Document Zbl 07783771

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Document Zbl 07783771 - zbMATH Open</title> <meta name="viewport" content="width=device-width, minimum-scale=0.1, maximum-scale=5.0"> <meta name="robots" content="noarchive, noindex"> <meta name="referrer" content="origin-when-cross-origin"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap-theme.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.css" rel="stylesheet" media="screen,print"> <link rel="stylesheet" href="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/css/bootstrap-select.min.css"> <link href="/static/css/smoothness/jquery-ui-1.10.1.custom.min.css" rel="stylesheet" media="screen"> <link href="/static/styles.css?v=20241024" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/zbMathJax/v0.1.38/zbmathjax.css" rel="stylesheet" media="screen,print"> <link rel="shortcut icon" href="/static/zbmath.ico"> <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "Organization", "url": "https://zbmath.org/", "logo": "https://zbmath.org/static/zbMATH.png" } </script> </head> <body> <div id="line"></div> <span id="clear" style="cursor: pointer;">×</span> <div id="page"> <div id="head"> <nav id="menu" class="navbar navbar-default"> <div class="container-fluid"> <div class="navbar-header"> <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#zbnav" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button> <a class="navbar-brand" href="#"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open logo"> </a> </div> <div id="zbnav" class="collapse navbar-collapse"> <ul class="nav navbar-nav pages"> <li class="about"> <a href="/about/">About</a> </li> <li class="frequently-asked-questions"> <a href="/frequently-asked-questions/">FAQ</a> </li> <li class="general-help"> <a href="/general-help/">General Help</a> </li> <li class="reviewer-service"> <a href="https://zbmath.org/reviewer-service/" target="_self" >Reviewer Service</a> </li> <li> <a href="/tools-and-resources/">Tools & Resources</a> </li> <li class="contact"> <a href="/contact/">Contact</a> </li> </ul> <ul class="nav navbar-nav navbar-right prefs"> <li class="preferences dropdown"> <a data-toggle="dropdown" href="#">Preferences <i class="caret"></i></a> <ul class="dropdown-menu preferences"> <li> <form id="preferences" class="navbar-form" method="post" action="/preferences/" onsubmit="return confirm('This website uses cookies for the purposes of storing preference information on your device. Do you agree to this?\n\nPlease refer to our Privacy Policy to learn more about our use of cookies.')" > <input type="hidden" name="path" value="/7783771?"> <span class=""> <label class="title">Search Form</label> <div class="form-group"> <input id="search-multi-line" type="radio" name="search" value="multi-line" checked> <label for="search-multi-line" class="radio">Multi-Line Search (default)</label> </div> <div class="form-group"> <input id="search-one-line" type="radio" name="search" value="one-line"> <label for="search-one-line" class="radio">One-Line Search</label> </div> </span> <span class="count"> <label class="title">Hits per Page</label> <div class="form-group"> <input id="count-10" type="radio" name="count" value="10"> <label for="count-10" class="radio">10</label> </div> <div class="form-group"> <input id="count-20" type="radio" name="count" value="20"> <label for="count-20" class="radio">20</label> </div> <div class="form-group"> <input id="count-50" type="radio" name="count" value="50"> <label for="count-50" class="radio">50</label> </div> <div class="form-group"> <input id="count-100" type="radio" name="count" value="100" checked> <label for="count-100" class="radio">100 (default)</label> </div> <div class="form-group"> <input id="count-200" type="radio" name="count" value="200"> <label for="count-200" class="radio">200</label> </div> </span> <span class="format"> <label class="title">Display Format</label> <div class="form-group"> <input id="format-mathjax" type="radio" name="format" value="mathjax" checked> <label for="format-mathjax" class="radio">MathJax (default)</label> </div> <div class="form-group"> <input id="format-amstex" type="radio" name="format" value="latex"> <label for="format-amstex" class="radio">LaTeX</label> </div> </span> <span class="ranking"> <label class="title">Documents Sorting</label> <div class="form-group"> <input id="documents-ranking-default" type="radio" name="documents_ranking" value="date" checked> <label for="documents-ranking-default" class="radio">Newest first (default)</label> </div> <div class="form-group"> <input id="documents-ranking-references" type="radio" name="documents_ranking" value="references"> <label for="documents-ranking-references" class="radio">Citations</label> </div> <div class="form-group"> <input id="documents-ranking-relevance" type="radio" name="documents_ranking" value="relevance"> <label for="documents-ranking-relevance" class="radio">Relevance</label> </div> </span> <span class="ranking"> <label class="title">Authors Sorting</label> <div class="form-group"> <input id="authors-ranking-default" type="radio" name="authors_ranking" value="alpha" checked> <label for="authors-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="authors-ranking-references" type="radio" name="authors_ranking" value="references"> <label for="authors-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Serials Sorting</label> <div class="form-group"> <input id="serials-ranking-default" type="radio" name="serials_ranking" value="alpha" checked> <label for="serials-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="serials-ranking-references" type="radio" name="serials_ranking" value="references"> <label for="serials-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Software Sorting</label> <div class="form-group"> <input id="software-ranking-default" type="radio" name="software_ranking" value="references" checked> <label for="software-ranking-default" class="radio">Citations (default)</label> </div> <div class="form-group"> <input id="software-ranking-alpha" type="radio" name="software_ranking" value="alpha"> <label