Solitone di Davydov

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</nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Da Wikipedia, l'enciclopedia libera.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="it" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Davydov-soliton.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/Davydov-soliton.gif/510px-Davydov-soliton.gif" decoding="async" width="510" height="376" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/7/76/Davydov-soliton.gif 1.5x" data-file-width="576" data-file-height="425" /></a><figcaption>Dinamica quantistica di un solitone di Davydov.<sup id="cite_ref-Georgiev2019_1-0" class="reference"><a href="#cite_note-Georgiev2019-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>Un <b>solitone di <a href="/wiki/Alexander_Davydov" class="mw-redirect" title="Alexander Davydov">Davydov</a></b> è una <a href="/wiki/Quasiparticella" title="Quasiparticella">quasiparticella</a> quantica indicante un'eccitazione che si propaga lungo l'<a href="/wiki/Ammidi" title="Ammidi">ammide I</a> auto-intrappolato dell'<a href="/wiki/Alfa_elica" title="Alfa elica">α elica</a> della <a href="/wiki/Proteina" class="mw-redirect" title="Proteina">proteina</a>. È una soluzione dell'<a href="/wiki/Operatore_hamiltoniano" title="Operatore hamiltoniano">operatore hamiltoniano</a> di Davydov. Il modello di Davydov descrive l'interazione delle <a href="/wiki/Vibrazione" title="Vibrazione">vibrazioni</a> dell'ammide con i <a href="/wiki/Legame_idrogeno" class="mw-redirect" title="Legame idrogeno">legami idrogeno</a> che stabilizzano l'<a href="/wiki/Alfa_elica" title="Alfa elica">α elica</a> delle <a href="/wiki/Proteina" class="mw-redirect" title="Proteina">proteine</a>. Le eccitazioni elementari all'interno dell'α elica sono fornite dai <a href="/wiki/Fonone" title="Fonone">fononi</a> che corrispondono alle oscillazioni deformazionali del reticolo, e dagli <a href="/wiki/Eccitone" title="Eccitone">eccitoni</a> che descrivono le eccitazioni interne dell'<a href="/wiki/Ammidi" title="Ammidi">ammide I</a> del <a href="/wiki/Legame_peptidico" title="Legame peptidico">gruppo peptide</a>. Facendo riferimento alla struttura atomica di una regione dell'α elica della proteina, il meccanismo che crea il solitone di Davydov (<a href="/wiki/Polarone" title="Polarone">polarone</a>, <a href="/wiki/Eccitone" title="Eccitone">eccitone</a>) può essere descritto come segue: l'<a href="/wiki/Energia" title="Energia">energia</a> <a href="/wiki/Vibrazione" title="Vibrazione">vibrazionale</a> degli <a href="/wiki/Oscillatore" title="Oscillatore">oscillatori</a> di <a href="/wiki/Stretching_molecolare" title="Stretching molecolare">stretching</a> di <a href="/wiki/Carbonile" title="Carbonile">C=O</a> (o <a href="/wiki/Ammidi" title="Ammidi">ammide I</a>) localizzata sull'α elica agisce attraverso un effetto di accoppiamento fononico per distorcere la struttura dell'α-elica, mentre la distorsione elicoidale reagisce di nuovo attraverso l'accoppiamento dei fononi per intrappolare l'energia oscillatoria dell'ammide I impedendone la sua dispersione. Questo effetto è chiamato <i>auto-localizzazione</i> o <i>auto-intrappolamento</i>.<sup id="cite_ref-Davydov1973_2-0" class="reference"><a href="#cite_note-Davydov1973-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Davydov1974_3-0" class="reference"><a href="#cite_note-Davydov1974-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Davydov1977_4-0" class="reference"><a href="#cite_note-Davydov1977-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> I <a href="/wiki/Solitone" title="Solitone">solitoni</a> in cui l'<a href="/wiki/Energia" title="Energia">energia</a> viene distribuita in modo da preservare la <a href="/wiki/Simmetria" title="Simmetria">simmetria</a> <a href="/wiki/Elica" title="Elica">elicoidale</a> sono dinamicamente instabili, e tali solitoni <a href="/wiki/Simmetria" title="Simmetria">simmetrici</a> una volta che si sono formati, quando si propagano, decadono rapidamente. D'altra parte, un solitone <a href="/wiki/Simmetria" title="Simmetria">asimmetrico</a>, che <a href="/wiki/Rottura_spontanea_di_simmetria" title="Rottura spontanea di simmetria">spontaneamente rompe le simmetrie locali traslazionali ed elicoidali</a>, possiede l'energia minore ed è una solida entità localizzata.<sup id="cite_ref-Brizhik2004_5-0" class="reference"><a href="#cite_note-Brizhik2004-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>L'<a href="/wiki/Meccanica_hamiltoniana" title="Meccanica hamiltoniana">hamiltoniana</a> di Davydov è formalmente simile all'<a href="/wiki/Polarone#Teoria_del_polarone" title="Polarone">hamiltoniana di Fröhlich-Holstein</a> per l'interazione di elettroni con un reticolo polarizzabile. Perciò l'<a href="/wiki/Meccanica_hamiltoniana" title="Meccanica hamiltoniana">hamiltoniana</a> dell'<a href="/wiki/Osservabile" title="Osservabile">operatore</a> di <a href="/wiki/Energia" title="Energia">energia</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bb06de5217295d7fbdbf68fb9c5309a513fc99e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.843ex;" alt="{\displaystyle {\hat {H}}}"></span> è </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {H}}={\hat {H}}_{\text{qp}}+{\hat {H}}_{\text{ph}}+{\hat {H}}_{\text{int}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>qp</mtext> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>ph</mtext> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>int</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}={\hat {H}}_{\text{qp}}+{\hat {H}}_{\text{ph}}+{\hat {H}}_{\text{int}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bb4110eb193d2f24aa6e6f4976609eb9b588d94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:23.351ex; height:3.509ex;" alt="{\displaystyle {\hat {H}}={\hat {H}}_{\text{qp}}+{\hat {H}}_{\text{ph}}+{\hat {H}}_{\text{int}}}"></span></dd></dl> <p>dove <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {H}}_{\text{qp}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>qp</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}_{\text{qp}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1774e7c1847f8f56320929ba3f7de0a3c80483cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.078ex; height:3.509ex;" alt="{\displaystyle {\hat {H}}_{\text{qp}}}"></span> è l'<a href="/wiki/Meccanica_hamiltoniana" title="Meccanica hamiltoniana">hamiltoniana</a> della <a href="/wiki/Quasiparticella" title="Quasiparticella">quasiparticella</a> (<a href="/wiki/Eccitone" title="Eccitone">eccitone</a>), che descrive il moto delle eccitazioni dell'ammide I tra siti adiacenti; <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {H}}_{\text{ph}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>ph</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}_{\text{ph}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4cb24532bbfec6cdbaaa5bd86341c29e7271875e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.124ex; height:3.509ex;" alt="{\displaystyle {\hat {H}}_{\text{ph}}}"></span> è l'<a href="/wiki/Meccanica_hamiltoniana" title="Meccanica hamiltoniana">hamiltoniana</a> del <a href="/wiki/Fonone" title="Fonone">fonone</a>, che descrive le <a href="/wiki/Vibrazione" title="Vibrazione">vibrazioni</a> del <a href="/wiki/Reticolo_cristallino" class="mw-redirect" title="Reticolo cristallino">reticolo cristallino</a>; e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {H}}_{\text{int}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>int</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}_{\text{int}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbed73204fe7bbbff9f15274c778c4005eb979ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.307ex; height:3.176ex;" alt="{\displaystyle {\hat {H}}_{\text{int}}}"></span> è l'<a href="/wiki/Meccanica_hamiltoniana" title="Meccanica hamiltoniana">hamiltoniana</a> di <a href="/wiki/Interazione" title="Interazione">interazione</a>, la quale descrive l'interazione dell'eccitazione dell'ammide I con il reticolo.<sup id="cite_ref-Davydov1973_2-1" class="reference"><a href="#cite_note-Davydov1973-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Davydov1974_3-1" class="reference"><a href="#cite_note-Davydov1974-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Davydov1977_4-1" class="reference"><a href="#cite_note-Davydov1977-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>L'<a href="/wiki/Meccanica_hamiltoniana" title="Meccanica hamiltoniana">hamiltoniana</a> della <a href="/wiki/Quasiparticella" title="Quasiparticella">quasiparticella</a> (<a href="/wiki/Eccitone" title="Eccitone">eccitone</a>) <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {H}}_{\text{qp}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>qp</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}_{\text{qp}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1774e7c1847f8f56320929ba3f7de0a3c80483cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.078ex; height:3.509ex;" alt="{\displaystyle {\hat {H}}_{\text{qp}}}"></span> è: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {H}}_{\text{qp}}=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>qp</mtext> </mrow> </msub> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}_{\text{qp}}=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02f142ebe97fe62e2b4252ae37361890f69bb298" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:6.531ex; height:3.509ex;" alt="{\displaystyle {\hat {H}}_{\text{qp}}=}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{n,\alpha }E_{0}{\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n,\alpha }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> </munder> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>†</mo> </mrow> </msubsup> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{n,\alpha }E_{0}{\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n,\alpha }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96a98e9cda30dcbbae17eab6471746fca33202e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:15.518ex; height:6.176ex;" alt="{\displaystyle \sum _{n,\alpha }E_{0}{\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n,\alpha }}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -K\sum _{n,\alpha }\left({\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n+1,\alpha }+{\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n-1,\alpha }\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi>K</mi> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> </munder> <mrow> <mo>(</mo> <mrow> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>†</mo> </mrow> </msubsup> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>α</mi> </mrow> </msub> <mo>+</mo> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>†</mo> </mrow> </msubsup> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mi>α</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -K\sum _{n,\alpha }\left({\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n+1,\alpha }+{\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n-1,\alpha }\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5cc769099bf035ca58813565b14b46a35876d7c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:35.834ex; height:6.176ex;" alt="{\displaystyle -K\sum _{n,\alpha }\left({\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n+1,\alpha }+{\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n-1,\alpha }\right)}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +L\sum _{n,\alpha }\left({\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n,\alpha +1}+{\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n,\alpha -1}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> <mi>L</mi> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> </munder> <mrow> <mo>(</mo> <mrow> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>†</mo> </mrow> </msubsup> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>†</mo> </mrow> </msubsup> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +L\sum _{n,\alpha }\left({\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n,\alpha +1}+{\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n,\alpha -1}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c41785b7ee72d7df5ffd5af5ef9d7fa30ff87d88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:35.351ex; height:6.176ex;" alt="{\displaystyle +L\sum _{n,\alpha }\left({\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n,\alpha +1}+{\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n,\alpha -1}\right)}"></span></dd></dl> <p>dove: </p> <ul><li>l'indice <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=1,2,\cdots ,N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=1,2,\cdots ,N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b17d3ec089e72ca2f581c0f786b9b687c23326a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.094ex; height:2.509ex;" alt="{\displaystyle n=1,2,\cdots ,N}"></span> calcola i <a href="/wiki/Legame_peptidico" title="Legame peptidico">gruppi del peptide</a> lungo la dorsale dell'<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span>-elica</li> <li>l'indice <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha =1,2,3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha =1,2,3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e70c36a23e94c1aa3e6b4778e3db3fc598ad458d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.141ex; height:2.509ex;" alt="{\displaystyle \alpha =1,2,3}"></span> calcola ogni dorsale dell'<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span>-elica</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{0}=32.8\;\mathrm {zJ} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>32.8</mn> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">z</mi> <mi mathvariant="normal">J</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0}=32.8\;\mathrm {zJ} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/973caf8eb5496896d3132ce5b719847b053da4b4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.875ex; height:2.509ex;" alt="{\displaystyle E_{0}=32.8\;\mathrm {zJ} }"></span> è l'energia della vibrazione dell'ammide I (stretching <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\ce {CO}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>CO</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {CO}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf2a888c2c193ddb2937e2c7e85aadaa0a4e9513" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.486ex; height:2.176ex;" alt="{\displaystyle {\ce {CO}}}"></span>) (nell'unità di misura, il prefisso <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32df2a6cf3210ef4f1cfcb85c749091d32272a5f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.032ex; height:1.676ex;" alt="{\displaystyle \mathrm {z} }"></span> sta per <a href="/wiki/Zepto" title="Zepto">zepto</a> e la lettera <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {J} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">J</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {J} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed0b3ef0cc0c96ab4e418ef3de9037d68d8a8ba0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.195ex; height:2.176ex;" alt="{\displaystyle \mathrm {J} }"></span> indica il <a href="/wiki/Joule" title="Joule">Joule</a>)</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K=0.155\;\mathrm {zJ} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> <mo>=</mo> <mn>0.155</mn> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">z</mi> <mi mathvariant="normal">J</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K=0.155\;\mathrm {zJ} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4007c8269f2691354c3b81eb0d17bab68027b869" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.334ex; height:2.176ex;" alt="{\displaystyle K=0.155\;\mathrm {zJ} }"></span> è l'energia di accoppiamento dipolo-dipolo tra un legame particolare di ammide I e quelli davanti e dietro lungo la dorsale stessa</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L=0.246\;\mathrm {zJ} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>=</mo> <mn>0.246</mn> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">z</mi> <mi mathvariant="normal">J</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L=0.246\;\mathrm {zJ} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f8410597818e14ef4cfdb064101c45ae6f213fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.85ex; height:2.176ex;" alt="{\displaystyle L=0.246\;\mathrm {zJ} }"></span> è l'energia di accoppiamento dipolo-dipolo tra un legame particolare di ammide I e quelli sulle dorsali adiacenti nella stessa unità cellulare della <a href="/wiki/Alfa_elica" title="Alfa elica">α elica</a> della <a href="/wiki/Proteina" class="mw-redirect" title="Proteina">proteina</a></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {A}}_{n,\alpha }^{\dagger }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>†</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {A}}_{n,\alpha }^{\dagger }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ddd7b058d844eb4f6f9d46c7cf48e97f353f9b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:4.503ex; height:4.176ex;" alt="{\displaystyle {\hat {A}}_{n,\alpha }^{\dagger }}"></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {A}}_{n,\alpha }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {A}}_{n,\alpha }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3afddad5c7a91e95cb9c05ddb088782dd1cebcb8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.503ex; height:3.509ex;" alt="{\displaystyle {\hat {A}}_{n,\alpha }}"></span> sono rispettivamente gli <a href="/wiki/Operatori_di_creazione_e_annichilazione" class="mw-redirect" title="Operatori di creazione e annichilazione">operatori di creazione e annichilazione</a> del <a href="/wiki/Bosone_(fisica)" title="Bosone (fisica)">bosone</a> per una quasiparticella del <a href="/wiki/Legame_peptidico" title="Legame peptidico">gruppo peptide</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n,\alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n,\alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7bdaacc649599c91627714e59d5d54a93d572d75" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.916ex; height:2.009ex;" alt="{\displaystyle n,\alpha }"></span>.