3942 y SDict begin H.S end 1380 3942 a Black Fq(6)p Black 1426 3884 a SDict begin H.R end 1426 3884 a 1426 3942 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.BloDalZwe-08) cvn H.B /ANN pdfmark end 1426 3942 a Fq(,)1485 3942 y SDict begin H.S end 1485 3942 a Black Fq(42)p Black 1576 3884 a SDict begin H.R end 1576 3884 a 1576 3942 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Viefers-08) cvn H.B /ANN pdfmark end 1576 3942 a Fq(])f(for)g(reviews\))g(that)h(Laughlin)d(w)m(a)m(v)m(e)k (functions)d(could)g(b)s(e)86 4050 y(created)22 b(in)e(cold)h(atomic)g (gases,)j(either)d(b)m(y)g(rapid)e(rotation)j(or)f(b)m(y)g(applying)e (arti\014cial)h(magnetic)h(\014elds.)86 4158 y(In)36 b(this)f(con)m(text,)40 b(a)d(magneto-optical)g(trap)f(con\014nes)g (the)h(gas.)59 b(Some)37 b(recen)m(t)g(prop)s(osals)e(to)i(reac)m(h)86 4266 y(the)e(Laughlin)e(state)j([)884 4266 y SDict begin H.S end 884 4266 a Black Fq(30)p Black 975 4208 a SDict begin H.R end 975 4208 a 975 4266 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.MorFed-07) cvn H.B /ANN pdfmark end 975 4266 a Fq(,)1035 4266 y SDict begin H.S end 1035 4266 a Black Fq(33)p Black 1126 4208 a SDict begin H.R end 1126 4208 a 1126 4266 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RonRizDal-11) cvn H.B /ANN pdfmark end 1126 4266 a Fq(])f(in)m(v)m(olv)m(e)g(some)g(non-trivial)e(engineering)h(of)h(the)g (trapping)e(p)s(oten)m(tial.)86 4374 y(Ho)m(w)e(the)g(Laughlin)d(state) j(resp)s(onds)e(is,)h(therefore,)h(of)f(imp)s(ortance)g(for)g(the)g (exp)s(erimen)m(tal)g(set-up.)186 4482 y(In)21 b(addition,)h(the)f (precursor)g(of)h(F)m(QHE)g(states)h(in)e(a)h(rapidly)d(rotating)j (Bose)h(gas)g(is)d(a)j(Bose-Einstein)86 4590 y(condensate)31 b(\(see)g([)758 4590 y SDict begin H.S end 758 4590 a Black Fq(21)p Black 850 4531 a SDict begin H.R end 850 4531 a 850 4590 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.LewSei-09) cvn H.B /ANN pdfmark end 850 4590 a Fq(,)905 4590 y SDict begin H.S end 905 4590 a Black Fq(27)p Black 996 4531 a SDict begin H.R end 996 4531 a 996 4590 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.LieSeiYng-09) cvn H.B /ANN pdfmark end 996 4590 a Fq(])g(and)e(references)i(therein\).)40 b(Observing)29 b(the)h(distinctly)e(\015at)j(pro\014le)e(of)i(the)86 4698 y(Laughlin)20 b(state)j(w)m(ould)e(already)h(b)s(e)f(a)i(strong)f (indication)e(of)i(the)h(transition)d(to)j(the)f(F)m(QHE)h(regime.)38 b(A)86 4806 y(more)23 b(complete)h(prob)s(e)e(could)g(b)s(e)g(the)h (resp)s(onse)f(of)h(the)h(gas)f(to)h(v)-5 b(ariations)22 b(of)h(the)h(trapping)d(p)s(oten)m(tial:)86 4914 y(the)26 b(Bose)i(condensate)f(follo)m(ws)f(the)g(trap)g(b)m(y)h(taking)f(a)h (Thomas-F)-8 b(ermi-lik)m(e)25 b(shap)s(e)h(\(see)h([)3248 4914 y SDict begin H.S end 3248 4914 a Black Fq(1)p Black 3294 4855 a SDict begin H.R end 3294 4855 a 3294 4914 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.AftBlaDal-05) cvn H.B /ANN pdfmark end 3294 4914 a Fq(,)3345 4914 y SDict begin H.S end 3345 4914 a Black Fq(2)p Black 3391 4855 a SDict begin H.R end 3391 4855 a 3391 4914 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.AftBlaNie-06a) cvn H.B /ANN pdfmark end 3391 4914 a Fq(,)3442 4914 y SDict begin H.S end 3442 4914 a Black Fq(5)p Black 3488 4855 a SDict begin H.R end 3488 4855 a 3488 4914 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.BlaRou-08) cvn H.B /ANN pdfmark end 3488 4914 a Fq(])f(and)86 5022 y(references)33 b(therein\).)46 b(The)32 b(Laughlin)e(state)k(essen)m(tially)d(do)s(es)i(not)f(resp)s (ond)f(to)i(suc)m(h)f(v)-5 b(ariations,)33 b(as)86 5130 y(exempli\014ed)28 b(b)m(y)i(our)g(main)g(theorem.)186 5238 y(W)-8 b(e)33 b(also)g(p)s(oin)m(t)f(out)g(that)i(a)f(com)m (bination)f(of)g(Theorem)2222 5238 y SDict begin H.S end 2222 5238 a Black Fq(1)p Black 2267 5179 a SDict begin H.R end 2267 5179 a 2267 5238 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (teo.1) cvn H.B /ANN pdfmark end 2267 5238 a 33 w Fq(with)f(estimates)i(obtained)f(in)g([)3421 5238 y SDict begin H.S end 3421 5238 a Black Fq(35)p Black 3512 5179 a SDict begin H.R end 3512 5179 a 3512 5238 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouSerYng-13a) cvn H.B /ANN pdfmark end 3512 5238 a Fq(,)3570 5238 y SDict begin H.S end 3570 5238 a Black Fq(36)p Black 3661 5179 a SDict begin H.R end 3661 5179 a 3661 5238 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouSerYng-13b) cvn H.B /ANN pdfmark end 3661 5238 a Fq(])86 5345 y(leads)e(to)h(the)f(follo)m(wing)f (impro)m(v)m(emen)m(t)i(of)f([)1639 5345 y SDict begin H.S end 1639 5345 a Black Fq(37)p Black 1731 5287 a SDict begin H.R end 1731 5287 a 1731 5345 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouYng-14) cvn H.B /ANN pdfmark end 1731 5345 a Fq(,)g(Corollary)f(2.3]:)86 5518 y SDict begin H.S end 86 5518 a 86 5518 a SDict begin 13 H.A end 86 5518 a 86 5518 a SDict begin [/View [/XYZ H.V]/Dest (teo.2) cvn /DEST pdfmark end 86 5518 a Black Fv(Corollary)36 b(2)g Fq(\()p Fv(Optimization)e(of)h(the)f(energy)h(in)g(radial)g (traps)p Fq(\))p Fv(.)p Black 86 5626 a Fr(L)-5 b(et)35 b Fo(V)21 b Fq(\()p Fo(x)p Fq(\))30 b(=)g Fn(j)p Fo(x)p Fn(j)674 5593 y Fk(s)746 5626 y Fr(with)36 b Fo(s)30 b(>)f Fq(0)p Fr(.)50 b(Then)35 b(the)h(p)-5 b(otential)37 b(ener)-5 b(gy)36 b(within)g(the)f(class)44 b Fq(\()2995 5626 y SDict begin H.S end 2995 5626 a Black Fq(1.3)p Black 3111 5567 a SDict begin H.R end 3111 5567 a 3111 5626 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.1.3) cvn H.B /ANN pdfmark end 3111 5626 a Fq(\))36 b Fr(is)f(minimize)-5 b(d)p Black Black eop end end %%Page: 5 5 TeXDict begin HPSdict begin 5 4 bop -300 300 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end -300 300 a -222 785 a SDict begin H.S end -222 785 a -222 785 a SDict begin H.R end -222 785 a -222 785 a SDict begin [/View [/XYZ H.V]/Dest (page.5) cvn /DEST pdfmark end -222 785 a Black 1210 559 a Fm(RIGIDITY)32 b(OF)f(THE)f(LA)n(UGHLIN)h (LIQUID)1090 b(5)p Black 86 759 a Fr(by)32 b(the)h(L)-5 b(aughlin)34 b(state)f(\()p Fo(F)39 b Fq(=)25 b(1)p Fr(\):)1135 969 y SDict begin H.S end 1135 969 a 