for="software-ranking-alpha" class="radio">Alphabetically</label> </div> </span> <button type="submit" class="btn btn-default">OK</button> <div class="clearfix"> </form> </li> </ul> </li> </ul> </div> </div> </nav> <div id="tabs"> <h1 class="logo"> <a class="logo" href="/"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open — the first resource for mathematics" > </a> </h1> <nav> <ul class="nav nav-tabs"> <li class="tab-documents active"> <a href="/">Documents</a> </li> <li class="tab-authors"> <a href="/authors/">Authors</a> </li> <li class="tab-serials"> <a href="/serials/">Serials</a> </li> <li class="tab-software"> <a href="/software/">Software</a> </li> <li class="tab-classification"> <a href="/classification/">Classification</a> </li> <li class="tab-formulae"> <a href="/formulae/">Formulæ</a> </li> </ul> </nav> <div class="clearfix"></div> </div> <div class="content-fixed"> <div class="content-formular"> <div style="display: none;"> <div class="row ml-0"id="multi-line-new-line" style="display: none;"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-0-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-0-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input"> <span class="multi-line-value" id="multi-line-type-range"><span style="padding-left: 5px;">from</span> <input name="ml-0-v1" class="form-control multi-line-input" type="text" value="" aria-label="value"> until <input name="ml-0-v2" class="form-control multi-line-input" type="text" value="" aria-label="value"></span> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-la" placeholder="use name or ISO code"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-rv" placeholder="enter name or zbMATH reviewer number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-an" placeholder="Zbl, JFM or ERAM number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-en" placeholder="e.g. DOI, ISBN, arXiv ID"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-sw" placeholder="use * to find all documents using software"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-br" placeholder="find documents about the life or work of a person"> <span class="multi-line-value" id="multi-line-type-multiselect-db"> <select class="multi-line-selectpicker" data-width="100%" multiple> <option value="zbl">Zbl</option> <option value="arxiv">arXiv</option> <option value="jfm">JFM</option> <option value="eram">ERAM</option> </select> <input type="hidden" class="multi-line-input" name="ml-0-v" value=""> </span> </div> <form name="documents" method="GET" action="/" autocomplete="off"> <div class="documents multi-line" style="display: none;"> <div class="forms"> <ul class="nav forms"> <li class="one-line"> <span tabindex="0" class="glyphicon glyphicon-question-sign" title="One-Line Search allows for free logical combinations of search fields" aria-label="One-Line Search allows for free logical combinations of search fields" data-placement="bottom"></span> <a style="display: inline-block;" href="#">One-Line Search <span class="glyphicon glyphicon-search"></span></a> </li> </ul> </div> <div class="clearfix"></div> <div class="container-fluid"> <input type="hidden" id="multi-line-ml" name="ml" value="3"> <div id="multi-line-row-wrapper"> <div class="row ml-1"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-1-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-1-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-1-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-2"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-2-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au" selected>Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-2-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-2-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-3"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-3-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti" selected>Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-3-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><div id="multi-line-plus"> <a href="#"><span class="glyphicon glyphicon-plus" aria-hidden="true"></span> add line</a> </div></div> </div> </div> <div class="row"> <div class="col-xs-12 form-inline"> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-test" style="visibility: hidden; position: fixed;"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label title="search for Articles in Journals"> <input type="checkbox" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label title="search for arXiv Preprints"> <input type="checkbox" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-real"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label for="dt-j" title="search for Articles in Journals"> <input type="checkbox" id="dt-j" name="dt" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label for="dt-a" title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" id="dt-a" name="dt" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label for="dt-b" title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" id="dt-b" name="dt" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label for="dt-p" title="search for arXiv Preprints"> <input type="checkbox" id="dt-p" name="dt" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> </div> </div> <div class="row"> <div class="col-xs-12 buttons"> <a tabindex="0" class="btn btn-default clear-all">Reset all <span class="glyphicon glyphicon-remove"></span></a> <div class="submit"> <button class="btn btn-default search" type="submit">Search <span class="glyphicon glyphicon-search"></span></button> </div> </div> </div> </div> </div> </form> <form class="form-inline" name="documents" method="GET" action="/"> <div class="documents one-line" style="display: block;"> <div class="forms"> <ul class="nav forms"> <li class="multi-line"><a href="#">New Multi-Line Search <span class="glyphicon glyphicon-list"></span></a></li> </ul> </div> <div id="search-row" class="input-group box"> <span> <div id="search-field"> <input class="query form-control" type="text" name="q" value="an:7783771" aria-label="Search