<sup id="cite_ref-Scott1992_6-0" class="reference"><a href="#cite_note-Scott1992-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Takeno1997_7-0" class="reference"><a href="#cite_note-Takeno1997-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></li></ul> <p>L'<a href="/wiki/Meccanica_hamiltoniana" title="Meccanica hamiltoniana">hamiltoniana</a> del <a href="/wiki/Fonone" title="Fonone">fonone</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {H}}_{\text{ph}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>ph</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}_{\text{ph}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4cb24532bbfec6cdbaaa5bd86341c29e7271875e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.124ex; height:3.509ex;" alt="{\displaystyle {\hat {H}}_{\text{ph}}}"></span> è </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {H}}_{\text{ph}}={\frac {1}{2}}\sum _{n,\alpha }\left[w({\hat {u}}_{n+1,\alpha }-{\hat {u}}_{n,\alpha })^{2}+{\frac {{\hat {p}}_{n,\alpha }^{2}}{M}}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>ph</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> </munder> <mrow> <mo>[</mo> <mrow> <mi>w</mi> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>α</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mi>M</mi> </mfrac> </mrow> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}_{\text{ph}}={\frac {1}{2}}\sum _{n,\alpha }\left[w({\hat {u}}_{n+1,\alpha }-{\hat {u}}_{n,\alpha })^{2}+{\frac {{\hat {p}}_{n,\alpha }^{2}}{M}}\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbfede9b5dc3d98ad66eeb7dd8afe9b43208a005" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:41.408ex; height:7.676ex;" alt="{\displaystyle {\hat {H}}_{\text{ph}}={\frac {1}{2}}\sum _{n,\alpha }\left[w({\hat {u}}_{n+1,\alpha }-{\hat {u}}_{n,\alpha })^{2}+{\frac {{\hat {p}}_{n,\alpha }^{2}}{M}}\right]}"></span></dd></dl> <p>dove: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {u}}_{n,\alpha }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {u}}_{n,\alpha }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68686cd863db9f18db6dcd391cee23afecbbf712" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.057ex; height:2.843ex;" alt="{\displaystyle {\hat {u}}_{n,\alpha }}"></span> è l'<a href="/w/index.php?title=Operatore_di_spostamento&action=edit&redlink=1" class="new" title="Operatore di spostamento (la pagina non esiste)">operatore di spostamento</a> dalla posizione di equilibrio del <a href="/wiki/Legame_peptidico" title="Legame peptidico">gruppo peptide</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n,\alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n,\alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7bdaacc649599c91627714e59d5d54a93d572d75" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.916ex; height:2.009ex;" alt="{\displaystyle n,\alpha }"></span></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {p}}_{n,\alpha }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {p}}_{n,\alpha }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9076e5e13df601e8d08cb2c8ea8edc3477d0d99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; margin-left: -0.089ex; width:4.177ex; height:3.009ex;" alt="{\displaystyle {\hat {p}}_{n,\alpha }}"></span> è l'<a href="/wiki/Operatore_impulso" title="Operatore impulso">operatore del momento</a> del <a href="/wiki/Legame_peptidico" title="Legame peptidico">gruppo peptide</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n,\alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n,\alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7bdaacc649599c91627714e59d5d54a93d572d75" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.916ex; height:2.009ex;" alt="{\displaystyle n,\alpha }"></span></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span> è la <a href="/wiki/Massa_(fisica)" title="Massa (fisica)">massa</a> di ogni <a href="/wiki/Legame_peptidico" title="Legame peptidico">gruppo peptide</a></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w=13\;-\;19\;Nm^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> <mo>=</mo> <mn>13</mn> <mspace width="thickmathspace" /> <mo>−</mo> <mspace width="thickmathspace" /> <mn>19</mn> <mspace width="thickmathspace" /> <mi>N</mi> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w=13\;-\;19\;Nm^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8a6c78b3f4f9dc4310eda6b8fd64b536af82728" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:20.625ex; height:2.843ex;" alt="{\displaystyle w=13\;-\;19\;Nm^{-1}}"></span> è un <a href="/wiki/Elasticit%C3%A0_(meccanica)" class="mw-redirect" title="Elasticità (meccanica)">coefficiente di elasticità effettiva</a> del reticolo (la <a href="/wiki/Legge_di_Hooke" title="Legge di Hooke">costante di elasticità</a> di un <a href="/wiki/Legame_a_idrogeno" title="Legame a idrogeno">legame a idrogeno</a>).</li></ul> <p>Infine, l'<a href="/wiki/Meccanica_hamiltoniana" title="Meccanica hamiltoniana">hamiltoniana</a> dell'<a href="/wiki/Interazione" title="Interazione">interazione</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {H}}_{\text{int}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>int</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}_{\text{int}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbed73204fe7bbbff9f15274c778c4005eb979ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.307ex; height:3.176ex;" alt="{\displaystyle {\hat {H}}_{\text{int}}}"></span> è </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {H}}_{\text{int}}=\chi \sum _{n,\alpha }\left[({\hat {u}}_{n+1,\alpha }-{\hat {u}}_{n,\alpha }){\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n,\alpha }\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>int</mtext> </mrow> </msub> <mo>=</mo> <mi>χ</mi> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> </munder> <mrow> <mo>[</mo> <mrow> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>α</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>u</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> </msub> <mo stretchy="false">)</mo> <msubsup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>†</mo> </mrow> </msubsup> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>,</mo> <mi>α</mi> </mrow> </msub> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {H}}_{\text{int}}=\chi \sum _{n,\alpha }\left[({\hat {u}}_{n+1,\alpha }-{\hat {u}}_{n,\alpha }){\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n,\alpha }\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d63982d348447a3b73a89477b18ff5c5b141bf7e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:39.056ex; height:6.176ex;" alt="{\displaystyle {\hat {H}}_{\text{int}}=\chi \sum _{n,\alpha }\left[({\hat {u}}_{n+1,\alpha }-{\hat {u}}_{n,\alpha }){\hat {A}}_{n,\alpha }^{\dagger }{\hat {A}}_{n,\alpha }\right]}"></span></dd></dl> <p>dove <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi =35\;-62\;pN}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> <mo>=</mo> <mn>35</mn> <mspace width="thickmathspace" /> <mo>−</mo> <mn>62</mn> <mspace width="thickmathspace" /> <mi>p</mi> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi =35\;-62\;pN}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/deb88bf7db8f78d39d0314431e45940d12b136ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.567ex; height:2.509ex;" alt="{\displaystyle \chi =35\;-62\;pN}"></span> è un parametro anarmonico che scaturisce dall'accoppiamento tra la <a href="/wiki/Quasiparticella" title="Quasiparticella">quasiparticella</a> (eccitone) e gli spostamenti del reticolo (fonone) e parametrizza la forza dell'<a href="/wiki/Interazione" title="Interazione">interazione</a> <a href="/wiki/Eccitone" title="Eccitone">eccitone</a>-<a href="/wiki/Fonone" title="Fonone">fonone</a>. Il valore di questo parametro per l'<a href="/wiki/Alfa_elica" title="Alfa elica">α elica</a> è stato determinato tramite il confronto delle forme di linea di assorbimento calcolate teoricamente con quelle misurate sperimentalmente <sup id="cite_ref-Cruzeiro2005_8-0" class="reference"><a href="#cite_note-Cruzeiro2005-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> e dovrebbero essere considerate come la migliore stima aggiornata. </p><p>Le tecniche matematiche che sono utilizzate per analizzare il solitone di Davydov sono simili ad alcune sviluppate nella teoria del <a href="/wiki/Polarone" title="Polarone">polarone</a>. In questo contesto il solitone di Davydov corrisponde a un <a href="/wiki/Polarone" title="Polarone">polarone</a> che è (i) <i>grande</i> da giustificare l'approssimazione del limite, (ii) <i>acustico</i> perché l'auto-localizzazione sorge da interazioni con altri modi acustici del reticolo, e (iii) <i>debolmente accoppiato</i> perché l'energia anarmonica è piccola rispetto alla larghezza di banda dei fononi.<sup id="cite_ref-Scott1992_6-1" class="reference"><a href="#cite_note-Scott1992-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Il solitone di Davydov è una <i>quasiparticella quantistica</i> e obbedisce al <a href="/wiki/Principio_di_indeterminazione_di_Heisenberg" title="Principio di indeterminazione di Heisenberg">principio di indeterminazione di Heisenberg</a>. Pertanto, qualsiasi modello che non impone invarianza traslazionale è difettoso nella costruzione.<sup id="cite_ref-Scott1992_6-2" class="reference"><a href="#cite_note-Scott1992-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> La supposizione che il solitone di Davydov sia localizzato a 5 giri dell'<a href="/wiki/Alfa_elica" title="Alfa elica">α elica</a> risulta nell'indeterminazione nella <a href="/wiki/Velocit%C3%A0" title="Velocità">velocità</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta v=133{\frac {m}{s}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>v</mi> <mo>=</mo> <mn>133</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>m</mi> <mi>s</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta v=133{\frac {m}{s}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c117c8ef8ee1a016012bbf30ecbb90215f4f70a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.526ex; height:4.676ex;" alt="{\displaystyle \Delta v=133{\frac {m}{s}}}"></span> del <a href="/wiki/Solitone" title="Solitone">solitone</a>, un fatto che è oscurato se si modella il solitone di Davydov come un oggetto classico. </p><p>Ci sono tre possibili approcci fondamentali verso il modello di Davydov:<sup id="cite_ref-Takeno1997_7-1" class="reference"><a href="#cite_note-Takeno1997-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Cruzeiro1997_9-0" class="reference"><a href="#cite_note-Cruzeiro1997-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> (i) la <a href="/wiki/Meccanica_quantistica" title="Meccanica quantistica">teoria quantistica</a>, in cui sia la vibrazione (<a href="/wiki/Eccitone" title="Eccitone">eccitoni</a>) dell'ammide I che il movimento della posizione del reticolo (<a href="/wiki/Fonone" title="Fonone">fononi</a>) si comportano meccanicamente come quanti; (ii) la teoria mista quantistica-classica, in cui la vibrazione dell'ammide I è trattata meccanicamente in modo quantistico, ma il reticolo è classico; e (iii) la <a href="/w/index.php?title=Teoria_classica&action=edit&redlink=1" class="new" title="Teoria classica (la pagina non esiste)">teoria classica</a>, dove sia l'ammide I che i movimenti del reticolo sono trattati classicamente. </p> <div class="mw-heading mw-heading2"><h2 id="Note">Note</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Solitone_di_Davydov&veaction=edit&section=1" title="Modifica la sezione Note" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Solitone_di_Davydov&action=edit&section=1" title="Edit section's source code: Note"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Georgiev2019-1"><a href="#cite_ref-Georgiev2019_1-0"><b>^</b></a> <span class="reference-text"><cite class="citation pubblicazione" style="font-style:normal">(<span style="font-weight:bolder; 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font-size:80%"><abbr title="inglese">EN</abbr></span>) Davydov AS, <a rel="nofollow" class="external text" href="https://oadoi.org/10.1016/0022-5193(77)90178-3"><span style="font-style:italic;">Solitons and energy transfer along protein molecules</span></a>, in <span style="font-style:italic;">Journal of Theoretical Biology</span>, vol. 66, 1977, pp. 379–387, <a href="/wiki/Digital_object_identifier" title="Digital object identifier">DOI</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1016%2F0022-5193%2877%2990178-3">10.1016/0022-5193(77)90178-3</a>.