1135 969 a SDict begin 13 H.A end 1135 969 a 1135 969 a SDict begin [/View [/XYZ H.V]/Dest (equation.2.7) cvn /DEST pdfmark end 1135 969 a 54 w Fq(lim)1150 1030 y Fk(N)7 b Fj(!1)1407 829 y Fl(R)1450 934 y Fc(R)1497 915 y Fg(2)1552 902 y Fo(V)20 b(\032)1672 916 y Fm(1)p 1380 948 360 4 v 1380 1032 a Fo(E)1447 1046 y Fk(V)1508 1032 y Fq(\()p Fo(`;)15 b(N)10 b Fq(\))1775 969 y(=)64 b(lim)1871 1030 y Fk(N)7 b Fj(!1)2154 907 y Fo(E)2226 874 y Fm(bt)2221 934 y Fk(V)2297 907 y Fq(\()p Fo(`)p Fq(\))p 2100 948 V 2100 1032 a Fo(E)2167 1046 y Fk(V)2228 1032 y Fq(\()p Fo(`;)15 b(N)10 b Fq(\))2495 969 y(=)25 b(1)863 b(\(2.7\))86 1180 y Fr(wher)-5 b(e)34 b Fo(E)410 1194 y Fk(V)471 1180 y Fq(\()p Fo(N)5 b(;)15 b(`)p Fq(\))33 b Fr(and)h Fo(E)979 1147 y Fm(bt)974 1207 y Fk(V)1050 1180 y Fq(\()p Fo(`)p Fq(\))f Fr(ar)-5 b(e)33 b(de\014ne)-5 b(d)34 b(in)40 b Fq(\()1806 1180 y SDict begin H.S end 1806 1180 a Black Fq(2.4)p Black 1922 1121 a SDict begin H.R end 1922 1121 a 1922 1180 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.2.4) cvn H.B /ANN pdfmark end 1922 1180 a Fq(\))33 b Fr(and)43 b Fq(\()2211 1180 y SDict begin H.S end 2211 1180 a Black Fq(2.5)p Black 2327 1121 a SDict begin H.R end 2327 1121 a 2327 1180 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.2.5) cvn H.B /ANN pdfmark end 2327 1180 a Fq(\))33 b Fr(r)-5 b(esp)g(e)g(ctively.) 186 1342 y Fq(It)23 b(is)f(remark)-5 b(able)22 b(that)i(the)f(Laughlin) e(state)j(sta)m(ys)g(an)f(appro)m(ximate)g(minimizer)e(in)g(an)m(y)j(p) s(o)m(w)m(er-la)m(w)86 1450 y(trap)g(\(the)g(result)f(actually)g(holds) f(for)i(more)g(general)g(radial)e(increasing)h(p)s(oten)m(tials\).)38 b(No)24 b(matter)h(ho)m(w)86 1558 y(steep)36 b(and)f(narro)m(w)g(a)h(p) s(oten)m(tial)f(w)m(ell)g(one)g(imp)s(oses,)h(it)f(is)g(imp)s(ossible)d (to)k(compress)f(the)h(Laughlin)86 1666 y(state)26 b(while)c(k)m (eeping)i(the)h(form)f(\()1251 1666 y SDict begin H.S end 1251 1666 a Black Fq(1.3)p Black 1367 1607 a SDict begin H.R end 1367 1607 a 1367 1666 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.1.3) cvn H.B /ANN pdfmark end 1367 1666 a Fq(\))q(,)h(i.e.,)h(without)e(jumping)e(across)j(the)f(sp)s (ectral)g(gap.)39 b(Extensions)86 1774 y(of)23 b(Corollary)576 1774 y SDict begin H.S end 576 1774 a Black Fq(2)p Black 622 1715 a SDict begin H.R end 622 1715 a 622 1774 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (teo.2) cvn H.B /ANN pdfmark end 622 1774 a 22 w Fq(to)h(general)e(traps)h(w)m(ere)g(recen) m(tly)g(pro)m(v)m(ed)g(in)e([)2228 1774 y SDict begin H.S end 2228 1774 a Black Fq(39)p Black 2319 1715 a SDict begin H.R end 2319 1715 a 2319 1774 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouYng-17) cvn H.B /ANN pdfmark end 2319 1774 a Fq(]:)37 b(F)-8 b(or)24 b(a)f(trap)f(of)h Fr(arbitr)-5 b(ary)25 b Fq(shap)s(e,)f(the)86 1882 y(minimal)19 b(energy)k(is)f(asymptotically)f(equal)h(to)h(the)g(bath)m(tub)f (energy)h(and)e(can)i(alw)m(a)m(ys)g(b)s(e)f(ac)m(hiev)m(ed)h(b)m(y)86 1990 y(adding)k(uncorrelated)h(quasi-holes)f(on)i(top)g(of)g (Laughlin's)d(function,)i(i.e.,)h(b)m(y)g(using)e(w)m(a)m(v)m(e)j (functions)86 2098 y(of)g(the)h(form)f(\()596 2098 y SDict begin H.S end 596 2098 a Black Fq(2.1)p Black 712 2039 a SDict begin H.R end 712 2039 a 712 2098 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.2.1) cvn H.B /ANN pdfmark end 712 2098 a Fq(\))q(.)86 2197 y SDict begin H.S end 86 2197 a 86 2197 a SDict begin 13 H.A end 86 2197 a 86 2197 a SDict begin [/View [/XYZ H.V]/Dest (section.3) cvn /DEST pdfmark end 86 2197 a 983 2282 a Fq(3.)47 b Fp(Pr)n(oof)33 b(stra)-6 b(tegy:)44 b(the)33 b(ex)n(clusion)g(r)n (ule)186 2444 y Fq(W)-8 b(e)46 b(no)m(w)f(turn)f(to)i(sk)m(etc)m(hing)f (the)g(pro)s(of)g(of)g(Theorem)2256 2444 y SDict begin H.S end 2256 2444 a Black Fq(1)p Black 2301 2385 a SDict begin H.R end 2301 2385 a 2301 2444 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (teo.1) cvn H.B /ANN pdfmark end 2301 2444 a Fq(.)85 b(Details)45 b(are)g(giv)m(en)g(in)f(the)h (longer)86 2552 y(pap)s(er)19 b([)356 2552 y SDict begin H.S end 356 2552 a Black Fq(25)p Black 447 2493 a SDict begin H.R end 447 2493 a 447 2552 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.LieRouYng-17) cvn H.B /ANN pdfmark end 447 2552 a Fq(].)38 b(It)21 b(is)e(con)m(v)m(enien)m(t)j(to)f(c)m (hange)g(v)-5 b(ariables)19 b(and)h(consider)g(the)g(scaled)g Fo(N)10 b Fq(-particle)20 b(probabilit)m(y)86 2660 y(densit)m(y)1243 2807 y SDict begin H.S end 1243 2807 a 1243 2807 a SDict begin 13 H.A end 1243 2807 a 1243 2807 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.1) cvn /DEST pdfmark end 1243 2807 a Fo(\026)1298 2821 y Fk(F)1356 2807 y Fq(\()p Fo(Z)1453 2821 y Fk(N)1521 2807 y Fq(\))25 b(:=)h Fo(N)1786 2770 y Fk(N)1868 2703 y Fl(\014)1868 2757 y(\014)1868 2812 y(\014)1898 2807 y Fq(\011)1969 2821 y Fk(F)2043 2706 y Fl(\020)2097 2726 y Fn(p)p 2173 2726 83 4 v 81 x Fo(N)k(Z)2338 2821 y Fk(N)2405 2706 y Fl(\021)2459 2703 y(\014)2459 2757 y(\014)2459 2812 y(\014)2490 2729 y Fm(2)3499 2807 y Fq(\(3.1\))86 2962 y(corresp)s(onding)39 b(to)k(the)e(w)m(a)m(v)m(e-function)i(\()1596 2962 y SDict begin H.S end 1596 2962 a Black Fq(1.3)p Black 1712 2903 a SDict begin H.R end 1712 2903 a 1712 2962 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.1.3) cvn H.B /ANN pdfmark end 1712 2962 a Fq(\).)74 b(This)40 b(has)h(an)h(extension)f Fo(O)s Fq(\(1\))h(for)g(the)f(Laughlin)86 3070 y(state,)32 b Fo(F)38 b Fq(=)25 b(1.)41 b(Here)31 b Fo(Z)914 3084 y Fk(N)1012 3070 y Fq(stands)f(for)g(\()p Fo(z)1512 3084 y Fm(1)1552 3070 y Fo(;)15 b(:)g(:)g(:)h(;)f(z)1795 3084 y Fk(N)1863 3070 y Fq(\).)41 b(The)30 b(scaled)g(1-particle)h (probabilit)m(y)d(densit)m(y)h(is)705 3263 y SDict begin H.S end 705 3263 a 705 3263 a SDict begin 13 H.A end 705 3263 a 705 3263 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.2) cvn /DEST pdfmark end 705 3263 a Fo(\026)760 3215 y Fm(\(1\))760 3291 y Fk(F)854 3263 y Fq(\()p Fo(z)t Fq(\))e(=)1093 3139 y Fl(Z)1143 3345 y Fc(R)1190 3325 y Fg(2\()p Fh(N)5 b Fd(\000)p Fg(1\))1425 3263 y Fo(\026)1480 3277 y Fk(F)1538 3263 y Fq(\()p