for documents" placeholder="Search for documents" autocomplete="off"> </div> <div class="search-buttons input-group-btn"> <div class="btn-group"> <button class="btn btn-default search" type="submit"><span class="virtual">Search</span> <span class="glyphicon glyphicon-search" style="top: 2px;"></span></button> </div> </div> </span> <span> <div class="search-buttons input-group-btn"> <div class="btn-group"> <div class="btn-group fields"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Fields <i class="caret"></i></button> <ul id="fields" class="dropdown-menu pull-right"> <li><a href="#"><span class="token item">any:</span><span> </span>anywhere (default)</a></li> <li><a href="#"><span class="token item">ab:</span><span>  </span>review text</a></li> <li><a href="#"><span class="token item">an:</span><span>  </span>zbmath id</a></li> <li><a href="#"><span class="token item">any:</span><span>  </span>anywhere</a></li> <li><a href="#"><span class="token item">au:</span><span>  </span>contributor name</a></li> <li><a href="#"><span class="token item">br:</span><span>  </span>biographic reference name</a></li> <li><a href="#"><span class="token item">cc:</span><span>  </span>msc title</a></li> <li><a href="#"><span class="token item">dt:</span><span>  </span>document type</a></li> <li><a href="#"><span class="token item">doi:</span><span>  </span>doi</a></li> <li><a href="#"><span class="token item">en:</span><span>  </span>external id</a></li> <li><a href="#"><span class="token item">la:</span><span>  </span>language</a></li> <li><a href="#"><span class="token item">pu:</span><span>  </span>publisher</a></li> <li><a href="#"><span class="token item">py:</span><span>  </span>year</a></li> <li><a href="#"><span class="token item">rv:</span><span>  </span>reviewer name</a></li> <li><a href="#"><span class="token item">so:</span><span>  </span>source</a></li> <li><a href="#"><span class="token item">sw:</span><span>  </span>software name</a></li> <li><a href="#"><span class="token item">ti:</span><span>  </span>title</a></li> <li><a href="#"><span class="token item">ut:</span><span>  </span>keyword</a></li> </ul> </div> <div class="btn-group operators"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Operators <i class="caret"></i></button> <ul id="operators" class="dropdown-menu pull-right"> <li><a href="#"><span class="token">a <span class="item">&</span> b </span><span> </span>logical and (default)</a></li> <li><a href="#"><span class="token">a <span class="item">|</span> b </span><span> </span>logical or</a></li> <li><a href="#"><span class="token"><span class="item">!</span>ab   </span><span> </span>logical not</a></li> <li><a href="#"><span class="token">abc<span class="item">*</span>  </span><span> </span>right wildcard</a></li> <li><a href="#"><span class="token"><span class="item">"</span>ab c<span class="item">"</span></span><span> </span>phrase</a></li> <li><a href="#"><span class="token"><span class="item">(</span>ab c<span class="item">)</span></span><span> </span>parentheses</a></li> </ul> </div> </div> </div> <div class="special"> <ul class="nav help-button"> <li class="dropdown pull-right"> <a href="#">Help <i class="caret"></i></a> </li> </ul> </div> </span> </div> <div class="help"><h2>Examples</h2> <div id="help-terms" role="table"> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Geometry">Geometry</a></span> <span class="search-explanation" role="cell" role="cell">Search for the term <em>Geometry</em> in <strong>any</strong> field. Queries are <strong>case-independent</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Funct%2A">Funct*</a></span> <span class="search-explanation" role="cell"><strong>Wildcard</strong> queries are specified by <strong><u>*</u></strong> (e.g. <em>functions</em>, <em>functorial</em>, etc.). Otherwise the search is <strong>exact</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Topological+group%22">"Topological group"</a></span> <span class="search-explanation" role="cell"><strong>Phrases</strong> (multi-words) should be set in <u>"</u>straight quotation marks<u>"</u>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=au%3A+Bourbaki+%26+ti%3A+Algebra">au: Bourbaki & ti: Algebra</a></span> <span class="search-explanation" role="cell">Search for <strong><u>au</u>thor</strong> and <strong><u>ti</u>tle</strong>. The <strong>and-operator &</strong> is default and can be omitted.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Chebyshev+%7C+Tschebyscheff">Chebyshev | Tschebyscheff</a></span> <span class="search-explanation" role="cell">The <strong>or-operator |</strong> allows to search for <em>Chebyshev</em> or <em>Tschebyscheff</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Quasi%2A+map%2A+py%3A+1989">Quasi* map* py: 1989</a></span> <span class="search-explanation" role="cell">The resulting documents have <strong><u>p</u>ublication <u>y</u>ear</strong> <em>1989</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=so%3A+Eur%2A+J%2A+Mat%2A+Soc%2A+cc%3A+14">so: Eur* J* Mat* Soc* cc: 14</a></span> <span class="search-explanation" role="cell">Search for publications in a particular <strong><u>so</u>urce</strong> with a <strong>Mathematics Subject <u>C</u>lassification <u>c</u>ode (<u>cc</u>)</strong> in <em>14</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Partial+diff%2A+eq%2A%22+%21+elliptic">"Partial diff* eq*" ! elliptic</a></span> <span class="search-explanation" role="cell">The <strong>not</strong>-operator <strong>!</strong> eliminates all results containing the word <em>elliptic</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=dt%3A+b+%26+au%3A+Hilbert">dt: b & au: Hilbert</a></span> <span class="search-explanation" role="cell">The <strong><u>d</u>ocument <u>t</u>ype</strong> is set to books; alternatively: <u>j</u> for <strong>journal articles</strong>, <u>a</u> for <strong>book articles</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=py%3A+2000-2015+cc%3A+%2894A+%7C+11T%29">py: 2000-2015 cc: (94A | 11T)</a></span> <span class="search-explanation" role="cell">Number <strong>ranges</strong> are accepted. Terms can be grouped within <strong><u>(</u>parentheses<u>)</u></strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=la%3A+chinese">la: chinese</a></span> <span class="search-explanation" role="cell">Find documents in a given <strong><u>la</u>nguage</strong>. <a href="http://en.wikipedia.org/wiki/ISO_639-1">ISO 639-1</a> language codes can also be used.