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href="https://en.wikipedia.org/wiki/Wigner_crystal" title="Wigner crystal - inglese" lang="en" hreflang="en" data-title="Wigner crystal" data-language-autonym="English" data-language-local-name="inglese" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Cristal_de_Wigner" title="Cristal de Wigner - francese" lang="fr" hreflang="fr" data-title="Cristal de Wigner" data-language-autonym="Français" data-language-local-name="francese" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A6%E3%82%A3%E3%82%B0%E3%83%8A%E3%83%BC%E7%B5%90%E6%99%B6" title="ウィグナー結晶 - giapponese" lang="ja" hreflang="ja" data-title="ウィグナー結晶" data-language-autonym="日本語" data-language-local-name="giapponese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link 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typeof="mw:File/Thumb"><a href="/wiki/File:Wigner_cluster_600.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Wigner_cluster_600.png/220px-Wigner_cluster_600.png" decoding="async" width="220" height="206" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Wigner_cluster_600.png/330px-Wigner_cluster_600.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Wigner_cluster_600.png/440px-Wigner_cluster_600.png 2x" data-file-width="635" data-file-height="595" /></a><figcaption>Struttura di un cristallo bidimensionale di Wigner in una trappola con potenziale parabolico con 600 elettroni. I triangoli e i quadrati segnano le posizioni dei difetti topologici</figcaption></figure> <p>Il <b>cristallo di Wigner</b> è uno <a href="/wiki/Stato_della_materia" title="Stato della materia">stato della materia</a> teorizzato dal fisico ungherese <a href="/wiki/Eugene_Paul_Wigner" class="mw-redirect" title="Eugene Paul Wigner">Eugene Paul Wigner</a> nel 1934<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> e realizzato per la prima volta in un esperimento presso il <a href="/wiki/Politecnico_federale_di_Zurigo" title="Politecnico federale di Zurigo">Politecnico federale di Zurigo</a> il 30 giugno 2021<sup id="cite_ref-:0_2-0" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>. L'articolo originale di Wigner (che però contiene un errore) predice l'esistenza di uno stato in cui gli <a href="/wiki/Elettrone" title="Elettrone">elettroni</a> di una sostanza si localizzano attorno ai punti di un <a href="/wiki/Reticolo_cristallino" class="mw-redirect" title="Reticolo cristallino">reticolo</a>. Si tratta quindi di un modello di cristallo elettronico. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Descrizione">Descrizione</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cristallo_di_Wigner&veaction=edit&section=1" title="Modifica la sezione Descrizione" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cristallo_di_Wigner&action=edit&section=1" title="Edit section's source code: Descrizione"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La descrizione teorica del cristallo di Wigner si basa su un'approssimazione, talvolta usata in <a href="/wiki/Fisica_dello_stato_solido" title="Fisica dello stato solido">fisica dello stato solido</a>, detta <i><a href="/w/index.php?title=Jellium&action=edit&redlink=1" class="new" title="Jellium (la pagina non esiste)">jellium</a></i>: un gas omogeneo di elettroni immerso in un continuo di carica positiva che ha densità di carica esattamente uguale a quella media degli elettroni, così da garantire la neutralità del sistema. L'<a href="/wiki/Metodo_di_Hartree-Fock" title="Metodo di Hartree-Fock">approssimazione di Hartree-Fock</a> è uno strumento oggigiorno superato, ma comunque utile per capire, almeno qualitativamente e coerentemente con la <a href="/wiki/Teoria_delle_perturbazioni" class="mw-redirect" title="Teoria delle perturbazioni">teoria delle perturbazioni</a> al primo ordine, il comportamento di questo gas di elettroni. In particolare questo approccio variazionale consente una deduzione teorica abbastanza precisa per le energie di coesione dei <a href="/wiki/Metalli_alcalini" title="Metalli alcalini">metalli alcalini</a>: il continuo positivo è infatti un'approssimazione non troppo forzata solo nel caso in cui gli ioni del reticolo cristallino presentino struttura elettronica a shell chiuse, come nel caso alcalino. Tutto questo vale per densità di elettroni tipiche dei metalli. </p><p>Per densità più basse si evince, sempre grazie a questa modellizzazione, che il modo per minimizzare l'energia del sistema è quello di polarizzare gli <a href="/wiki/Spin" title="Spin">spin</a> degli elettroni e di localizzarli: l'energia di ogni singolo elettrone è quindi quella dello <a href="/wiki/Stato_fondamentale" title="Stato fondamentale">stato