Fo(z)t(;)15 b(z)1701 3277 y Fm(2)1742 3263 y Fo(;)g(:)g(:)g(:)i(;)e(z)1986 3277 y Fk(N)2053 3263 y Fq(\))p Fo(dz)2177 3277 y Fm(2)2233 3263 y Fo(:)g(:)g(:)h(dz)2443 3277 y Fk(N)2536 3263 y Fq(=)25 b Fo(\032)2679 3277 y Fk(F)2753 3162 y 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Fq(and)k(the)i(`Hamiltonian')842 4047 y SDict begin H.S end 842 4047 a 842 4047 a SDict begin 13 H.A end 842 4047 a 842 4047 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.4) cvn /DEST pdfmark end 842 4047 a Fo(H)918 4061 y Fk(N)985 4047 y Fq(\()p Fo(Z)1082 4061 y Fk(N)1149 4047 y Fq(\))26 b(=)1340 3934 y Fk(N)1306 3961 y Fl(X)1310 4156 y Fk(j)t Fm(=1)1452 4047 y Fn(j)p Fo(z)1519 4061 y Fk(j)1556 4047 y Fn(j)1581 4010 y Fm(2)1641 4047 y Fn(\000)1742 3986 y Fq(2)p Fo(`)p 1742 4026 84 4 v 1742 4110 a(N)1851 3961 y Fl(X)1861 4156 y Fk(i<j)1997 4047 y Fq(log)17 b Fn(j)p Fo(z)2197 4061 y Fk(i)2246 4047 y Fn(\000)i Fo(z)2378 4061 y Fk(j)2415 4047 y Fn(j)i Fq(+)f Fo(W)2638 4061 y Fk(N)2705 4047 y Fq(\()p Fo(Z)2802 4061 y Fk(N)2869 4047 y Fq(\))p Fo(;)570 b Fq(\(3.4\))86 4288 y(where)1186 4417 y SDict begin H.S end 1186 4417 a 1186 4417 a SDict begin 13 H.A end 1186 4417 a 1186 4417 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.5) cvn /DEST pdfmark end 1186 4417 a Fo(W)1272 4431 y 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Fn(\025)g Fq(0)31 b(for)f(all)f Fo(i:)1053 b Fq(\(3.6\))86 4870 y(This)35 b(holds)g(simply)f(b)s(ecause)j Fo(F)50 b Fq(is)36 b(analytic)g(and)g(is,)i(in)d(fact,)40 b(the)d(only)f(prop)s(ert)m(y)g(of)h Fo(W)3318 4884 y Fk(N)3421 4870 y Fq(that)h(is)86 4978 y(used)29 b(in)h(our)f(metho)s (d.)186 5086 y(A)h(precursor)g(of)h(the)f(desired)g(b)s(ound)e(\()1570 5086 y SDict begin H.S end 1570 5086 a Black Fq(2.3)p Black 1687 5027 a SDict begin H.R end 1687 5027 a 1687 5086 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.2.3) cvn H.B /ANN pdfmark end 1687 5086 a Fq(\))j(for)f Fo(\032)1939 5100 y Fk(F)2028 5086 y Fq(is)g(the)h(fact)g(that)h(the)e(lo)s(cal)g (densit)m(y)g(of)h(p)s(oin)m(ts)86 5194 y(in)36 b(a)i(minimizing)c (con\014guration)j(for)g Fo(H)1539 5208 y Fk(N)1606 5194 y Fq(\()p Fo(Z)1703 5208 y Fk(N)1771 5194 y Fq(\))h(is)e(ev)m(erywhere) i(b)s(ounded)d(ab)s(o)m(v)m(e)k(b)m(y)f Fo(N)10 b Fq(\()p Fo(\031)s(`)p Fq(\))3445 5161 y Fj(\000)p Fm(1)3577 5194 y Fq(for)86 5302 y(large)24 b Fo(N)10 b Fq(.)39 b(This)22 b(is)i(the)g(core)h(of)g(the)f(pro)s(of)g(of)g(the)g(theorem,)j(and)c (a)i(signature)e(of)i(screening)e(prop)s(erties)86 5410 y(of)32 b(the)h(e\013ectiv)m(e)h(plasma.)45 b(T)-8 b(o)33 b(establish)e(it,)h(w)m(e)h(in)m(tro)s(duce)e(and)h(study)g(an)g (auxiliary)e(minimization)86 5518 y(problem,)46 b(whic)m(h)d(is,)k (mathematically)-8 b(,)48 b(a)d(cousin)e(of)i(the)f(Thomas-F)-8 b(ermi)44 b(energy)h(minimization)86 5626 y(problem)29 b(for)h(molecules)f([)1013 5626 y SDict begin H.S end 1013 5626 a Black Fq(23)p Black 1105 5567 a SDict begin H.R end 1105 5567 a 1105 5626 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Lieb-81b) cvn H.B /ANN pdfmark end 1105 5626 a Fq(].)p Black Black eop end end %%Page: 6 6 TeXDict begin HPSdict begin 6 5 bop -300 300 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch 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Fq([)p Fo(\033)s Fq(])25 b(=)g Fn(\000)1542 923 y Fl(Z)1593 1129 y Fc(R)1640 1110 y Fg(2)1695 1047 y Fo(V)1748 1062 y Fm(n)n(ucl)1879 1047 y Fq(\()p Fo(x)p Fq(\))p Fo(\033)s Fq(\()p Fo(x)p Fq(\))15 b Fo(dx)22 b Fq(+)e Fo(D)s Fq(\()p Fo(\033)n(;)15 b(\033)s Fq(\))801 b(\(3.7\))86 1245 y(with)1342 1446 y SDict begin H.S end 1342 1446 a 1342 1446 a SDict begin 13 H.A end 1342 1446 a 1342 1446 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.8) cvn /DEST pdfmark end 1342 1446 a Fo(V)1395 1461 y Fm(n)n(ucl)1527 1446 y Fq(\()p Fo(x)p Fq(\))26 b(=)f Fn(\000)1890 1333 y Fk(K)1857 1360 y Fl(X)1865 1555 y Fk(i)p Fm(=1)2003 1446 y Fq(log)17 b Fn(j)p Fo(x)j Fn(\000)g Fo(x)2376 1460 y Fk(i)2404 1446 y Fn(j)1070 b Fq(\(3.8\))86 1680 y(and)858 1837 y SDict begin H.S end 858 1837 a 858 1837 a SDict begin 13 H.A end 858 1837 a 858 1837 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.9) cvn /DEST pdfmark end 858 1837 a Fo(D)s Fq(\()p Fo(\033)n(;)15 b(\033)1116 1800 y Fj(0)1140 1837 y Fq(\))25 b(=)g 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Fq(\()p Fo(R)q Fq(\))f Fr(denote)h(the)f(maximum)i(numb)-5 b(er)42 b(of)f(any)h(p)-5 b(oints)43 b Fn(f)p Fo(y)2831 3422 y Fm(1)2870 3408 y Fo(;)15 b(:)g(:)g(:)i(;)e(y)3117 3422 y Fk(n)3164 3408 y Fn(g)41 b Fr(that)i(a)f(disk)86 3516 y Fo(D)s Fq(\()p Fo(R)q Fq(\))33 b Fr(of)g(r)-5 b(adius)34 b Fo(R)f Fr(c)-5 b(an)33 b(ac)-5 b(c)g(ommo)g(date)36 b(while)e(r)-5 b(esp)g(e)g(cting) 34 b(the)f(exclusion)g(rule)39 b Fq(\()2961 3516 y SDict begin H.S end 2961 3516 a Black Fq(3.13)p Black 3123 3457 a SDict begin H.R end 3123 3457 a 3123 3516 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.13) cvn H.B /ANN pdfmark end 3123 3516 a Fq(\))p Fr(.)j(Then)1528 3739 y SDict begin H.S end 1528 3739 a 1528 3739 a SDict begin 13 H.A end 1528 3739 a 1528 3739 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.14) cvn /DEST pdfmark end 1528 3739 a 15 w Fq(lim)15 b(sup)1585 3817 y Fk(R)p Fj(!1)1847 3677 y Fo(n)p Fq(\()p Fo(R)q Fq(\))p 1847 3718 196 4 v 1862 3801 a Fo(\031)s(R)1987 3775 y Fm(2)2077 3739 y Fn(\024)25 b Fq(1)p Fo(:)1211 b Fq(\(3.14\))186 3966 y(W)-8 b(e)33 b(sk)m(etc)m(h)h(a)g(pro)s(of)d(in)h(the)h(App)s(endix.) 