</span> </div> </div> <div id="help-fields"> <h2>Fields</h2> <table> <tr> <td class="nowrap padding" role="rowheader"><strong>any</strong></td> <td class="padding">anywhere</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>an</strong></td> <td class="padding">internal document identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>au</strong></td> <td class="padding">author, editor</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ai</strong></td> <td class="padding">internal author identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ti</strong></td> <td class="padding">title</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>la</strong></td> <td class="padding">language</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>so</strong></td> <td class="padding">source</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ab</strong></td> <td class="padding">review, abstract</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>py</strong></td> <td class="padding">publication year</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>rv</strong></td> <td class="padding">reviewer</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>cc</strong></td> <td class="padding">MSC code</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ut</strong></td> <td class="padding">uncontrolled term</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>dt</strong></td> <td class="padding" colspan="4">document type (<strong>j</strong>: journal article; <strong>b</strong>: book; <strong>a</strong>: book article)</td> </tr> </table> </div> <div id="help-operators"> <h2>Operators</h2> <table> <tr> <td class="nowrap padding" role="rowheader">a <strong>&</strong> b</td> <td class="padding">logic and</td> </tr> <tr> <td class="nowrap padding" role="rowheader">a <strong>|</strong> b</td> <td class="padding">logic or</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>!</strong>ab</td> <td class="padding">logic not</td> </tr> <tr> <td class="nowrap padding" role="rowheader">abc<strong>*</strong></td> <td class="padding">right wildcard</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>"</strong>ab c<strong>"</strong></td> <td class="padding">phrase</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>(</strong>ab c<strong>)</strong></td> <td class="padding">parentheses</td> </tr> </table> </div> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> <div class="clearfix"></div> </div> <div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="documents"> <div class="content-main"> <div class="content-item"><div class="item"> <article> <div class="author"><a href="/authors/kornilovitch.pavel-e" title="Author Profile">Kornilovitch, Pavel E.</a></div> <h2 class="title"> <strong>Two-particle bound states on a lattice.</strong> <i>(English)</i> <a class="label nowrap" href="/7783771">Zbl 07783771</a> </h2> <div class="source"> <a href="/serials/1548" title="Journal Profile">Ann. Phys.</a> <a href="/?q=in%3A506548" title="Articles in this Issue">460, Article ID 169574, 61 p. (2024)</a>. </div> <div class="abstract">Summary: Two-particle lattice states are important for physics of magnetism, superconducting oxides, and cold quantum gases. The quantum-mechanical lattice problem is exactly solvable for finite-range interaction potentials. A two-body Schrödinder equation can be reduced to a system of linear equations whose numbers scale with the number of interacting sites. For the simplest cases such as on-site or nearest-neighbor attractions, many pair properties can be derived analytically, although final expressions can be quite complicated. In this work, we systematically investigate bound pairs in one-, two-, and three-dimensional lattices. We derive pairing conditions, plot phase diagrams, and compute energies, effective masses and radii. Along the way, we analyze nontrivial physical effects such as light pairs and the dependence of binding thresholds on pair momenta. At the end, we discuss the preformed-pair mechanism of superconductivity and stability of many-pair systems against phase separation. The paper is a combination of original work and pedagogical tutorial.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7783771">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A82-XX" title="MSC2020">82-XX</a> </td> <td class="space"> Statistical mechanics, structure of matter </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A81-XX" title="MSC2020">81-XX</a> </td> <td class="space"> Quantum theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Atwo-particle+states">two-particle states</a>; <a href="/?q=ut%3Abound+states">bound states</a>; <a href="/?q=ut%3Alattice">lattice</a>; <a href="/?q=ut%3Apreformed+pairs">preformed pairs</a>; <a href="/?q=ut%3Asuperconductivity">superconductivity</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 07783771" data-ciurl="/ci/07783771" data-biburl="/bibtex/07783771.bib" data-amsurl="/amsrefs/07783771.bib" data-xmlurl="/xml/07783771.