fondamentale</a> di un <a href="/wiki/Oscillatore_armonico_quantistico" title="Oscillatore armonico quantistico">oscillatore armonico quantistico</a> (che ben descrive il moto di oscillazione attorno al sito del reticolo elettronico) più quella dovuta al potenziale mutuo di interazione (minimizzata invece dalla conveniente scelta geometrica del reticolo). </p><p>Mentre il lavoro di Wigner si basava su un calcolo essenzialmente di <a href="/wiki/Elettrostatica" title="Elettrostatica">elettrostatica</a>, l'approccio moderno si basa su metodi computazionali di tipo <a href="/wiki/Metodo_Monte_Carlo" title="Metodo Monte Carlo">Monte Carlo</a> o RPA (<i><a href="/w/index.php?title=Random_phase_approximation&action=edit&redlink=1" class="new" title="Random phase approximation (la pagina non esiste)">random phase approximation</a></i>) e recenti sviluppi sperimentali (che hanno portato ad un'evidenza della localizzazione di elettroni sulla superficie di gocce di <a href="/wiki/Elio" title="Elio">elio</a> liquido) hanno ultimamente ridestato l'interesse per questo inusuale stato della materia. </p><p>Nel <a href="/wiki/2013" title="2013">2013</a> è stato realizzato in laboratorio un cristallo di Wigner di cui si è avuto una conferma indiretta<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>. </p><p>Nel 2021 i ricercati dell'<a href="/wiki/Politecnico_federale_di_Zurigo" title="Politecnico federale di Zurigo">ETH</a> di <a href="/wiki/Zurigo" title="Zurigo">Zurigo</a> hanno avuto la prova diretta della realizzazione del cristallo usando un <a href="/wiki/Semiconduttore" title="Semiconduttore">semiconduttore</a> di <a href="/w/index.php?title=Diseleniuro_di_molibdeno&action=edit&redlink=1" class="new" title="Diseleniuro di molibdeno (la pagina non esiste)">diseleniuro di molibdeno</a> portato a temperature vicino a 0 K<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:0_2-1" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>. </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=Cristallo_di_Wigner&veaction=edit&section=2" 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=Cristallo_di_Wigner&action=edit&section=2" 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-1"><a href="#cite_ref-1"><b>^</b></a> <span class="reference-text"><cite class="citation pubblicazione" style="font-style:normal"> E. Wigner, <a rel="nofollow" class="external text" href="https://oadoi.org/10.1103/PhysRev.46.1002"><span style="font-style:italic;">On the Interaction of Electrons in Metals</span></a>, in <span style="font-style:italic;"><a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a></span>, vol. 46, 1934, p. 1002, <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>:<a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1934PhRv...46.1002W">1934PhRv...46.1002W</a>, <a href="/wiki/Digital_object_identifier" title="Digital object identifier">DOI</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1103%2FPhysRev.46.1002">10.1103/PhysRev.46.1002</a>.</cite></span> </li> <li id="cite_note-:0-2"><span class="mw-cite-backlink"><b>^</b> <sup><i><a href="#cite_ref-:0_2-0">a</a></i></sup> <sup><i><a href="#cite_ref-:0_2-1">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>) Tomasz Smoleński, Pavel E. Dolgirev e Clemens Kuhlenkamp, <a rel="nofollow" class="external text" href="http://www.nature.com/articles/s41586-021-03590-4"><span style="font-style:italic;">Signatures of Wigner crystal of electrons in a monolayer semiconductor</span></a>, in <span style="font-style:italic;">Nature</span>, vol. 595, n. 7865, 1º luglio 2021, pp. 53–57, <a href="/wiki/Digital_object_identifier" title="Digital object identifier">DOI</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1038%2Fs41586-021-03590-4">10.1038/s41586-021-03590-4</a>. <small>URL consultato l'8 giugno 2022</small>.</cite></span> </li> <li id="cite_note-3"><a href="#cite_ref-3"><b>^</b></a> <span class="reference-text"><cite class="citation pubblicazione" style="font-style:normal"> S. Pecker, <a rel="nofollow" class="external text" href="https://oadoi.org/10.1038/nphys2692"><span style="font-style:italic;">Observation and spectroscopy of a two-electron Wigner molecule in an ultraclean carbon nanotube</span></a>, in <span style="font-style:italic;"><a href="/wiki/Nature_Physics" title="Nature Physics">Nature Physics</a></span>, vol. 9, 2013, p. 576, <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>:<a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1934PhRv...46.1002W">1934PhRv...46.1002W</a>, <a href="/wiki/Digital_object_identifier" title="Digital object identifier">DOI</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1038%2Fnphys2692">10.1038/nphys2692</a>.