45 b(The)32 b(main)f(p)s(oin)m(t)h(is)g(that)h(if)f(a)h(large)f(region) h(con)m(tains)f(a)86 4074 y(densit)m(y)e(of)g(p)s(oin)m(ts)f Fo(>)c Fq(1)31 b(w)m(e)g(can)g(reac)m(h)g(a)f(con)m(tradiction)h(b)m(y) f(considering)f(t)m(w)m(o)i(facts:)86 4213 y Fn(\017)k Fq(the)g(p)s(oten)m(tial)f(\010)781 4180 y Fm(TF)916 4213 y Fq(generated)i(b)m(y)e(the)h(p)s(oin)m(ts)f Fo(y)1949 4227 y Fk(i)2011 4213 y Fq(con)m(tained)h(in)e Fo(D)s Fq(\()p Fo(R)q Fq(\))i(and)f(the)h(corresp)s(onding)86 4322 y(exclusion)27 b(set)h(\006)681 4289 y Fm(TF)782 4322 y Fq(\()p Fo(y)862 4336 y Fm(1)902 4322 y Fo(;)15 b(:)g(:)g(:)h(;)f(y)1148 4336 y Fk(n)1195 4322 y Fq(\))29 b(m)m(ust)f(v)-5 b(anish)26 b(at)j(all)e(the)i(p)s(oin)m(ts)e Fo(y)2464 4336 y Fk(j)2528 4322 y Fq(lying)g(outside)g(of)i Fo(D)s Fq(\()p Fo(R)q Fq(\),)g(b)m(y)f(the)86 4436 y(exclusion)h(rule)g (and)h(\()872 4436 y SDict begin H.S end 872 4436 a Black Fq(3.11)p Black 1034 4377 a SDict begin H.R end 1034 4377 a 1034 4436 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.11) cvn H.B /ANN pdfmark end 1034 4436 a Fq(\).)41 b(This)28 b(leads)i(to)h(a)g(uniform)d(upp)s(er)g(b)s(ound)h(on)h(\010) 2831 4403 y Fm(TF)2962 4436 y Fq(outside)g(of)g Fo(D)s Fq(\()p Fo(R)q Fq(\).)86 4543 y Fn(\017)36 b Fq(the)g(same)g(p)s(oten)m (tial)f(is)f(generated)j(b)m(y)e(an)h(o)m(v)m(erall)g(p)s(ositiv)m(e)e (c)m(harge)j(densit)m(y)-8 b(,)37 b(b)s(ecause)e(the)h(total)86 4651 y(n)m(uclear)e(c)m(harge)i(in)d Fo(D)s Fq(\()p Fo(R)q Fq(\),)j(whic)m(h)d(is)g Fo(>)f(\031)s(R)1672 4618 y Fm(2)1746 4651 y Fq(b)m(y)i(assumption,)g(is)g(not)g(fully)f(screened)h (b)m(y)g(the)h(part)86 4761 y(of)f(the)f(negativ)m(e)i(c)m(harge)g (densit)m(y)e Fo(\033)1375 4728 y Fm(TF)1510 4761 y Fq(lying)e(in)i Fo(D)s Fq(\()p Fo(R)q Fq(\),)h(at)h(most)f(equal)f(to)h(the)g(area)g Fo(\031)s(R)3307 4728 y Fm(2)3380 4761 y Fq(b)s(ecause)86 4870 y Fo(\033)141 4837 y Fm(TF)268 4870 y Fn(\024)24 b Fq(1.)42 b(A)30 b(lo)m(w)m(er)h(b)s(ound)d(on)i(the)h(circular)e(a)m (v)m(erage)k(of)d(\010)2198 4837 y Fm(TF)2329 4870 y Fq(outside)g(of)g Fo(D)s Fq(\()p Fo(R)q Fq(\))h(follo)m(ws.)186 5009 y(It)j(turns)f(out)i(that,)i(for)d Fo(R)h Fq(large)g(enough,)g (the)g(t)m(w)m(o)h(estimates)f(obtained)f(in)f(this)h(w)m(a)m(y)-8 b(,)37 b(if)k(\()3489 5009 y SDict begin H.S end 3489 5009 a Black Fq(3.14)p Black 3651 4951 a SDict begin H.R end 3651 4951 a 3651 5009 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.14) cvn H.B /ANN pdfmark end 3651 5009 a Fq(\))86 5117 y(fails,)29 b(will)f(con)m(tradict)j(one)g(another.)40 b(Consequen)m(tly)-8 b(,)31 b(\()2057 5117 y SDict begin H.S end 2057 5117 a Black Fq(3.14)p Black 2219 5059 a SDict begin H.R end 2219 5059 a 2219 5117 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.14) cvn H.B /ANN pdfmark end 2219 5117 a Fq(\))f(m)m(ust)h(hold.)186 5263 y(After)36 b(scaling,)h Fo(x)e Fn(!)g Fo(z)k Fq(=)1160 5156 y Fl(q)p 1251 5156 92 4 v 1261 5227 a Fk(\031)r(`)p 1261 5242 72 4 v 1265 5295 a(N)1358 5263 y Fo(x)p Fq(,)f(Lemma)e(2)h(applies)d (to)j(the)f(Hamiltonian)f(\()3037 5263 y SDict begin H.S end 3037 5263 a Black Fq(3.4)p Black 3153 5205 a SDict begin H.R end 3153 5205 a 3153 5263 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.4) cvn H.B /ANN pdfmark end 3153 5263 a Fq(\))i(and)f(implies)86 5400 y(that)23 b(in)e(an)m(y)i(minimizing)c(con\014guration)i Fn(f)p Fo(z)1632 5367 y Fm(0)1628 5424 y(1)1673 5400 y Fo(;)15 b(:)g(:)g(:)h(;)f(z)1920 5367 y Fm(0)1916 5427 y Fk(N)1984 5400 y Fn(g)23 b Fq(of)30 b(\()2190 5400 y SDict begin H.S end 2190 5400 a Black Fq(3.4)p Black 2306 5341 a SDict begin H.R end 2306 5341 a 2306 5400 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.4) cvn H.B /ANN pdfmark end 2306 5400 a Fq(\))23 b(the)g(n)m(um)m(b)s(er)e(of)h(p)s(oin)m(ts)g Fo(z)3243 5367 y Fm(0)3239 5425 y Fk(i)3305 5400 y Fq(con)m(tained)86 5518 y(in)36 b(an)m(y)j(disc)e(of)h(radius)e Fo(R)i Fn(\035)g Fo(N)1280 5485 y Fj(\000)p Fm(1)p Fk(=)p Fm(2)1482 5518 y Fq(is)f(not)h(larger)g(than)g Fo(N)10 b Fq(\()p Fo(\031)s(`)p Fq(\))2482 5485 y Fj(\000)p Fm(1)2614 5518 y Fq(times)38 b(the)g(area)h(of)f(the)g(disc.)86 5626 y(This)31 b(is)g(the)i(gist)f (of)h(the)f(pro)s(of.)47 b(F)-8 b(rom)33 b(there,)g(the)g(main)e (argumen)m(t)i(left)f(to)h(conclude)f(the)h(pro)s(of)f(of)p Black Black eop end end %%Page: 8 8 TeXDict begin HPSdict begin 8 7 bop -300 300 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end -300 300 a -222 785 a SDict begin H.S end -222 785 a -222 785 a SDict begin H.R end -222 785 a -222 785 a SDict begin [/View [/XYZ H.V]/Dest (page.8) cvn /DEST pdfmark end -222 785 a Black 86 559 a Fm(8)624 b(ELLIOTT)24 b(H.)f(LIEB,)h (NICOLAS)g(R)n(OUGERIE,)f(AND)g(JAK)n(OB)h(YNGV)-8 b(ASON)p Black 86 759 a Fq(Theorem)470 759 y SDict begin H.S end 470 759 a Black Fq(1)p Black 516 700 a SDict begin H.R end 516 700 a 516 759 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (teo.1) cvn H.B /ANN pdfmark end 516 759 a 31 w Fq(is)30 b(to)h(sho)m(w)g(that)g(the)g(densit)m(y)f(b)s(ound)f(for)i(ground)f (states)i(of)38 b(\()2779 759 y SDict begin H.S end 2779 759 a Black Fq(3.4)p Black 2895 700 a SDict begin H.R end 2895 700 a 2895 759 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.4) cvn H.B /ANN pdfmark end 2895 759 a Fq(\))31 b(applies)e(also)i(to)h(the)86 867 y(Gibbs)d(state)i(\()607 867 y SDict begin H.S end 607 867 a Black Fq(3.3)p Black 724 808 a SDict begin H.R end 724 808 a 724 867 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.3) cvn H.B /ANN pdfmark end 724 867 a Fq(\).)186 975 y(In)d(this)g(argumen)m(t,)i(w)m (e)f(use)g(crucially)e(that)i(the)h(temp)s(erature)e Fo(T)42 b Fq(in)28 b(\()2660 975 y SDict begin H.S end 2660 975 a Black Fq(3.3)p Black 2776 916 a SDict begin H.R end 2776 916 a 2776 975 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.3) cvn H.B /ANN pdfmark end 2776 975 a Fq(\))h(scales)h(as)f Fo(N)3286 942 y Fj(\000)p Fm(1)3409 975 y Fq(so)g(that)86 1083 y(the)37 b(Gibbs)e(measure)h(c)m(harges)i(mostly)e(ground)g(state) h(con\014gurations)f(for)h(large)f Fo(N)10 b Fq(.)60 b(T)-8 b(urning)34 b(this)86 1190 y(in)m(tuition)23 b(in)m(to)h(a)i (pro)s(of)e(follo)m(ws)g(the)h(lines)e(of)i([)1702 1190 y SDict begin H.S end 1702 1190 a Black Fq(38)p Black 1793 1132 a SDict begin H.R end 1793 1132 a 1793 1190 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RouYng-15) cvn H.B /ANN pdfmark end 1793 1190 a Fq(,)h(Section)f(3],)i(see)e([)2445 1190 y SDict begin H.S end 2445 1190 a Black Fq(25)p Black 2537 1132 a SDict begin H.R end 2537 1132 a 2537 1190 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.LieRouYng-17) cvn H.B /ANN pdfmark end 2537 1190 a Fq(,)h(Section)e(5])i(for)f(the)g (details.)38 b(In)86 1298 y(brief,)22 