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07783771.pdf" title="Zbl 07783771 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.aop.2023.169574" aria-label="DOI for “Two-particle bound states on a lattice”" title="10.1016/j.aop.2023.169574">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2305.02548"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Mattis, D. C., Rev. Modern Phys., 361-379 (1986)</td> </tr><tr> <td>[2]</td> <td class="space">Mattis, D. C., The Theory of Magnetism (1981), Springer: Springer Berlin</td> </tr><tr> <td>[3]</td> <td class="space">Bednorz, J. G.; Müller, K. A., Z. Phys. B — Condensed Matter, 189-193 (1986)</td> </tr><tr> <td>[4]</td> <td class="space">Worthington, T. K.; Gallagher, W. J.; Dinger, T. R., Phys. Rev. Lett., 1160-1163 (1987)</td> </tr><tr> <td>[5]</td> <td class="space">Uemura, Y. J.; Luke, G. M.; Sternlieb, B. J.; Brewer, J. H.; Carolan, J. F.; Hardy, W. N.; Kadono, R.; Kempton, J. R.; Kiefl, R. F.; Kreitzman, S. R.; Mulhern, P.; Riseman, T. M.; D. Ll. Williams; Yang, B. X.; Uchida, S.; Takagi, H.; Gopalakrishnan, J.; Sleight, A. W.; Subramanian, M. A.; Chien, C. L.; Cieplak, M. Z.; Xiao, Gang.; Lee, V. Y.; Statt, B. W.; Stronach, C. E.; Kossler, W. J.; Yu, X. H., Phys. Rev. Lett., 2317-2320 (1989)</td> </tr><tr> <td>[6]</td> <td class="space">Uemura, Y. J.; Le, L. P.; Luke, G. M.; Sternlieb, B. J.; Wu, W. D.; Brewer, J. H.; Riseman, T. M.; Seaman, C. L.; Maple, M. B.; Ishikawa, M.; Hinks, D. G.; Jorgensen, J. D.; Saito, G.; Yamochi, H., Phys. Rev. Lett., 2665-2668 (1991)</td> </tr><tr> <td>[7]</td> <td class="space">Ogg Jr., R. A., Phys. Rev.. Physical Review, 544-244 (1946)</td> </tr><tr> <td>[8]</td> <td class="space">Schafroth, M. R., Phys. Rev., 1149 (1954)</td> </tr><tr> <td>[9]</td> <td class="space">Schafroth, M. R., Phys. Rev., 1442 (1954)</td> </tr><tr> <td>[10]</td> <td class="space">Schafroth, M. R.; Butler, S. T.; Blatt, J. M., Helv. Phys. Acta, 93-134 (1957)</td> </tr><tr> <td>[11]</td> <td class="space">Micnas, R.; Ranninger, J.; Robaszkiewicz, S., Rev. Modern Phys., 113-171 (1990)</td> </tr><tr> <td>[12]</td> <td class="space">Alexandrov, A. S.; Mott, N. F., Supercond. Sci. Technol., 215-224 (1993)</td> </tr><tr> <td>[13]</td> <td class="space">Alexandrov, A. S.; Mott, N. F., High Temperature Superconductors and Other Superfluids (1994), Taylor & Francis: Taylor & Francis London</td> </tr><tr> <td>[14]</td> <td class="space">Geshkenbein, V. B.; Ioffe, L. B.; Larkin, A. I., Phys. Rev. B, 3173-3180 (1997)</td> </tr><tr> <td>[15]</td> <td class="space">Alexandrov, A. S.; Kabanov, V. V., Phys. Rev. B, 13628-13631 (1999)</td> </tr><tr> <td>[16]</td> <td class="space">Chen, Q.; Stajic, J.; Tan, S.; Levin, K., Phys. Rep., 1 (2005)</td> </tr><tr> <td>[17]</td> <td class="space">Seo, Y. I.; Choi, W. J.; Kimura, Shin-ichi.; Kwon, Y. S., Sci. Rep., 3987 (2019)</td> </tr><tr> <td>[18]</td> <td class="space">Kang, B. L.; Shi, M. Z.; Li, S. J.; Wang, H. H.; Zhang, Q.; Zhao, D.; Li, J.; Song, D. W.; Zheng, L. X.; Nie, L. P.; Wu, T.; Chen, X. H., Phys. Rev. Lett. (2020)</td> </tr><tr> <td>[19]</td> <td class="space">Zhou, Panpan; Chen, Liyang; Liu, Yue; Sochnikov, Ilya; Bollinger, Anthony T.; Han, Myung-Geun; Zhu, Yimei; He, Xi; Bozóvic̆, Ivan; Natelson, Douglas, Nature, 493-496 (2019)</td> </tr><tr> <td>[20]</td> <td class="space">Q. Chen, Z. Wang, R. Boyack, S. Yang, K. Levin, When superconductivity crosses over: From BCS to BEC, arXiv:2208.01774</td> </tr><tr> <td>[21]</td> <td class="space">Alexandrov, A. S., Strong-Coupling Theory of High-TemPerature Superconductivity (2013), Cambridge University Press: Cambridge University Press Cambridge, UK</td> </tr><tr> <td>[22]</td> <td class="space">Mihailovic, D.; Kabanov, V. V., Phys. Rev. B (2001)</td> </tr><tr> <td>[23]</td> <td class="space">Kabanov, V. V.; Mihailovic, D., Phys. Rev. B (2002)</td> </tr><tr> <td>[24]</td> <td class="space">Mihailovic, D.</td> </tr><tr> <td>[25]</td> <td class="space">Scalapino, D. J., Rev. Modern Phys., 1383-1417 (2012)</td> </tr><tr> <td>[26]</td> <td class="space">Callaway, J.; Kanhere, D. G.; Misra, P. K., Phys. Rev. B, 7141-7144 (1987)</td> </tr><tr> <td>[27]</td> <td class="space">Bussmann-Holder, A.; Simon, A.; Büttner, H., Phys. Rev. B, 207-214 (1989)</td> </tr><tr> <td>[28]</td> <td class="space">Berciu, M.; Elfimov, I.; Sawatzky, G. A., Phys. Rev. B (2009)</td> </tr><tr> <td>[29]</td> <td class="space">Y. Yacoby, D. Ceresoli, L. Giordano, Yang Shao Horn, Electronic polarizability induced Cooper-like pairing and energy gap in high-$ T_c$ arXiv:2105.05124</td> </tr><tr> <td>[30]</td> <td class="space">Nozières, P.; Schmitt-Rink, S., J. Low Temp. Phys., 195-211 (1985)</td> </tr><tr> <td>[31]</td> <td class="space">Paiva, Th.; dos Santos, R. R.; Scalettar, R. T.; Denteneer, P. J.H., Phys. Rev. B (2004)</td> </tr><tr> <td>[32]</td> <td class="space">Kornilovitch, P. E.; Hague, J. P., J. Phys.: Condens. Matter (2015)</td> </tr><tr> <td>[33]</td> <td class="space">Emery, V. J.; Kivelson, S. A.; Lin, H. Q., Phys. Rev. Lett., 475-478 (1990)</td> </tr><tr> <td>[34]</td> <td class="space">Dagotto, E.; Riera, J., Phys. Rev. Lett., 682 (1993)</td> </tr><tr> <td>[35]</td> <td class="space">Kornilovitch, P. E., Phys. Rev. B (2023)</td> </tr><tr> <td>[36]</td> <td class="space">Bogoliubov, N. N., 34-41</td> </tr><tr> <td>[37]</td> <td class="space">Bak, M.; Micnas, R., 168-176, arXiv:cond-mat/9909089</td> </tr><tr> <td>[38]</td> <td class="space">Chen, Su-Di; Hashimoto, M.; He, Yu.; Song, D.; Xu, K.-J.; He, J.-F.; Devereaux, T. P.; Eisaki, H.; Lu, D.-H.; Zaanen, J.; Shen, Zhi-Xun, Science, 1099-1102 (2019)</td> </tr><tr> <td>[39]</td> <td class="space">Ivanov, V. A.; Kornilovitch, P. E.; Bobryshev, V. V., Physica C, 2369-2370 (1994)</td> </tr><tr> <td>[40]</td> <td class="space">Zhang, C.; Prokof’ev, N. V.; Svistunov, B. V., Phys. Rev. B (2022)</td> </tr><tr> <td>[41]</td> <td class="space">Micnas, R.; Ranninger, J.; Robaszkiewicz, S., J. Phys. C, L145-L151 (1988)</td> </tr><tr> <td>[42]</td> <td class="space">Micnas, R.; Ranninger, J.; Robaszkiewicz, S.; Tabor, S., Phys. Rev. B, 9410-9422 (1988)</td> </tr><tr> <td>[43]</td> <td class="space">Micnas, R.; Ranninger, J.; Robaszkiewicz, S., Phys. Rev. B, 11653-11662 (1989)</td> </tr><tr> <td>[44]</td> <td class="space">Nayak, S.; Kumar, S., J. Phys.: Condens. Matter (2018)</td> </tr><tr> <td>[45]</td> <td class="space">Boudjada, N.; Buessen, F. L.; Paramekanti, A., Phys. Rev. B (2020)</td> </tr><tr> <td>[46]</td> <td class="space">Kheirkhah, M.; Yan, Z.; Nagai, Y.; Marsiglio, F., Phys. Rev. Lett. (2020)</td> </tr><tr> <td>[47]</td> <td class="space">Jiang, M., Phys. Rev. B (2022)</td> </tr><tr> <td>[48]</td> <td class="space">Zhang, L.; Guo, T.; Mou, Y.; Chen, Q.; Ma, T., Phys. Rev. B (2022)</td> </tr><tr> <td>[49]</td> <td class="space">Qu, D.