</cite></span> </li> <li id="cite_note-4"><a href="#cite_ref-4"><b>^</b></a> <span class="reference-text"><cite class="citation news" style="font-style:normal"> <a rel="nofollow" class="external text" href="https://www.hwupgrade.it/news/scienza-tecnologia/cristalli-di-soli-elettroni-osservati-per-la-prima-volta-i-cristalli-di-wigner-teorizzati-nel-1934_99003.html"><span style="font-style:italic;">Cristalli di soli elettroni: osservati per la prima volta i cristalli di Wigner, teorizzati nel 1934</span></a>, in <span style="font-style:italic;">hwupgrade.it</span>, 6 luglio 2021. <small>URL consultato il 6 luglio 2021</small>.</cite></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cristallo_di_Wigner&veaction=edit&section=3" title="Modifica la sezione Bibliografia" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cristallo_di_Wigner&action=edit&section=3" title="Edit section's source code: Bibliografia"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="citation libro" style="font-style:normal"> G.D. Mahan, <a rel="nofollow" class="external text" href="https://archive.org/details/manyparticlephys0000maha_r7o3"><span style="font-style:italic;">Many-particle physics</span></a>, 3. ed, Kluwer/Plenum Publishers, 2000, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Speciale:RicercaISBN/0-306-46338-5" title="Speciale:RicercaISBN/0-306-46338-5">0-306-46338-5</a>.</cite></li></ul> <div class="mw-heading mw-heading2"><h2 id="Voci_correlate">Voci correlate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cristallo_di_Wigner&veaction=edit&section=4" title="Modifica la sezione Voci correlate" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cristallo_di_Wigner&action=edit&section=4" title="Edit section's source code: Voci correlate"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Gas_di_Fermi" title="Gas di Fermi">Gas di Fermi</a></li></ul> <div class="noprint" style="width:100%; padding: 3px 0; display: flex; flex-wrap: wrap; row-gap: 4px; column-gap: 8px; box-sizing: border-box;"><div style="flex-grow: 1"><style data-mw-deduplicate="TemplateStyles:r140555418">.mw-parser-output .itwiki-template-occhiello{width:100%;line-height:25px;border:1px solid #CCF;background-color:#F0EEFF;box-sizing:border-box}.mw-parser-output .itwiki-template-occhiello-progetto{background-color:#FAFAFA}@media screen{html.skin-theme-clientpref-night .mw-parser-output .itwiki-template-occhiello{background-color:#202122;border-color:#54595D}html.skin-theme-clientpref-night .mw-parser-output .itwiki-template-occhiello-progetto{background-color:#282929}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .itwiki-template-occhiello{background-color:#202122;border-color:#54595D}html.skin-theme-clientpref-os .mw-parser-output .itwiki-template-occhiello-progetto{background-color:#282929}}</style><div class="itwiki-template-occhiello"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_katomic.svg" class="mw-file-description" title="Fisica"><img alt=" " src="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Nuvola_apps_katomic.svg/25px-Nuvola_apps_katomic.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Nuvola_apps_katomic.svg/38px-Nuvola_apps_katomic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/55/Nuvola_apps_katomic.svg/50px-Nuvola_apps_katomic.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> <b><a href="/wiki/Portale:Fisica" title="Portale:Fisica">Portale Fisica</a></b>: accedi alle voci di Wikipedia che trattano di fisica</div></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Estratto da "<a dir="ltr" href="https://it.wikipedia.org/w/index.php?title=Cristallo_di_Wigner&oldid=137336131">https://it.wikipedia.org/w/index.php?title=Cristallo_di_Wigner&oldid=137336131</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Categoria:Categorie" title="Categoria:Categorie">Categoria</a>: <ul><li><a href="/wiki/Categoria:Fisica_dello_stato_solido" title="Categoria:Fisica dello stato solido">Fisica dello stato solido</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Categoria nascosta: <ul><li><a href="/wiki/Categoria:Voci_con_modulo_citazione_e_parametro_pagina" title="Categoria:Voci con modulo citazione e parametro pagina">Voci con modulo citazione e parametro pagina</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Questa pagina è stata modificata per l'ultima volta il 14 gen 2024 alle 05:03.</li> <li id="footer-info-copyright">Il testo è disponibile secondo la <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.it">licenza Creative Commons Attribuzione-Condividi allo stesso modo</a>; possono applicarsi condizioni ulteriori. 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