b(to)g(access)h(the)f(1-particle) f(densit)m(y)g(w)m(e)h(rely)e(on)i(the)f(fact)i(that)f(a)g(Gibbs)d (state)k(minimizes)c(the)j(free)86 1406 y(energy)k(of)g(the)g(corresp)s (onding)d(Hamiltonian)h(and)h(use)h(a)g(F)-8 b(eynman-Hellmann-t)m(yp)s (e)25 b(argumen)m(t:)39 b(W)-8 b(e)86 1514 y(p)s(erturb)25 b(the)i(Hamiltonian)f(\()1122 1514 y SDict begin H.S end 1122 1514 a Black Fq(3.4)p Black 1238 1456 a SDict begin H.R end 1238 1456 a 1238 1514 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.4) cvn H.B /ANN pdfmark end 1238 1514 a Fq(\))i(b)m(y)f(adding)f(a)h(term)g Fo(")2062 1446 y Fl(P)2159 1541 y Fk(i)2202 1514 y Fo(U)10 b Fq(\()p Fo(z)2351 1528 y Fk(i)2380 1514 y Fq(\))27 b(with)f Fo(U)37 b Fq(of)28 b(compact)g(supp)s(ort)d(and)86 1622 y(pro)m(v)m(e)34 b(free)f(energy)h(upp)s(er)d(and)i(lo)m(w)m(er)h(b)s(ounds)d(for)i (this)f(p)s(erturb)s(ed)f(Hamiltonian.)48 b(After)33 b(dividing)86 1730 y(b)m(y)i Fo(")g Fq(w)m(e)h(obtain)f(a)g(b)s(ound)e (on)1217 1657 y Fl(R)1293 1730 y Fo(U)10 b Fq(\()p Fo(z)t Fq(\))p Fo(\032)1528 1697 y Fk(")1566 1730 y Fq(\()p Fo(z)t Fq(\))p Fo(dz)40 b Fq(where)35 b Fo(\032)2126 1697 y Fk(")2198 1730 y Fq(is)f(the)h(1-particle)g(densit)m(y)g(of)g (the)g(Gibbs)86 1842 y(state)29 b(for)e(the)h(p)s(erturb)s(ed)d (Hamiltonian)h(and)h(sho)m(w)h(that)g(this)f(tends)g(to)2652 1769 y Fl(R)2728 1842 y Fo(U)10 b Fq(\()p Fo(z)t Fq(\))p Fo(\032)2963 1809 y Fm(0)3004 1842 y Fq(\()p Fo(z)t Fq(\))p Fo(dz)33 b Fq(in)26 b(the)i(limit)86 1954 y Fo(")e Fn(!)f Fq(0,)31 b(where)f Fo(\032)681 1921 y Fm(0)750 1954 y Fq(is)g(the)g(empirical)f(measure)h(of)g(the)h(ground)e(state.)186 2062 y(Strictly)c(sp)s(eaking,)h(this)g(strategy)i(requires)d(an)i (priori)d(b)s(ound)g(ensuring)h(that)i(\011)3032 2076 y Fk(F)3117 2062 y Fq(liv)m(es)f(on)g(length)86 2171 y(scales)k(of)h(order)f Fo(N)764 2138 y Fm(1)p Fk(=)p Fm(2)874 2171 y Fq(,)g(e.g.,)1459 2289 y SDict begin H.S end 1459 2289 a 1459 2289 a SDict begin 13 H.A end 1459 2289 a 1459 2289 a SDict begin [/View [/XYZ H.V]/Dest (equation.3.15) cvn /DEST pdfmark end 1459 2289 a 15 w Fn(h)p Fq(\011)1580 2303 y Fk(F)1639 2289 y Fo(;)15 b(L)1741 2303 y Fk(N)1808 2289 y Fq(\011)1879 2303 y Fk(F)1937 2289 y Fn(i)26 b(\024)f Fo(C)7 b(N)2249 2251 y Fm(2)2288 2289 y Fo(;)1141 b Fq(\(3.15\))86 2426 y(where)41 b Fo(L)422 2440 y Fk(N)530 2426 y Fq(is)g(the)g(total)h(angular)f(momen)m(tum)g (op)s(erator)h(and)f Fo(C)47 b Fq(is)41 b(indep)s(enden)m(t)e(of)j Fo(N)51 b Fq(and)41 b Fo(F)13 b Fq(.)86 2534 y(This)25 b(asumption)g(is)h(v)m(ery)i(reasonable)e(ph)m(ysically)-8 b(,)27 b(and)f(can)h(in)f(fact)h(b)s(e)g(eliminated)e(using)g(a)i (suitable)86 2642 y(lo)s(calization)i(pro)s(cedure)g(\([)1050 2642 y SDict begin H.S end 1050 2642 a Black Fq(25)p Black 1142 2583 a SDict begin H.R end 1142 2583 a 1142 2642 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.LieRouYng-17) cvn H.B /ANN pdfmark end 1142 2642 a Fq(],)i(Section)f(5.2\).)186 2750 y(W)-8 b(e)36 b(p)s(oin)m(t)e(out)i(that)g(our)f(densit)m(y)g(upp) s(er)e(b)s(ound)g(holds)h(do)m(wn)h(to)h(the)g(\014nest)f(p)s(ossible)d (scale)k(for)86 2859 y Fr(gr)-5 b(ound)44 b(states)e Fq(of)g(the)f(plasma)f(Hamiltonian)g(\()1831 2859 y SDict begin H.S end 1831 2859 a Black Fq(3.4)p Black 1948 2800 a SDict begin H.R end 1948 2800 a 1948 2859 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.4) cvn H.B /ANN pdfmark end 1948 2859 a Fq(\),)k(i.e.,)h(on)c(length)f(scales)i Fn(\035)h Fo(N)3145 2826 y Fj(\000)p Fm(1)p Fk(=)p Fm(2)3351 2859 y Fq(\(see)g([)3570 2859 y SDict begin H.S end 3570 2859 a Black Fq(34)p Black 3661 2800 a SDict begin H.R end 3661 2800 a 3661 2859 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.RotSer-14) cvn H.B /ANN pdfmark end 3661 2859 a Fq(])86 2967 y(where)26 b(the)g(corresp)s(onding)e(lo)m(w)m(er)i(b)s (ound)f(is)g(pro)m(v)m(ed)h(in)f(the)h(purely)f(Coulom)m(bic)g(case)i Fo(W)38 b Fq(=)24 b(0\).)41 b(Note)86 3075 y(that)e(w)m(e)f(are)h(here) f(referring)f(to)i(the)f(scaled)g(v)-5 b(ariables)37 b(as)i(in)e(\()2385 3075 y SDict begin H.S end 2385 3075 a Black Fq(3.1)p Black 2501 3016 a SDict begin H.R end 2501 3016 a 2501 3075 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.1) cvn H.B /ANN pdfmark end 2501 3075 a Fq(\).)65 b(When)38 b(applying)e(this)h(result)86 3188 y(to)f Fr(Gibbs)h(states)f Fq(of)42 b(\()866 3188 y SDict begin H.S end 866 3188 a Black Fq(3.4)p Black 983 3130 a SDict begin H.R end 983 3130 a 983 3188 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.3.4) cvn H.B /ANN pdfmark end 983 3188 a Fq(\))35 b(w)m(e)h(ha)m(v)m(e)g(to)g(restrict)f (ourselv)m(es)g(to)h(length)e(scales)i Fn(\035)d Fo(N)3095 3155 y Fj(\000)p Fm(1)p Fk(=)p Fm(4)3295 3188 y Fq(to)i(con)m(trol)86 3296 y(the)f(error)f(terms)g(arising)f(from)h(the)h(en)m(tropic)g(con)m (tribution)e(to)i(the)g(free)f(energy)h(in)e(the)i(F)-8 b(eynman-)86 3404 y(Hellmann)22 b(t)m(yp)s(e)h(argumen)m(t,)j(but)d (this)f(is)h(lik)m(ely)f(to)i(b)s(e)f(due)g(to)h(a)g(tec)m(hnical)f (limitation)f(of)h(our)g(metho)s(d.)86 3512 y(It)34 b(w)m(as,)h (indeed,)f(recen)m(tly)g(pro)m(v)m(ed)g(that,)i(for)d(the)h(purely)f (Coulom)m(bic)f(Hamiltonian,)h(the)h(exp)s(ected)86 3620 y(microscopic)43 b(densit)m(y)h(estimate)g(holds)f(for)h(lo)m(w)g(temp) s(erature)f(Gibbs)g(states)i([)2984 3620 y SDict begin H.S end 2984 3620 a Black Fq(4)p Black 3030 3562 a SDict begin H.R end 3030 3562 a 3030 3620 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.BauBouNikYau-15) cvn H.B /ANN pdfmark end 3030 3620 a Fq(,)3099 3620 y SDict begin H.S end 3099 3620 a Black Fq(3)p Black 3144 3562 a SDict begin H.R end 3144 3562 a 3144 3620 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.BauBouNikYau-16) cvn H.B /ANN pdfmark end 3144 3620 a Fq(,)3214 3620 y SDict begin H.S end 3214 3620 a Black Fq(19)p Black 3305 3562 a SDict begin H.R end 3305 3562 a 3305 3620 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Leble-15b) cvn H.B /ANN pdfmark end 3305 3620 a Fq(,)3374 3620 y SDict begin H.S end 3374 3620 a Black Fq(20)p Black 3465 3562 a SDict begin H.R end 3465 3562 a 3465 3620 