-W.; Chen, B.-B.; Jiang, H.-C.; Wang, Y.; Li, W., Commun. Phys., 257 (2022)</td> </tr><tr> <td>[50]</td> <td class="space">Singh, D. K.; Kadge, S.; Bang, Y.; Majumdar, P., Phys. Rev. B (2022)</td> </tr><tr> <td>[51]</td> <td class="space">Zhong-Bing Huang, Shi-Chao Fang, Hai-Qing Lin, Superconductivity, nematicity, and charge density wave in high-$ T_c$ arXiv:2109.05519</td> </tr><tr> <td>[52]</td> <td class="space">Chen, Wei-Chih; Wang, Yao; Chen, Cheng-Chien, Phys. Rev. B (2023)</td> </tr><tr> <td>[53]</td> <td class="space">Peng, C.; Wang, Y.; Wen, J.; Lee, Y. S.; Devereaux, T. P.; Jiang, H.-C., Phys. Rev. B (2023)</td> </tr><tr> <td>[54]</td> <td class="space">E. Linnér, C. Dutreix, S. Biermann, E.A. Stepanov, Coexistence of $s$ arXiv:2301.10755</td> </tr><tr> <td>[55]</td> <td class="space">S. dos Anjos Sousa-Júnior, N.C. Costa, R.R. dos Santos, Phase diagram for the extended Hubbard model on a square lattice, arXiv:2304.08683</td> </tr><tr> <td>[56]</td> <td class="space">Zhipeng Sun, Hai-Qing Lin, Exploring high-temperature superconductivity in the extended Hubbard model with antiferromagnetic tendencies, arXiv:2304.07490</td> </tr><tr> <td>[57]</td> <td class="space">Alexandrov, A. S.; Kornilovitch, P. E., J. Phys.: Condens. Matter, 5337-5348 (2002)</td> </tr><tr> <td>[58]</td> <td class="space">Alexandrov, A. S.; Kornilovitch, P. E., Phys. Lett. A, 650-655 (2002)</td> </tr><tr> <td>[59]</td> <td class="space">Chao, K. A.; Spałek, J.; Oleś, A. M., Phys. Rev. B, 3453-3464 (1978)</td> </tr><tr> <td>[60]</td> <td class="space">Lin, H. Q., Phys. Rev. B, 4674-4676 (1991)</td> </tr><tr> <td>[61]</td> <td class="space">Petukhov, A. G.; Galán, J.; Vergés, J. A., Phys. Rev. B, 6212-6216 (1992)</td> </tr><tr> <td>[62]</td> <td class="space">Kagan, M. Yu.; Rice, T. M., J. Phys.: Condens. Matter, 3771-3780 (1994)</td> </tr><tr> <td>[63]</td> <td class="space">Chernyshev, A. L.; Leung, P. W., Phys. Rev. B, 1592-1606 (1999)</td> </tr><tr> <td>[64]</td> <td class="space">Bloch, I.; Dalibard, J.; Zwerger, W., Rev. Modern Phys., 885-964 (2008)</td> </tr><tr> <td>[65]</td> <td class="space">Blume, D., Rep. Progr. Phys. (2012)</td> </tr><tr> <td>[66]</td> <td class="space">Sowiński, T.; García-March, M.Á., Rep. Progr. Phys. (2019)</td> </tr><tr> <td>[67]</td> <td class="space">Mistakidis, S. I.; Volosniev, A. G.; Barfknecht, R. E.; Fogarty, T.; Busch, Th.; Foerster, A.; Schmelcher, P.; Zinner, N. T., Phys. Rep., 1 (2023)</td> </tr><tr> <td>[68]</td> <td class="space">Chin, C.; Grimm, R.; Julienne, P.; Tiesinga, E., Rev. Modern Phys., 1225-1286 (2010)</td> </tr><tr> <td>[69]</td> <td class="space">Jördens, R.; Strohmaier, N.; Günter, K.; Moritz, H.; Esslinger, T., Nature, 204 (2008)</td> </tr><tr> <td>[70]</td> <td class="space">Strohmaier, N.; Takasu, Y.; Günter, K.; Jördens, R.; Köhl, M.; Moritz, H.; Esslinger, T., Phys. Rev. Lett. (2007)</td> </tr><tr> <td>[71]</td> <td class="space">Hague, J. P.; MacCormick, C., Phys. Rev. Lett. (2012)</td> </tr><tr> <td>[72]</td> <td class="space">Lahaye, T.; Menotti, C.; Santos, L.; Lewenstein, M.; Pfau, T., Rep. Progr. Phys. (2009)</td> </tr><tr> <td>[73]</td> <td class="space">Serwane, F.; Zürn, G.; Lompe, T.; Ottenstein, T. B.; Wenz, A. N.; Jochim, S., Science, 336-338 (2011)</td> </tr><tr> <td>[74]</td> <td class="space">Zürn, G.; Serwane, F.; Lompe, T.; Wenz, A. N.; Ries, M. G.; Bohn, J. E.; Jochim, S., Phys. Rev. Lett. (2012)</td> </tr><tr> <td>[75]</td> <td class="space">Zürn, G.; Wenz, A. N.; Murmann, S.; Bergschneider, A.; Lompe, T.; Jochim, S., Phys. Rev. Lett. (2013)</td> </tr><tr> <td>[76]</td> <td class="space">Greiner, M.; Regal, C. A.; Jin, D. S., Nature, 537-540 (2003)</td> </tr><tr> <td>[77]</td> <td class="space">Mitra, D.; Brown, P. T.; Guardado-Sanchez, E.; Kondov, S. S.; Devakul, Trithep; Huse, D. A.; Schauß, P.; Bakr, W. S., Nat. Phys., 173-177 (2018)</td> </tr><tr> <td>[78]</td> <td class="space">Hartke, T.; Oreg, B.; Turnbaugh, C.; Jia, N.; Zwierlein, M., Science, 82-86 (2023)</td> </tr><tr> <td>[79]</td> <td class="space">Wortis, M., Phys. Rev., 85 (1963)</td> </tr><tr> <td>[80]</td> <td class="space">Hanus, J., Phys. Rev. Lett., 336-338 (1963)</td> </tr><tr> <td>[81]</td> <td class="space">Akhiezer, A. I.; Bar’yakhtar, V. G.; Peletminskii, S. V., Spin Waves (1968), North-Holland Publishing Company: North-Holland Publishing Company Amsterdam</td> </tr><tr> <td>[82]</td> <td class="space">Kuzian, R. O.; Drechsler, S.-L., Phys. Rev. B (2007)</td> </tr><tr> <td>[83]</td> <td class="space">Mook, A.; Hoyer, R.; Klinovaja, J.; Loss, D., Phys. Rev. B (2023), and references therein</td> </tr><tr> <td>[84]</td> <td class="space">Ueda, H. T.; Totsuka, K., Phys. Rev. B (2009)</td> </tr><tr> <td>[85]</td> <td class="space">Zhitomirsky, M. E.; Tsunetsugu, H., Europhys. Lett., 37001 (2010)</td> </tr><tr> <td>[86]</td> <td class="space">Jiang, S.; Romhányi, J.; White, S. R.; Zhitomirsky, M. E.; Chernyshev, A. L., Rev. Lett. (2023)</td> </tr><tr> <td>[87]</td> <td class="space">Kornilovitch, P., Phys. Rev. B (2004)</td> </tr><tr> <td>[88]</td> <td class="space">Bak, M., Phys. Status Solidi b, 2421-2426 (2007)</td> </tr><tr> <td>[89]</td> <td class="space">Adebanjo, G. D.; Kornilovitch, P. E.; Hague, J. P., Phys. Lett. A (2021)</td> </tr><tr> <td>[90]</td> <td class="space">Adebanjo, G. D.; Kornilovitch, P. E.; Hague, J. P., J. Phys.: Condens. Matter (2022)</td> </tr><tr> <td>[91]</td> <td class="space">Joyce, G. S., Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 463-477 (1994) · <a href="/0808.33015" class="nowrap">Zbl 0808.33015</a></td> </tr><tr> <td>[92]</td> <td class="space">Joyce, G. S., J. Phys. A: Math. Gen., 5105-5115 (1998) · <a href="/0940.33012" class="nowrap">Zbl 0940.33012</a></td> </tr><tr> <td>[93]</td> <td class="space">Glasser, M. L.; Boersma, J., J. Phys. A: Math. Gen., 5017-5023 (2000) · <a href="/0973.82010" class="nowrap">Zbl 0973.82010</a></td> </tr><tr> <td>[94]</td> <td class="space">Delves, R. T.; Joyce, G. S., Ann. Phys., 71-133 (2001) · <a