</cite></span> </li> <li id="cite_note-Brizhik2004-5"><a href="#cite_ref-Brizhik2004_5-0"><b>^</b></a> <span class="reference-text"> <cite class="citation pubblicazione" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) Brizhik L., Eremko A.; Piette B.; Zakrzewski W., <a rel="nofollow" class="external text" href="https://arxiv.org/abs/cond-mat/0402644"><span style="font-style:italic;">Solitons in α-helical proteins</span></a>, in <span style="font-style:italic;">Physical Review E</span>, vol. 70, 2004, pp. 031914, 1–16.</cite></span> </li> <li id="cite_note-Scott1992-6"><span class="mw-cite-backlink"><b>^</b> <sup><i><a href="#cite_ref-Scott1992_6-0">a</a></i></sup> <sup><i><a href="#cite_ref-Scott1992_6-1">b</a></i></sup> <sup><i><a href="#cite_ref-Scott1992_6-2">c</a></i></sup></span> <span class="reference-text"> <cite class="citation pubblicazione" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) Scott AS, <a rel="nofollow" class="external text" href="https://oadoi.org/10.1016/0370-1573(92)90093-F"><span style="font-style:italic;">Davydov's soliton</span></a>, in <span style="font-style:italic;">Physics Reports</span>, vol. 217, 1992, pp. 1–67, <a href="/wiki/Digital_object_identifier" title="Digital object identifier">DOI</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1016%2F0370-1573%2892%2990093-F">10.1016/0370-1573(92)90093-F</a>.</cite></span> </li> <li id="cite_note-Takeno1997-7"><span class="mw-cite-backlink"><b>^</b> <sup><i><a href="#cite_ref-Takeno1997_7-0">a</a></i></sup> <sup><i><a href="#cite_ref-Takeno1997_7-1">b</a></i></sup></span> <span class="reference-text"> <cite class="citation pubblicazione" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) Cruzeiro-Hansson L, Takeno S., <span style="font-style:italic;"><a rel="nofollow" class="external text" href="https://prola.aps.org/abstract/PRE/v56/i1/p894_1">Davydov model: the quantum, mixed quantum-classical, and full classical systems</a></span>, in <span style="font-style:italic;">Physical Review E</span>, vol. 56, 1997, pp. 894–906.</cite></span> </li> <li id="cite_note-Cruzeiro2005-8"><a href="#cite_ref-Cruzeiro2005_8-0"><b>^</b></a> <span class="reference-text"> <cite class="citation pubblicazione" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) Cruzeiro-Hansson L, <a rel="nofollow" class="external text" href="https://oadoi.org/10.1063/1.2138705"><span style="font-style:italic;">[http://link.aip.org/link/?JCPSA6/123/234909/1 Influence of the nonlinearity and dipole strength on the amide I band of protein α-helices]</span></a>, in <span style="font-style:italic;"><a href="/wiki/Journal_of_Chemical_Physics" title="Journal of Chemical Physics">The Journal of Chemical Physics</a></span>, vol. 123, 2005, pp. 234909, 1–7, <a href="/wiki/Digital_object_identifier" title="Digital object identifier">DOI</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1063%2F1.2138705">10.1063/1.2138705</a>.</cite></span> </li> <li id="cite_note-Cruzeiro1997-9"><a href="#cite_ref-Cruzeiro1997_9-0"><b>^</b></a> <span class="reference-text"> <cite class="citation pubblicazione" style="font-style:normal"> Cruzeiro-Hansson L, <span style="font-style:italic;">Short timescale energy transfer in proteins</span>, in <span style="font-style:italic;">Solphys '97 Proceedings</span>, 1997.</cite></span> </li> </ol></div> <style data-mw-deduplicate="TemplateStyles:r141815314">.mw-parser-output .navbox{border:1px solid #aaa;clear:both;margin:auto;padding:2px;width:100%}.mw-parser-output .navbox th{padding-left:1em;padding-right:1em;text-align:center}.mw-parser-output .navbox>tbody>tr:first-child>th{background:#ccf;font-size:90%;width:100%;color:var(--color-base,black)}.mw-parser-output .navbox_navbar{float:left;margin:0;padding:0 10px 0 0;text-align:left;width:6em}.mw-parser-output .navbox_title{font-size:110%}.mw-parser-output .navbox_abovebelow{background:#ddf;font-size:90%;font-weight:normal}.mw-parser-output .navbox_group{background:#ddf;font-size:90%;padding:0 10px;white-space:nowrap}.mw-parser-output .navbox_list{font-size:90%;width:100%}.mw-parser-output .navbox_list a{white-space:nowrap}html:not(.vector-feature-night-mode-enabled) .mw-parser-output .navbox_odd{background:#fdfdfd;color:var(--color-base,black)}html:not(.vector-feature-night-mode-enabled) .mw-parser-output .navbox_even{background:#f7f7f7;color:var(--color-base,black)}.mw-parser-output .navbox a.mw-selflink{color:var(--color-base,black)}.mw-parser-output .navbox_center{text-align:center}.mw-parser-output .navbox .navbox_image{padding-left:7px;vertical-align:middle;width:0}.mw-parser-output .navbox+.navbox{margin-top:-1px}.mw-parser-output .navbox .mw-collapsible-toggle{font-weight:normal;text-align:right;width:7em}body.skin--responsive .mw-parser-output .navbox_image img{max-width:none!important}.mw-parser-output .subnavbox{margin:-3px;width:100%}.mw-parser-output .subnavbox_group{background:#e6e6ff;padding:0 10px}@media screen{html.skin-theme-clientpref-night .mw-parser-output .navbox>tbody>tr:first-child>th{background:var(--background-color-interactive)!important}html.skin-theme-clientpref-night .mw-parser-output .navbox th{color:var(--color-base)!important}html.skin-theme-clientpref-night .mw-parser-output .navbox_abovebelow,html.skin-theme-clientpref-night .mw-parser-output .navbox_group{background:var(--background-color-interactive-subtle)!important}html.skin-theme-clientpref-night .mw-parser-output .subnavbox_group{background:var(--background-color-neutral-subtle)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbox>tbody>tr:first-child>th{background:var(--background-color-interactive)!important}html.skin-theme-clientpref-os .mw-parser-output .navbox th{color:var(--color-base)!important}html.skin-theme-clientpref-os .mw-parser-output .navbox_abovebelow,html.skin-theme-clientpref-os .mw-parser-output .navbox_group{background:var(--background-color-interactive-subtle)!important}html.skin-theme-clientpref-os .mw-parser-output .subnavbox_group{background:var(--background-color-neutral-subtle)!important}}</style><table class="navbox mw-collapsible mw-collapsed noprint metadata" id="navbox-Particelle"><tbody><tr><th colspan="3"><div class="navbox_navbar"><div class="noprint plainlinks" style="background-color:transparent; 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Usa l'anteprima prima di salvare">M</span></a></div></div><span class="navbox_title"><a