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.LebSer-16) cvn H.B /ANN pdfmark end 3465 3620 a Fq(])f(\(see)86 3728 y(also)c([)303 3728 y SDict begin H.S end 303 3728 a Black Fq(32)p Black 394 3669 a SDict begin H.R end 394 3669 a 394 3728 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.PetRot-16) cvn H.B /ANN pdfmark end 394 3728 a Fq(])g(for)g(ground)f(states)i(of)f (higher)f(dimensional)e(Coulom)m(b)i(and)g(Riesz)h(gases\).)71 b(It)40 b(remains)86 3836 y(to)34 b(b)s(e)f(seen)h(whether)f(a)h(com)m (bination)f(of)h(our)f(metho)s(ds)g(with)f(those)i(of)g([)2705 3836 y SDict begin H.S end 2705 3836 a Black Fq(4)p Black 2751 3777 a SDict begin H.R end 2751 3777 a 2751 3836 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.BauBouNikYau-15) cvn H.B /ANN pdfmark end 2751 3836 a Fq(,)2809 3836 y SDict begin H.S end 2809 3836 a Black Fq(19)p Black 2900 3777 a SDict begin H.R end 2900 3777 a 2900 3836 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Leble-15b) cvn H.B /ANN pdfmark end 2900 3836 a Fq(])g(could)f(impro)m(v)m(e)g(our)86 3944 y(results.)86 4049 y SDict begin H.S end 86 4049 a 86 4049 a SDict begin 13 H.A end 86 4049 a 86 4049 a SDict begin [/View [/XYZ H.V]/Dest (section.4) cvn /DEST pdfmark end 86 4049 a 1566 4157 a Fq(4.)46 b Fp(Conclusion)186 4319 y Fq(W)-8 b(e)31 b(ha)m(v)m(e)g(considered)e(p)s(erturbations)f (of)i(the)g(Laughlin)e(state)j(that)g(ma)m(y)g(arise)e(to)i(accommo)s (date)86 4427 y(external)39 b(p)s(oten)m(tials,)h(while)d(k)m(eeping)i (the)g(system)f(in)g(the)h(lo)m(w)m(est)h(Landau)d(band)h(and)g (preserving)86 4535 y(the)j(original)e(correlations.)72 b(W)-8 b(e)42 b(pro)m(v)m(ed)f(rigorously)e(that)i(no)g(suc)m(h)f(p)s (erturbation)f(can)i(raise)g(the)86 4643 y(particle)e(densit)m(y)f(an)m (ywhere)i(b)s(ey)m(ond)f(the)g(Laughlin)e(v)-5 b(alue)39 b(1)p Fo(=)p Fq(\()p Fo(\031)s(`)p Fq(\).)70 b(This)38 b(is)g(one)i(of)g(the)g(criteria)86 4757 y(for)32 b(the)h(rigidit)m(y)e (of)i(the)g(Laughlin)d(state.)50 b(Our)31 b(theorem)i(holds)e(on)i (length)f(scales)h Fn(\035)c Fo(N)3273 4724 y Fm(1)p Fk(=)p Fm(4)3416 4757 y Fq(\(in)j(the)86 4865 y(original,)f(ph)m (ysical)g(v)-5 b(ariables\))32 b(whic)m(h,)g(while)e(large)i(compared)h (to)g(the)g(magnetic)g(length)e Fo(O)s Fq(\(1\),)j(are)86 4978 y(microscopic)c(compared)g(to)h(the)g(system's)f(macroscopic)h (size,)g Fo(N)2413 4945 y 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86 2357 a SDict begin [/View [/XYZ H.V]/Dest (cite.Ciftja-06) cvn /DEST pdfmark end 86 2357 a Black 124 2429 a Fu([7])p Black 40 w Ft(O.)35 b(Ciftj)566 2423 y(\023)564 2429 y(a)p Fu(,)g Fe(Monte)g(Carlo)f(study)i(of)e(Bose) h(Laughlin)f(wave)h(function)g(for)f(\014l)t(ling)f(factors)j Fu(1)p Fs(=)p Fu(2)p Fe(,)g Fu(1)p Fs(=)p Fu(4)g Fe(and)e Fu(1)p Fs(=)p Fu(6,)244 2521 y(Europh)n(ys.)25 b(Lett.,)h(74)h (\(2006\),)g(pp.)e(486{492.)86 2539 y SDict begin H.S end 86 2539 a 86 2539 a SDict begin 11 H.A end 86 2539 a 86 2539 a SDict begin [/View [/XYZ H.V]/Dest (cite.Cooper-08) cvn /DEST pdfmark end 86 2539 a Black 124 2612 a Fu([8])p Black 40 w Ft(N.)j(R.)g(Cooper)p Fu(,)e Fe(R)l(apid)t(ly)h(r)l(otating) i(atomic)f(gases)p Fu(,)f(Adv)l(ances)e(in)h(Ph)n(ysics,)g(57)g (\(2008\),)i(pp.)d(539{616.)86 2631 y SDict begin H.S end 86 2631 a 86 2631 a SDict begin 11 H.A end 86 2631 a 86 2631 a SDict begin [/View [/XYZ H.V]/Dest (cite.Frohlich-92) cvn /DEST pdfmark end 86 2631 a Black 124 2703 a 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86 2996 a Black 73 x Fu([11])p Black 40 w Ft(S.)g(Gir)-7 b(vin)p Fu(,)24 b Fe(Intr)l(o)l(duction)29 b(to)f(the)g(fr)l(actional)g (quantum)g(Hal)t(l)e(e\013e)l(ct)p Fu(,)i(S)n(\023)-36 b(eminaire)24 b(P)n(oincar)n(\023)-36 b(e,)27 b(2)f(\(2004\),)h(pp.)e (54{74.)86 3087 y SDict begin H.S end 86 3087 a 86 3087 a SDict begin 11 H.A end 86 3087 a 86 3087 a SDict begin [/View [/XYZ H.V]/Dest (cite.Goerbig-09) cvn /DEST pdfmark end 86 3087 a Black 73 x Fu([12])p Black 40 w Ft(M.)j(O.)g(Goerbig)p Fu(,)d Fe(Quantum)k(Hal)t(l)d(e\013e)l(cts)p Fu(.)i(arXiv:0909.1998,)i (2009.)86 3179 y SDict begin H.S end 86 3179 a 86 3179 a SDict begin 11 H.A end 86 3179 a 86 3179 a SDict begin [/View [/XYZ H.V]/Dest (cite.Haldane-83) cvn /DEST pdfmark end 86 3179 a Black 72 x Fu([13])p Black 40 w Ft(F.)e(D.)h(M.)f(Hald)n (ane)p Fu(,)e Fe(F)-6 b(r)l(actional)29 b(quantization)g(of)f(the)g (Hal)t(l)f(e\013e)l(ct:)37 b(A)28 b(hier)l(ar)l(chy)h(of)f(inc)l(ompr)l (essible)h(quantum)244 3343 y(\015uid)e(states)p Fu(,)h(Ph)n(ys.)e (Rev.)f(Lett.,)h(51)h(\(1983\),)g(pp.)e(605{608.)86 3361 y SDict begin H.S end 86 3361 a 86 3361 a SDict begin 11 H.A end 86 3361 a 86 3361 a SDict begin [/View [/XYZ H.V]/Dest (cite.Jain-07) cvn /DEST pdfmark end 86 3361 a Black 73 x Fu([14])p Black 40 w Ft(J.)j(K.)g(Jain)p Fu(,)e Fe(Comp)l(osite)i(fermions)p Fu(,)e(Cam)n(bridge)g(Univ)n(ersit)n(y)e (Press,)j(2007.)86 3453 y SDict begin H.S end 86 3453 a 86 3453 a SDict begin 11 H.A end 86 3453 a 86 3453 a SDict begin [/View [/XYZ H.V]/Dest (cite.Laughlin-81) cvn /DEST pdfmark end 86 3453 a Black 72 x Fu([15])p Black 40 w Ft(R.)h(B.)f(La)n(ughlin)p Fu(,)f Fe(Quantize)l(d)j(Hal)t(l)d(c)l (onductivity)k(in)d(two)h(dimensions)p Fu(,)e(Ph)n(ys.)g(Rev.)f(B,)h (23)h(\(1981\),)g(p.)e(5632.)86 3544 y SDict begin H.S end 86 3544 a 86 3544 a SDict begin 11 H.A end 86 3544 a 86 3544 a SDict begin [/View [/XYZ H.V]/Dest (cite.Laughlin-83) cvn /DEST pdfmark end 86 3544 a Black 73 x Fu([16])p Black 244 3604 191 4 v 231 w(,)j Fe(A)n(nomalous)h(quantum)i(Hal)t(l)d (e\013e)l(ct:)39 b(A)n(n)30 b(inc)l(ompr)l(essible)g(quantum)g(\015uid) f(with)g(fr)l(actional)t(ly)h(char)l(ge)l(d)h(ex-)244 3708 y(citations)p Fu(,)c(Ph)n(ys.)e(Rev.)h(Lett.,)g(50)g(\(1983\),)h (pp.)f(1395{1398.)86 3727 y SDict begin H.S end 86 3727 a 86 3727 a SDict begin 11 H.A end 86 3727 a 86 3727 a SDict begin [/View [/XYZ H.V]/Dest (cite.Laughlin-87) cvn /DEST pdfmark end 86 3727 a Black 72 x Fu([17])p Black 244 3786 191 4 v 231 w(,)d Fe(Elementary)j(the)l(ory)h(:)33 b(the)26 b(inc)l(ompr)l(essible)g(quantum)g(\015uid)p Fu(,)d(in)g(The)f(quan)n(tum)f(Hall)i(e\013ect,)g(R.)g(E.)g(Prange)244 