href="/1051.82011" class="nowrap">Zbl 1051.82011</a></td> </tr><tr> <td>[95]</td> <td class="space">Delves, R. T.; Joyce, G. S., J. Phys. A: Math. Gen., L59-L65 (2001) · <a href="/0978.82014" class="nowrap">Zbl 0978.82014</a></td> </tr><tr> <td>[96]</td> <td class="space">Joyce, G. S., J. Phys. A: Math. Gen., 9811-9828 (2002) · <a href="/1038.82016" class="nowrap">Zbl 1038.82016</a></td> </tr><tr> <td>[97]</td> <td class="space">Joyce, G. S.; Delves, R. T.; Zucker, I. J., J. Phys. A: Math. Gen., 8661-8672 (2003) · <a href="/1049.82066" class="nowrap">Zbl 1049.82066</a></td> </tr><tr> <td>[98]</td> <td class="space">Zucker, I. J., J. Stat. Phys., 591-612 (2011) · <a href="/1231.82026" class="nowrap">Zbl 1231.82026</a></td> </tr><tr> <td>[99]</td> <td class="space">Kornilovitch, P. E., 367-374</td> </tr><tr> <td>[100]</td> <td class="space">Kornilovitch, P. E., Electron-Phonon and Electron-Electron Correlation Effects on a Lattice (1997), Department of Physics, King’s College, University of London, (Ph.D. thesis)</td> </tr><tr> <td>[101]</td> <td class="space">Hague, J. P.; Kornilovitch, P. E., Phys. Rev. B (2010)</td> </tr><tr> <td>[102]</td> <td class="space">Davenport, A. R.; Hague, J. P.; Kornilovitch, P. E., Phys. Rev. B (2012)</td> </tr><tr> <td>[103]</td> <td class="space">Alexandrov, A. S.; Traven, S. V.; Kornilovich, P. E., J. Phys.: Condens. Matter, L89-L95 (1992)</td> </tr><tr> <td>[104]</td> <td class="space">Alexandrov, A. S.; Kornilovitch, P. E., Z. Phys. B, 47-50 (1993)</td> </tr><tr> <td>[105]</td> <td class="space">Prudnikov, A. P.; Brychkov, Yu. A.; Marichev, O. I., Integrals and Series, Volume 1: Elementary Functions (1998), Taylor & Francis · <a href="/1103.00301" class="nowrap">Zbl 1103.00301</a></td> </tr><tr> <td>[106]</td> <td class="space">Watson, G. N., Q. J. Math. Oxford, 266-276 (1939) · <a href="/0022.33202" class="nowrap">Zbl 0022.33202</a></td> </tr><tr> <td>[107]</td> <td class="space">Dong, S.-J.; Yang, C. N., Rev. Math. Phys., 139-146 (1989) · <a href="/0721.35058" class="nowrap">Zbl 0721.35058</a></td> </tr><tr> <td>[108]</td> <td class="space">Montroll, E. W., 209-246</td> </tr><tr> <td>[109]</td> <td class="space">Maradudin, A. A.; Montroll, E. W.; Weiss, G. H.; Herman, R.; Milnes, H. W., Green’s Functions for Monatomic Simple Cubic Lattices (1960)</td> </tr><tr> <td>[110]</td> <td class="space">In the standard source, [109](84)</td> </tr><tr> <td>[111]</td> <td class="space">Katsura, S.; Horiguchi, T., J. Math. Phys., 230-231 (1971) · <a href="/0272.33007" class="nowrap">Zbl 0272.33007</a></td> </tr><tr> <td>[112]</td> <td class="space">Morita, T.; Horiguchi, T., J. Math. Phys., 986-992 (1971) · <a href="/0218.35017" class="nowrap">Zbl 0218.35017</a></td> </tr><tr> <td>[113]</td> <td class="space">Joyce, G. S., J. Math. Phys., 1390-1414 (1971) · <a href="/0257.60038" class="nowrap">Zbl 0257.60038</a></td> </tr><tr> <td>[114]</td> <td class="space">Iwata, G., Natur. Sci. Rep. Ochanomizu Univ., 13-18 (1969) · <a href="/0202.34004" class="nowrap">Zbl 0202.34004</a></td> </tr><tr> <td>[115]</td> <td class="space">Hubbard, J., Proc. Roy. Soc. A, 238-257 (1963)</td> </tr><tr> <td>[116]</td> <td class="space">Dagotto, E., Rev. Modern Phys., 763-840 (1994)</td> </tr><tr> <td>[117]</td> <td class="space">Alexandrov, A. S.; Kabanov, V. V., Phys. Rev. Lett. (2011)</td> </tr><tr> <td>[118]</td> <td class="space">Qin, M.; Chung, C.-M.; Shi, H.; Vitali, E.; Hubig, C.; Schollwöck, U.; White, S. R.; Zhang, S., Phys. Rev. X (2020)</td> </tr><tr> <td>[119]</td> <td class="space">Sherman, A., Phys. Scr. (2021)</td> </tr><tr> <td>[120]</td> <td class="space">Jiang, S.; Scalapino, D. J.; White, S. R., Phys. Rev. B (2022)</td> </tr><tr> <td>[121]</td> <td class="space">Rømer, A. T.; Maier, T. A.; Kreisel, A.; Eremin, I.; Hirschfeld, P. J.; Andersen, B. M., Phys. Rev. Res. (2020)</td> </tr><tr> <td>[122]</td> <td class="space">Damascelli, A.; Hussain, Z.; Shen, Z.-X., Rev. Modern Phys., 473 (2003)</td> </tr><tr> <td>[123]</td> <td class="space">Marsiglio, F.; Hirsch, J. E., Phys. C, 554-560 (1990)</td> </tr><tr> <td>[124]</td> <td class="space">LeBlanc, J. P.F.; Antipov, A. E.; Becca, F.; Bulik, I. W.; Chan, G. K.-L.; Chung, C.-M.; Deng, Y.; Ferrero, M.; Henderson, T. M.; Jiménez-Hoyos, C. A.; Kozik, E.; Liu, X.-W.; Millis, A. J.; Prokof’ev, N. V.; Qin, M.; Scuseria, G. E.; Shi, H.; Svistunov, B. V.; Tocchio, L. F.; Tupitsyn, I. S.; White, S. R.; Zhang, S.; Zheng, B.-X.; Zhu, Z.; Gull, E., Phys. Rev. X (2015)</td> </tr><tr> <td>[125]</td> <td class="space">Micnas, R.; Pedersen, M. H.; Schafroth, S.; Schneider, T.; Rodríguez-Núñez, J. J.; Beck, H., Phys. Rev. B, 16223-16232 (1995)</td> </tr><tr> <td>[126]</td> <td class="space">Kyung, B.; Klepfish, E. G.; Kornilovitch, P. E., Phys. Rev. Lett., 3109-3112 (1998)</td> </tr><tr> <td>[127]</td> <td class="space">G.D. Adebanjo, J.P. Hague, P.E. Kornilovitch, Ubiquity of light small pairs in Hubbard models with long range hoppings and interactions, arXiv:2211.06498</td> </tr><tr> <td>[128]</td> <td class="space">Leung, P. W.; Gooding, R. J., Phys. Rev. B, R15711-R15714 (1995)</td> </tr><tr> <td>[129]</td> <td class="space">N. Harrison, M.K. Chan, Thermodynamic evidence for electron correlation-driven flattening of the quasiparticle bands in the high-$ T_c$ arXiv:2303.12956</td> </tr><tr> <td>[130]</td> <td class="space">Zhang, X.; Catlow, C. R.A., J. Mater. Chem., 233 (1991)</td> </tr><tr> <td>[131]</td> <td class="space">Catlow, C. R.A.; Islam, M. S.; Zhang, X., J. Phys.: Condens. Matter, L49 (1998)</td> </tr><tr> <td>[132]</td> <td class="space">Alexandrov, A. S.; Kornilovitch, P. E., J. Superconduct.: Incorporat. Novel Magn., 403-408 (2002)</td> </tr><tr> <td>[133]</td> <td class="space">Hague, J. P.; Kornilovitch, P. E.; Samson, J. H.; Alexandrov, A. S., J. Phys.: Condens. Matter (2007)</td> </tr><tr> <td>[134]</td> <td class="space">Hague, J. P.; Kornilovitch, P. E.; Samson, J. H.; Alexandrov, A. S., J. Phys.: Conf. Ser. (2007)</td> </tr><tr> <td>[135]</td> <td class="space">Hague, J. P.; Kornilovitch, P. E.; Samson, J. H.; Alexandrov, A. S., J. Phys. Chem. Solids, 3304-3306 (2008)</td> </tr><tr> <td>[136]</td> <td class="space">Alexandrov, A. S.; Kornilovitch, P. E., Phys. Rev. Lett., 807-810 (1999)</td> </tr><tr> <td>[137]</td> <td class="space">Hague, J. P.; Kornilovitch, P. E.; Samson, J. H.; Alexandrov, A. S., Phys. Rev. Lett. (2007)</td> </tr><tr> <td>[138]</td> <td class="space">Mihailovic, D., J. Supercond. Nov. Magn., 1769-1773 (2022)</td> </tr><tr> <td>[139]</td> <td class="space">Jochim, S.; Bartenstein, M.; Altmeyer, A.; Hendl, G.; Riedl, S.; Chin, C.; Denschlag, J. H.; Grimm, R., Science, 2101-2103 (2003)</td> </tr><tr> <td>[140]</td> <td class="space">Zwierlein, M. W.; Stan, C. A.; Schunck, C. H.; Raupach, S. M.F.; Gupta, S.; Hadzibabic, Z.; Ketterle, W., Phys. Rev. Lett. (2003)</td> </tr><tr> <td>[141]</td> <td class="space">Ţuţueanu, A.