href="/wiki/Particella_subatomica" title="Particella subatomica">Particelle in fisica</a></span></th></tr><tr><th colspan="1" class="navbox_group" style="width:5em;font-weight:normal; width:10%"><b><a href="/wiki/Particella_elementare" title="Particella elementare">Elementari</a></b></th><td colspan="1" class="navbox_list navbox_odd" style="background:transparent"><table class="subnavbox"><tbody><tr><th class="subnavbox_group" style="width:5em;font-weight:normal; width:9%;background:#e6e6ff"><b><a href="/wiki/Fermione" title="Fermione">Fermioni</a></b></th><td colspan="1"><table class="subnavbox"><tbody><tr><th class="subnavbox_group" style="width:5em;font-weight:normal; width:12%;background:#e6e6ff"><a href="/wiki/Quark_(particella)" title="Quark (particella)">Quark</a></th><td colspan="1"><a href="/wiki/Quark_up" title="Quark up">Up</a><b> ·</b> <a href="/wiki/Quark_down" title="Quark down">Down</a><b> ·</b> <a href="/wiki/Quark_charm" title="Quark charm">Charm</a><b> ·</b> <a href="/wiki/Quark_strange" title="Quark strange">Strange</a><b> ·</b> <a href="/wiki/Quark_top" title="Quark top">Top</a><b> ·</b> <a href="/wiki/Quark_bottom" title="Quark bottom">Bottom</a></td></tr><tr><th class="subnavbox_group" style="width:5em;font-weight:normal; 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width:9%;background:#e6e6ff"><b><a href="/wiki/Bosone_(fisica)" title="Bosone (fisica)">Bosoni</a></b></th><td colspan="1"><table class="subnavbox"><tbody><tr><th class="subnavbox_group" style="width:5em;font-weight:normal;width:12%;background:#e6e6ff"><a href="/wiki/Bosone_di_gauge" title="Bosone di gauge">Gauge</a></th><td colspan="1"><a href="/wiki/Fotone" title="Fotone">Fotone</a><b> ·</b> <a href="/wiki/Gluone" title="Gluone">Gluone</a><b> ·</b> <a href="/wiki/Bosoni_W_e_Z" title="Bosoni W e Z">Bosoni W e Z</a></td></tr><tr><th class="subnavbox_group" style="width:5em;font-weight:normal;width:12%;background:#e6e6ff"><a href="/wiki/Bosone_scalare" title="Bosone scalare">Scalari</a></th><td colspan="1"><a href="/wiki/Bosone_di_Higgs" title="Bosone di Higgs">Bosone di Higgs</a></td></tr></tbody></table></td></tr><tr><th class="subnavbox_group" style="width:5em;font-weight:normal; width:9%;background:#e6e6ff"><a href="/wiki/Lista_delle_particelle" class="mw-redirect" title="Lista delle particelle">Ipotetiche</a></th><td colspan="1"><table class="subnavbox"><tbody><tr><th class="subnavbox_group" style="font-weight:normal;width:12%;background:#e6e6ff"><a href="/wiki/Sparticella" title="Sparticella">Sparticelle</a></th><td colspan="1"><table class="subnavbox"><tbody><tr><th class="subnavbox_group" style="font-weight:normal;width:8%;background:#e6e6ff"><a href="/wiki/Gaugino" title="Gaugino">Gaugini</a></th><td colspan="1"><a href="/wiki/Gluino" class="mw-redirect" title="Gluino">Gluino</a><b> ·</b> <a href="/wiki/Gravitino" class="mw-redirect" title="Gravitino">Gravitino</a><b> ·</b> <a href="/wiki/Fotino" class="mw-redirect" title="Fotino">Fotino</a></td></tr><tr><th class="subnavbox_group" style="font-weight:normal;width:8%;background:#e6e6ff">Altre</th><td colspan="1"><a href="/wiki/Axino" title="Axino">Axino</a><b> ·</b> <a href="/wiki/Chargino" title="Chargino">Chargino</a><b> ·</b> <a href="/wiki/Higgsino" class="mw-redirect" title="Higgsino">Higgsino</a><b> ·</b> <a href="/wiki/Neutralino" title="Neutralino">Neutralino</a><b> ·</b> <a href="/wiki/Sfermione" title="Sfermione">Sfermione</a><b> ·</b> <a href="/wiki/Bosino_(particella)" title="Bosino (particella)">Bosino</a></td></tr></tbody></table></td></tr><tr><th class="subnavbox_group" style="font-weight:normal;width:12%;background:#e6e6ff">Altre</th><td colspan="1"><a href="/wiki/Assione" title="Assione">Assione</a><b> ·</b> <a href="/wiki/Dilatone" title="Dilatone">Dilatone</a><b> ·</b> <a href="/wiki/Gravitone" title="Gravitone">Gravitone</a><b> ·</b> <a href="/wiki/Monopolo_magnetico" title="Monopolo magnetico">Monopolo magnetico</a><b> ·</b> <a href="/wiki/Majorone" title="Majorone">Majorone</a><b> ·</b> <a href="/wiki/Tachione" title="Tachione">Tachione</a><b> ·</b> <a href="/wiki/Bosoni_X_e_Y" title="Bosoni X e Y">Bosoni X e Y</a><b> ·</b> <a href="/wiki/Bosoni_W%27_e_Z%27" title="Bosoni W' e Z'">bosoni W' e Z'</a><b> ·</b> <a href="/wiki/Neutrino_sterile" title="Neutrino sterile">Neutrino sterile</a><b> ·</b> <a href="/wiki/Preone_(fisica)" title="Preone (fisica)">Preone</a><b> ·</b> <a href="/wiki/Fermione_di_Majorana" title="Fermione di Majorana">Fermione di Majorana</a></td></tr></tbody></table></td></tr><tr><th class="subnavbox_group" style="width:5em;font-weight:normal; width:9%;background:#e6e6ff"><b>Altre</b></th><td colspan="1"><a href="/wiki/Ghost_di_Faddeev-Popov" title="Ghost di Faddeev-Popov">Ghost di Faddeev-Popov</a></td></tr></tbody></table></td><td rowspan="3" class="navbox_image"><span typeof="mw:File"><a href="/wiki/File:Modello_Standard_delle_Particelle_Elementari.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Modello_Standard_delle_Particelle_Elementari.svg/400px-Modello_Standard_delle_Particelle_Elementari.svg.png" decoding="async" width="400" height="383" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Modello_Standard_delle_Particelle_Elementari.svg/600px-Modello_Standard_delle_Particelle_Elementari.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/Modello_Standard_delle_Particelle_Elementari.svg/800px-Modello_Standard_delle_Particelle_Elementari.svg.png 2x" data-file-width="1390" data-file-height="1330" /></a></span></td></tr><tr><th colspan="1" class="navbox_group" style="width:5em;font-weight:normal; width:10%"><b><a href="/wiki/Stato_legato" class="mw-redirect" title="Stato legato">Composte</a></b></th><td colspan="1" class="navbox_list navbox_even" style="background:transparent"><table class="subnavbox"><tbody><tr><th class="subnavbox_group" style="width:5em;font-weight:normal; width:9%;background:#e6e6ff"><b><a href="/wiki/Adrone" title="Adrone">Adroni</a></b></th><td colspan="1"><table class="subnavbox"><tbody><tr><th class="subnavbox_group" style="width:5em;font-weight:normal; width:12%;background:#e6e6ff"><a href="/wiki/Barione" title="Barione">Barioni</a>/ <a href="/wiki/Iperone_(fisica)" title="Iperone (fisica)">iperoni</a></th><td colspan="1"><a href="/wiki/Nucleone" title="Nucleone">Nucleone</a> (<a href="/wiki/Protone" title="Protone">Protone</a><b> ·</b> <a href="/wiki/Neutrone" title="Neutrone">Neutrone</a>)<b> ·</b> <a href="/wiki/Barione_delta" title="Barione delta">Barione delta</a><b> ·</b> <a href="/wiki/Barione_lambda" title="Barione lambda">Barione lambda</a><b> ·</b> <a href="/wiki/Barione_sigma" title="Barione sigma">Barione sigma</a><b> ·</b> <a href="/wiki/Barione_Xi" title="Barione Xi">Barione Xi</a><b> ·</b> <a href="/wiki/Barione_omega" title="Barione omega">Barione omega</a></td></tr><tr><th class="subnavbox_group" style="width:5em;font-weight:normal; width:12%;background:#e6e6ff"><a href="/wiki/Mesone" title="Mesone">Mesoni</a>/ <a href="/wiki/Quarkonio" title="Quarkonio">quarkoni</a></th><td colspan="1"><a href="/wiki/Pione" title="Pione">Pione</a><b> ·</b> <a href="/wiki/Mesone_rho" title="Mesone rho">Mesone rho</a><b> ·</b> <a href="/wiki/Mesone_eta" title="Mesone eta">Mesoni eta e eta primo</a><b> ·</b> <a href="/wiki/Mesone_phi" title="Mesone phi">Mesone phi</a><b> ·</b> <a href="/wiki/Mesone_omega" title="Mesone omega">Mesone omega</a><b> ·</b> <a href="/wiki/Mesone_J/Psi" title="Mesone J/Psi">Mesone J/Psi</a><b> ·</b> <a href="/wiki/Mesone_upsilon" title="Mesone upsilon">Mesone upsilon</a><b> ·</b> <a href="/wiki/Kaone" title="Kaone">Kaone</a><b> ·</b> <a href="/wiki/Mesone_B" title="Mesone B">Mesone B</a><b> ·</b> <a href="/wiki/Mesone_D" title="Mesone D">Mesone D</a></td></tr><tr><th class="subnavbox_group" style="width:5em;font-weight:normal; width:12%;background:#e6e6ff"><a href="/wiki/Adrone_esotico" title="Adrone esotico">Adroni esotici</a></th><td colspan="1"><a href="/wiki/Tetraquark" title="Tetraquark">Tetraquark</a><b> ·</b> <a href="/wiki/Pentaquark" title="Pentaquark">Pentaquark</a></td></tr></tbody></table></td></tr><tr><th class="subnavbox_group" style="width:5em;font-weight:normal; width:9%;background:#e6e6ff"><a href="/wiki/Categoria:Particelle_composte_ipotetiche" title="Categoria:Particelle composte ipotetiche">Ipotetiche</a></th><td colspan="1"><table class="subnavbox"><tbody><tr><th class="subnavbox_group" style="font-weight:normal; width:12%;background:#e6e6ff"><a href="/wiki/Barione_esotico" title="Barione esotico">Barioni esotici</a></th><td colspan="1"><a href="/wiki/Esaquark" title="Esaquark">Esaquark</a></td></tr><tr><th class="subnavbox_group" style="font-weight:normal; width:12%;background:#e6e6ff"><a href="/wiki/Mesone_esotico" title="Mesone esotico">Mesoni esotici</a></th><td colspan="1"><a href="/wiki/Glueball" title="Glueball">Glueball</a> (<a href="/w/index.php?title=Odderone&action=edit&redlink=1" class="new" title="Odderone (la pagina non esiste)">Odderone</a>)<b> ·</b> <a href="/wiki/Mesone_theta" title="Mesone theta">Mesone theta</a><b> ·</b> <a href="/wiki/Mesone_T" title="Mesone T">Mesone T</a></td></tr><tr><th class="subnavbox_group" style="font-weight:normal; width:12%;background:#e6e6ff">Altre</th><td colspan="1"><a href="/wiki/Molecola_mesonica" title="Molecola mesonica">Molecola mesonica</a><b> ·</b> <a href="/wiki/Pomerone" title="Pomerone">Pomerone</a></td></tr></tbody></table></td></tr><tr><th class="subnavbox_group" style="width:5em;font-weight:normal; width:9%;background:#e6e6ff"><b>Altre</b></th><td colspan="1"><a href="/wiki/Nucleo_atomico" title="Nucleo atomico">Nuclei atomici</a><b> ·</b> <a href="/wiki/Atomo" title="Atomo">Atomi</a><b> ·</b> <a href="/wiki/Atomo_esotico" title="Atomo esotico">Atomi esotici</a> (<a href="/wiki/Positronio" title="Positronio">Positronio</a><b> ·</b> <a href="/wiki/Muonio_(fisica)" title="Muonio (fisica)">Muonio</a><b> ·</b> <a href="/wiki/Tauonio" class="mw-redirect" title="Tauonio">Tauonio</a><b> ·</b> <a href="/wiki/Pionio" title="Pionio">Pionio</a>)<b> ·</b> <a href="/wiki/Atomolecola" title="Atomolecola">Atomolecole</a><b> ·</b> <a href="/wiki/Molecola" title="Molecola">Molecole</a><b> ·</b> <a href="/wiki/Superatomo" title="Superatomo">Superatomo</a></td></tr></tbody></table></td></tr><tr><th colspan="1" class="navbox_group" style="width:5em;font-weight:normal; width:10%"><b><a href="/wiki/Quasiparticella" title="Quasiparticella">Quasiparticelle</a></b></th><td colspan="1" class="navbox_list navbox_odd" style="background:transparent"><a href="/wiki/Droplettone" title="Droplettone">Droplettone</a><b> ·</b> <a href="/wiki/Eccitone" title="Eccitone">Eccitone</a><b> ·</b> <a href="/wiki/Fasone" title="Fasone">Fasone</a><b> ·</b> <a href="/w/index.php?title=Frattone_(particella)&action=edit&redlink=1" class="new" title="Frattone (particella) (la pagina non esiste)">Frattone</a><b> ·</b> <a href="/wiki/Fonone" title="Fonone">Fonone</a><b> ·</b> <a href="/wiki/Lacuna_(fisica)" title="Lacuna (fisica)">Lacuna</a><b> ·</b> <a href="/wiki/Levitone" title="Levitone">Levitone</a><b> ·</b> <a href="/wiki/Magnone_(fisica)" title="Magnone (fisica)">Magnone</a><b> ·</b> <a href="/w/index.php?title=Plasmarone&action=edit&redlink=1" class="new" title="Plasmarone (la pagina non esiste)">Plasmarone</a><b> ·</b> <a href="/wiki/Plasmone" title="Plasmone">Plasmone</a><b> ·</b> <a href="/wiki/Polaritone" title="Polaritone">Polaritone</a><b> ·</b> <a href="/wiki/Polarone" title="Polarone">Polarone</a><b> ·</b> <a href="/wiki/Qualunquone" title="Qualunquone">Qualunquone</a><b> ·</b> <a href="/wiki/Rotone" title="Rotone">Rotone</a><b> ·</b> <a href="/wiki/Skyrmione" title="Skyrmione">Skyrmione</a><b> ·</b> <a href="/wiki/Skyrmione_magnetico" title="Skyrmione magnetico">Skyrmione magnetico</a><b> ·</b> <a href="/wiki/Solitone" title="Solitone">Solitone</a><b> ·</b> <a class="mw-selflink selflink">Solitone di Davydov</a><b> ·</b> <a href="/wiki/Spinone_(fisica)" title="Spinone (fisica)">Spinone</a><b> ·</b> <a href="/wiki/Topolaritone" title="Topolaritone">Topolaritone</a></td></tr><tr><th colspan="3" class="navbox_abovebelow"><a href="/wiki/Cronologia_della_scoperta_delle_particelle" title="Cronologia della scoperta delle particelle">Cronologia della scoperta delle particelle</a></th></tr></tbody></table> <div class="noprint" style="width:100%; 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Solitone di Davydov - Wikipedia