3891 y(and)i(S.)h(E.)g(Girvin,)g(eds.,)g(Springer,)g(Heidelb)r(erg,)h (1987.)86 3906 y SDict begin H.S end 86 3906 a 86 3906 a SDict begin 11 H.A end 86 3906 a 86 3906 a SDict begin [/View [/XYZ H.V]/Dest (cite.Laughlin-99) cvn /DEST pdfmark end 86 3906 a Black 76 x Fu([18])p Black 244 3969 191 4 v 231 w(,)f Fe(Nob)l(el)i(le)l(ctur)l(e:)36 b(F)-6 b(r)l(actional)29 b(quantization)p Fu(,)e(Rev.)e(Mo)r(d.)i(Ph)n(ys.,)f(71)g(\(1999\),)h (pp.)f(863{874.)86 4001 y SDict begin H.S end 86 4001 a 86 4001 a SDict begin 11 H.A end 86 4001 a 86 4001 a SDict begin [/View [/XYZ H.V]/Dest (cite.Leble-15b) cvn /DEST pdfmark end 86 4001 a Black 72 x Fu([19])p Black 40 w Ft(T.)31 b(Lebl)532 4067 y(\023)532 4073 y(e)p Fu(,)f Fe(L)l(o)l(c)l(al)h(micr)l(osc)l(opic)h(b)l(ehavior)g(for)e(2D)h (Coulomb)g(gases)p Fu(,)g(Probabilit)n(y)f(Theory)f(and)g(Related)g (Fields,)244 4165 y(169)e(\(2017\),)g(pp.)e(931{976.)86 4183 y SDict begin H.S end 86 4183 a 86 4183 a SDict begin 11 H.A end 86 4183 a 86 4183 a SDict begin [/View [/XYZ H.V]/Dest (cite.LebSer-16) cvn /DEST pdfmark end 86 4183 a Black 73 x Fu([20])p Black 40 w Ft(T.)j(Lebl)529 4250 y(\023)529 4256 y(e)g(and)f(S.)h(Serf)-7 b(a)i(ty)p Fu(,)26 b Fe(Fluctuations)j(of)e(two-dimensional)h(Coulomb)g(gases)p Fu(.)f(arXiv:1609.08088,)j(2016.)86 4275 y SDict begin H.S end 86 4275 a 86 4275 a SDict begin 11 H.A end 86 4275 a 86 4275 a SDict begin [/View [/XYZ H.V]/Dest (cite.LewSei-09) cvn /DEST pdfmark end 86 4275 a Black 72 x Fu([21])p Black 40 w Ft(M.)25 b(Lewin)g(and)g(R.)h(Seiringer)p Fu(,)21 b Fe(Str)l(ongly)27 b(c)l(orr)l(elate)l(d)h(phases)e(in)f(r)l (apid)t(ly)g(r)l(otating)i(Bose)f(gases)p Fu(,)g(J.)d(Stat.)h(Ph)n (ys.,)244 4438 y(137)j(\(2009\),)g(pp.)e(1040{1062.)86 4457 y SDict begin H.S end 86 4457 a 86 4457 a SDict begin 11 H.A end 86 4457 a 86 4457 a SDict begin [/View [/XYZ H.V]/Dest (cite.Lieb-76) cvn /DEST pdfmark end 86 4457 a Black 73 x Fu([22])p Black 40 w Ft(E.)j(H.)g(Lieb)p Fu(,)e Fe(The)i(stability)g(of)f(matter)p Fu(,)g(Rev.)f(Mo)r(d.)g(Ph)n (ys.,)g(48)g(\(1976\),)i(pp.)d(553{569.)86 4548 y SDict begin H.S end 86 4548 a 86 4548 a SDict begin 11 H.A end 86 4548 a 86 4548 a SDict begin [/View [/XYZ H.V]/Dest (cite.Lieb-81b) cvn /DEST pdfmark end 86 4548 a Black 73 x Fu([23])p Black 40 w Ft(E.)31 b(H.)f(Lieb)p Fu(,)f Fe(Thomas-Fermi)h(and)g(r)l(elate)l(d)h(the)l(ories)h(of)d(atoms)i(and) f(mole)l(cules)p Fu(,)f(Rev.)f(Mo)r(d.)h(Ph)n(ys.,)g(53)f(\(1981\),)244 4712 y(pp.)d(603{641.)86 4727 y SDict begin H.S end 86 4727 a 86 4727 a SDict begin 11 H.A end 86 4727 a 86 4727 a SDict begin [/View [/XYZ H.V]/Dest (cite.LieLos-01) cvn /DEST pdfmark end 86 4727 a Black 77 x Fu([24])p Black 40 w Ft(E.)h(H.)f(Lieb)g(and)g(M.)h(Loss)p Fu(,)f Fe(A)n(nalysis)p Fu(,)f(v)n(ol.)g(14)f(of)h(Graduate)g(Studies)f(in)g(Mathematics,)h (American)f(Mathemat-)244 4895 y(ical)k(So)r(ciet)n(y)-6 b(,)25 b(Pro)n(vidence,)h(RI,)f(2nd)h(ed.,)g(2001.)86 4910 y SDict begin H.S end 86 4910 a 86 4910 a SDict begin 11 H.A end 86 4910 a 86 4910 a SDict begin [/View [/XYZ H.V]/Dest (cite.LieRouYng-17) cvn /DEST pdfmark end 86 4910 a Black 76 x Fu([25])p Black 40 w Ft(E.)d(H.)g(Lieb,)g(N.)g(R)n (ougerie,)g(and)f(J.)h(Yngv)-7 b(ason)p Fu(,)22 b Fe(L)l(o)l(c)l(al)i (inc)l(ompr)l(essibility)f(estimates)i(for)e(the)g(Laughlin)g(phase)p Fu(.)244 5078 y(arXiv:1701.09064,)30 b(2017.)d(to)f(b)r(e)g(published)f (in)g(Comm.)g(Math.)h(Ph)n(ys.)86 5093 y SDict begin H.S end 86 5093 a 86 5093 a SDict begin 11 H.A end 86 5093 a 86 5093 a SDict begin [/View [/XYZ H.V]/Dest (cite.LieSei-09) cvn /DEST pdfmark end 86 5093 a Black 76 x Fu([26])p Black 40 w Ft(E.)d(H.)f(Lieb)h(and)f(R.)h(Seiringer)p Fu(,)c Fe(The)k(Stability)g(of)g(Matter)h(in)e(Quantum)i(Me)l(chanics)p Fu(,)e(Cam)n(bridge)f(Univ.)f(Press,)244 5260 y(2010.)86 5260 y SDict begin H.S end 86 5260 a 86 5260 a SDict begin 11 H.A end 86 5260 a 86 5260 a SDict begin [/View [/XYZ H.V]/Dest (cite.LieSeiYng-09) cvn /DEST pdfmark end 86 5260 a Black 92 x Fu([27])p Black 40 w Ft(E.)39 b(H.)g(Lieb,)j(R.)d (Seiringer,)g(and)g(J.)g(Yngv)-7 b(ason)p Fu(,)40 b Fe(Yr)l(ast)f(line) e(of)g(a)g(r)l(apid)t(ly)h(r)l(otating)h(Bose)f(gas:)56 b(Gr)l(oss-)244 5443 y(Pitaevskii)28 b(r)l(e)l(gime)p Fu(,)e(Ph)n(ys.)g(Rev.)f(A,)g(79)i(\(2009\),)g(p.)f(063626.)86 5462 y SDict begin H.S end 86 5462 a 86 5462 a SDict begin 11 H.A end 86 5462 a 86 5462 a SDict begin [/View [/XYZ H.V]/Dest (cite.MasMatOuv-07) cvn /DEST pdfmark end 86 5462 a Black 72 x Fu([28])p Black 40 w Ft(S.)g(Mashkevich,)h(S.)f(Ma)-5 b(tveenk)n(o,)28 b(and)e(S.)h(Ouvr)-5 b(y)p Fu(,)24 b Fe(Exact)k(r)l(esults)g(for)f(the)g(sp)l(e)l(ctr)l(a)i(of)d(b)l(osons)i (and)f(fermions)244 5626 y(with)g(c)l(ontact)j(inter)l(action)p Fu(,)e(Nuclear)d(Ph)n(ysics)h(B,)h(763)g(\(2007\),)g(pp.)e(431{444.)p Black Black eop end end %%Page: 11 11 TeXDict begin HPSdict begin 11 10 bop -300 300 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end -300 300 a -222 785 a SDict begin H.S end -222 785 a -222 785 a SDict begin H.R end -222 785 a -222 785 a SDict begin [/View [/XYZ H.V]/Dest (page.11) cvn /DEST pdfmark end -222 785 a Black 1210 559 a Fm(RIGIDITY)32 b(OF)f(THE)f(LA)n (UGHLIN)h(LIQUID)1054 b(11)p Black 86 676 a SDict begin H.S end 86 676 a 86 676 a SDict begin 11 H.A end 86 676 a 86 676 a SDict begin [/View [/XYZ H.V]/Dest (cite.MasMatOuv-13) cvn /DEST pdfmark end 86 676 a Black 83 x Fu([29])p Black 244 746 191 4 v 231 w(,)33 b Fe(Exact)h(r)l(esults)h(for)e(the)h (sp)l(e)l(ctr)l(a)h(of)e(inter)l(acting)h(b)l(osons)h(and)e(fermions)g (on)h(the)f(lowest)h(landau)g(level)p Fu(,)f(J.)244 850 y(Stat.)25 b(Mec)n(h.,)i(\(2013\),)g(p.)f(P02013.)86 869 y SDict begin H.S end 86 869 a 86 869 a SDict begin 11 H.A end 86 869 a 86 869 a SDict begin [/View [/XYZ H.V]/Dest (cite.MorFed-07) cvn /DEST pdfmark end 86 869 a Black 72 x Fu([30])p Black 40 w Ft(A.)36 b(Morris)g(and)g(D.)g(Feder)p Fu(,)f Fe(Gaussian)h(p)l(otentials)g(facilitate)f(ac)l(c)l(ess)i(to)e (quantum)h(Hal)t(l)e(states)j(in)d(r)l(otating)244 1033 y(Bose)28 b(gases)p Fu(,)f(Ph)n(ys.)f(Rev.)f(Lett.,)h(99)h(\(2007\),)g (p.)f(240401.)86 1051 y SDict begin H.S end 86 1051 a 86 1051 a SDict begin 11 H.A end 86 1051 a 86 1051 a SDict begin [/View [/XYZ H.V]/Dest (cite.PapBer-01) cvn /DEST pdfmark end 86 1051 a Black 73 x Fu([31])p Black 40 w Ft(T.)j(P)-7 b(apenbr)n(ock)31 b(and)e(G.)g(F.)h(Ber)-5 b(tsch)p Fu(,)28 b Fe(R)l(otational)h(sp)l(e)l(ctr)l(a)i(of)e(we)l(akly)g(inter)l (acting)i(Bose-Einstein)f(c)l(onden-)244 1215 y(sates)p Fu(,)d(Ph)n(ys.)f(Rev.)f(A,)h(63)g(\(2001\),)h(p.)f(023616.)86 1234 y SDict begin H.S end 86 1234 a 86 1234 a SDict begin 11 H.A end 86 1234 a 86 1234 a SDict begin [/View [/XYZ H.V]/Dest (cite.PetRot-16) cvn /DEST pdfmark end 86 1234 a Black 73 x Fu([32])p Black 40 w Ft(M.)h(Petra)n(che)h(and)f(S.)h(R)n (ot)-5 b(a-Nod)n(ari)p Fu(,)25 b Fe(Equidistribution)j(of)f(jel)t(lium) f(ener)l(gy)i(for)f(Coulomb)h(and)f(Riesz)h(inter-)244 1398 y(actions)p Fu(.)f(arXiv:1609.03849,)j(2016.)86 1413 y SDict begin H.S end 86 1413 a 86 1413 a SDict begin 11 H.A end 86 1413 a 86 1413 a SDict begin [/View [/XYZ H.V]/Dest (cite.RonRizDal-11) cvn /DEST pdfmark end 86 1413 a Black 76 x Fu([33])p Black 40 w Ft(M.)38 b(R)n(onca)n(glia,)i(M.)e (Rizzi,)g(and)f(J.)i(D)n(alibard)p Fu(,)e Fe(F)-6 b(r)l(om)37 b(r)l(otating)h(atomic)e(rings)h(to)g(quantum)h(Hal)t(l)d(states)p Fu(,)244 1581 y(www.nature.com,)27 b(Scien)n(ti\014c)e(Rep)r(orts,)h(1) g(\(2011\).)86 1599 y SDict begin H.S end 86 1599 a 86 1599 a SDict begin 11 H.A end 86 1599 a 86 1599 a SDict begin [/View [/XYZ H.V]/Dest (cite.RotSer-14) cvn /DEST pdfmark end 86 1599 a Black 73 x Fu([34])p Black 40 w Ft(S.)f(R)n(ot)-5 b(a)25 b(Nod)n(ari)g(and)g(S.)f(Serf)-7 b(a)i(ty)p Fu(,)24 b Fe(R)l(enormalize)l(d)h(ener)l(gy)i(e)l(quidistribution)f(and)g(lo)l (c)l(al)f(char)l(ge)h(b)l(alanc)l(e)g(in)f(2d)244 1763 y(Coulomb)i(systems)p Fu(,)h(In)n(t.)d(Math.)h(Res.)g(Not.,)g(11)h (\(2015\),)g(pp.)e(3035{3093.)86 1782 y SDict begin H.S end 86 1782 a 86 1782 a SDict begin 11 H.A end 86 1782 a 86 1782 a SDict begin [/View [/XYZ H.V]/Dest (cite.RouSerYng-13a) cvn /DEST pdfmark end 86 1782 a Black 73 x Fu([35])p Black 40 w Ft(N.)h(R)n(ougerie,)f(S.)g(Serf)-7 b(a)i(ty,)26 b(and)g(J.)g(Yngv)-7 b(ason)p Fu(,)24 b Fe(Quantum)j(Hal)t(l)d(states)k (of)d(b)l(osons)j(in)d(r)l(otating)i(anharmonic)244 1946 y(tr)l(aps)p Fu(,)g(Ph)n(ys.)f(Rev.)f(A,)h(87)g(\(2013\),)h(p.)f (023618.)86 1965 y SDict begin H.S end 86 1965 a 86 1965 a SDict begin 11 H.A end 86 1965 a 86 1965 a SDict begin [/View [/XYZ H.V]/Dest (cite.RouSerYng-13b) cvn /DEST pdfmark end 86 1965 a Black 72 x Fu([36])p Black 244 2024 191 4 v 231 w(,)34 b Fe(Quantum)g(Hal)t(l)e(phases)j(and)f(plasma)g(analo)l (gy)g(in)f(r)l(otating)j(tr)l(app)l(e)l(d)f(Bose)f(gases)p Fu(,)i(J.)d(Stat.)f(Ph)n(ys.,)i(154)244 2129 y(\(2014\),)27 b(pp.)e(2{50.)86 2147 y SDict begin H.S end 86 2147 a 86 2147 a SDict begin 11 H.A end 86 2147 a 86 2147 a SDict begin [/View [/XYZ H.V]/Dest (cite.RouYng-14) cvn /DEST pdfmark end 86 2147 a Black 73 x Fu([37])p Black 40 w Ft(N.)35 b(R)n(ougerie)f(and)g(J.)h(Yngv)-7 b(ason)p Fu(,)35 b Fe(Inc)l(ompr)l(essibility)f(estimates)i(for)d(the)i(Laughlin)f(phase)p Fu(,)i(Comm.)31 b(Math.)244 2311 y(Ph)n(ys.,)26 b(336)g(\(2015\),)i (pp.)d(1109{1140.)86 2330 y SDict begin H.S end 86 2330 a 86 2330 a SDict begin 11 H.A end 86 2330 a 86 2330 a SDict begin [/View [/XYZ H.V]/Dest (cite.RouYng-15) cvn /DEST pdfmark end 86 2330 a Black 73 x Fu([38])p Black 244 2390 191 4 v 231 w(,)36 b Fe(Inc)l(ompr)l(essibility)g(estimates)g(for) f(the)h(Laughlin)g(phase,)h(p)l(art)g(II)p Fu(,)c(Comm.)g(Math.)h(Ph)n (ys.,)i(339)f(\(2015\),)244 2494 y(pp.)25 b(263{277.)86 2509 y SDict begin H.S end 86 2509 a 86 2509 a SDict begin 11 H.A end 86 2509 a 86 2509 a SDict begin [/View [/XYZ H.V]/Dest (cite.RouYng-17) cvn /DEST pdfmark end 86 2509 a Black 76 x Fu([39])p Black 244 2572 191 4 v 231 w(,)43 b Fe(The)d(L)l(aughlin)h(liquid)e(in)h(an)g(external)i(p)l(otential)p Fu(,)j(Letters)39 b(in)h(Mathematical)g(Ph)n(ysics,)k(108)c(\(2018\),) 244 2677 y(pp.)25 b(1007{1029.)86 2692 y SDict begin H.S end 86 2692 a 86 2692 a SDict begin 11 H.A end 86 2692 a 86 2692 a SDict begin [/View [/XYZ H.V]/Dest (cite.StoTsuGos-99) cvn /DEST pdfmark end 86 2692 a Black 76 x Fu([40])p Black 40 w Ft(H.)33 b(St)455 2762 y(\177)452 2768 y(ormer,)i(D.)f (Tsui,)h(and)e(A.)h(Gossard)p Fu(,)e Fe(The)h(fr)l(actional)g(quantum)h (Hal)t(l)e(e\013e)l(ct)p Fu(,)i(Rev.)d(Mo)r(d.)h(Ph)n(ys.,)h(71)244 2859 y(\(1999\),)27 b(pp.)e(S298{S305.)86 2878 y SDict begin H.S end 86 2878 a 86 2878 a SDict begin 11 H.A end 86 2878 a 86 2878 a SDict begin [/View [/XYZ H.V]/Dest (cite.TruKiv-85) cvn /DEST pdfmark end 86 2878 a Black 73 x Fu([41])p Black 40 w Ft(S.)h(Tr)n(ugman)f(and)g(S.)h(Kivelson)p Fu(,)e Fe(Exact)j(r)l(esults)h(for)d(the)i(fr)l(actional)f(quantum)h (Hal)t(l)e(e\013e)l(ct)i(with)f(gener)l(al)h(inter-)244 3042 y(actions)p Fu(,)g(Ph)n(ys.)e(Rev.)h(B,)g(31)g(\(1985\),)i(p.)d (5280.)86 3061 y SDict begin H.S end 86 3061 a 86 3061 a SDict begin 11 H.A end 86 3061 a 86 3061 a SDict begin [/View [/XYZ H.V]/Dest (cite.Viefers-08) cvn /DEST pdfmark end 86 3061 a Black 72 x Fu([42])p Black 40 w Ft(S.)42 b(Viefers)p Fu(,)i Fe(Quantum)d(Hal)t(l)f(physics)i(in)f(r)l(otating)h (Bose-Einstein)h(c)l(ondensates)p Fu(,)k(J.)41 b(Ph)n(ys.)f(C,)h(20)g (\(2008\),)244 3224 y(p.)25 b(123202.)186 3396 y Ft(Dep)-5 b(ar)g(tments)23 b(of)i(Ma)-5 b(thema)g(tics)23 b(and)h(Physics,)h (Princeton)g(University,)e(Princeton,)j(NJ)e(08544,)j(USA)186 3487 y Fe(E-mail)g(addr)l(ess)6 b Fu(:)36 b Fa(lieb@princeton.edu)186 3642 y Ft(Universit)550 3636 y(\023)550 3642 y(e)i(Grenoble)j(Alpes)f (&)h(CNRS,)e(LPMMC)h(\(UMR)g(5493\),)k(B.P.)c(166,)45 b(F-38042)d(Grenoble,)86 3734 y(France)186 3825 y Fe(E-mail)27 b(addr)l(ess)6 b Fu(:)36 b Fa(nicolas.rougerie@lpmmc.cnrs.f)q(r)186 3980 y Ft(F)-9 b(a)n(cul)k(ty)29 b(of)g(Physics,)f(University)f(of)h (Vienna,)f(Bol)-5 b(tzmanngasse)27 b(5,)i(A-1090)g(Vienna,)e(A)n (ustria)186 4072 y Fe(E-mail)g(addr)l(ess)6 b Fu(:)36 b Fa(jakob.yngvason@univie.ac.at)p Black Black eop end end %%Trailer end userdict /end-hook known{end-hook}if %%EOF