-E.; Kamminga, M. E.; Tejsner, T. B.; Jacobsen, H.; Hansen, H. W.; Lăcătuşu, M.-E.; Baas, J.; Eliasen, K. L.; Grivel, J.-C.; Sassa, Y.; Christensen, N. B.; Steffens, P.; Boehm, M.; Piovano, A.; Lefmann, K.; Rømer, Astrid T., Phys. Rev. B (2023)</td> </tr><tr> <td>[142]</td> <td class="space">Su, G., Phys. Rev. B, R8281 (1996)</td> </tr><tr> <td>[143]</td> <td class="space">Emin, D., Phys. Rev. B, 9157 (1994), and references therein</td> </tr><tr> <td>[144]</td> <td class="space">Berciu, M., Phys. Rev. Lett. (2011)</td> </tr><tr> <td>[145]</td> <td class="space">Chakraborty, M.; Tezuka, M.; Min, B. I., Phys. Rev. B (2014)</td> </tr><tr> <td>[146]</td> <td class="space">Kornilovitch, P. E., Internat. J. Modern Phys. B (2020)</td> </tr><tr> <td>[147]</td> <td class="space">Kornilovitch, P. E., Europhys. Lett., 27005 (2013)</td> </tr><tr> <td>[148]</td> <td class="space">Kornilovitch, P. E., Phys. Rev. Lett. (2014)</td> </tr><tr> <td>[149]</td> <td class="space">Kornilovitch, P. E., Phys. Rev. B, 13531 (1999)</td> </tr><tr> <td>[150]</td> <td class="space">N.K. Rajak, D. Tirumalarao, G. Vaid, S. Kumar C, S. Athira, G. Prakash, A. Babu, T. Gaikwad, S. Chandradas, A.P. Andrews, A. Aneesh, B. Varghese, M. Raama Varma, A. Thamizhavel, S. Ramakrishnan, D. Jaiswal-Nagar, Superconductivity in single crystals of a quasi-one dimensional infinite chain cuprate $Sr{}_x{}_{1 - x}{}_2$ arXiv:2304.08675</td> </tr><tr> <td>[151]</td> <td class="space">Mertelj, T.; Kabanov, V. V.; Mihailovic, D., Phys. Rev. Lett. (2005)</td> </tr><tr> <td>[152]</td> <td class="space">Tranquada, J. M.; Sternlieb, B. J.; Axe, J. D.; Nkamura, Y.; Uchida, S., Nature, 561-563 (1995)</td> </tr><tr> <td>[153]</td> <td class="space">Chang, J.; Blackburn, E.; Holmes, A. T.; Christensen, N. B.; Larsen, J.; Mesot, J.; Liang, R.; Bonn, D. A.; Hardy, W. N.; Watenphul, A.; v. Zimmermann, M.; Forgan, E. M.; Hayden, S. M., Nat. Phys., 871-876 (2012)</td> </tr><tr> <td>[154]</td> <td class="space">Ghiringhelli, G.; Le Tacon, M.; Minola, M.; Blanco-Canosa, S.; Mazzoli, C.; Brookes, N. B.; De Luca, G. M.; Frano, A.; Hawthorn, D. G.; He, F.; Loew, T.; Moretti Sala, M.; Peets, D. C.; Salluzzo, M.; Schierle, E.; Sutarto, R.; Sawatzky, G. A.; Weschke, E.; Keimer, B.; Braicovich, L., Science, 821-825 (2012)</td> </tr><tr> <td>[155]</td> <td class="space">Comin, R.; Sutarto, R.; He, F.; da Silva Neto, E. H.; Chauviere, L.; Fraño, A.; Liang, R.; Hardy, W. N.; Bonn, D. A.; Yoshida, Y.; Eisaki, H.; Achkar, A. J.; Hawthorn, D. G.; Keimer, B.; Sawatzky, G. A.; Damascelli, A., Nature Mater., 796-800 (2015)</td> </tr><tr> <td>[156]</td> <td class="space">Miao, H.; Fabbris, G.; Koch, R. J.; Mazzone, D. G.; Nelson, C. S.; Acevedo-Esteves, R.; Gu, G. D.; Li, Y.; Yilimaz, T.; Kaznatcheev, K.; Vescovo, E.; Oda, M.; Kurosawa, T.; Momono, N.; Assefa, T.; Robinson, I. K.; Bozin, E. S.; Tranquada, J. M.; Johnson, P. D.; Dean, M. P.M., npj Quant. Mater., 31 (2021)</td> </tr><tr> <td>[157]</td> <td class="space">Noat, Y.; Mauger, A.; Nohara, M.; Eisaki, H.; Ishida, S.; Sacks, W., Solid State Commn. (2022)</td> </tr><tr> <td>[158]</td> <td class="space">Pickett, W. E., Rev. Modern Phys., 433-512 (1989)</td> </tr><tr> <td>[159]</td> <td class="space">Ramadhan, M. R.; Adiperdana, B.; Ramli, I.; Sari, D. P.; Putri, A. E.; Widyaiswari, U.; Rozak, H.b.; Zaharim, W. N.; Manaf, A.; Kurniawan, B.; Mohamed-Ibrahim, M. I.; Sulaiman, Sh.; Kawamata, T.; Adachi, T.; Koike, Y.; Watanabe, I., Phys. Rev. Res. (2022)</td> </tr><tr> <td>[160]</td> <td class="space">Bak, M., Internat. J. Theoret. Phys., 1173-1186 (2012) · <a href="/1252.82023" class="nowrap">Zbl 1252.82023</a></td> </tr><tr> <td>[161]</td> <td class="space">Hague, J. P.; Kornilovitch, P. E.; MacCormick, C., Phys. Rev. A (2020)</td> </tr><tr> <td>[162]</td> <td class="space">P.E. Kornilovitch, (unpublished).</td> </tr><tr> <td>[163]</td> <td class="space">Katsura, S.; Inawashiro, S., J. Math. Phys., 1622-1630 (1971) · <a href="/0224.33025" class="nowrap">Zbl 0224.33025</a></td> </tr><tr> <td>[164]</td> <td class="space">Hancock, H., Lectures on the Theory of Elliptic Functions (1910), John Wiley & Sons: John Wiley & Sons New York, chapter VIII, See, for example · <a href="/41.0503.05" class="nowrap">JFM 41.0503.05</a></td> </tr><tr> <td>[165]</td> <td class="space">Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions (1972), Dover Publications Inc.: Dover Publications Inc. New York · <a href="/0543.33001" class="nowrap">Zbl 0543.33001</a></td> </tr><tr> <td>[166]</td> <td class="space">Morita, T., J. Phys. A: Math. Gen., 478-489 (1975)</td> </tr><tr> <td>[167]</td> <td class="space">Prudnikov, A. P.; Brychkov, Yu. A.; Marichev, O. I., Integrals and Series, Volume 2: Special Functions (1986), Overseas Publishers Association: Overseas Publishers Association Amsterdam · <a href="/0733.00004" class="nowrap">Zbl 0733.00004</a></td> </tr><tr> <td>[168]</td> <td class="space">Petrashen, M. I.; Trifonov, E. D., Applications of Group Theory in Quantum Mechanics (1969), chapter 7 · <a href="/0194.28902" class="nowrap">Zbl 0194.28902</a></td> </tr><tr> <td>[169]</td> <td class="space">Whittaker, E. T.; Watson, G. N., section 22.8</td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

CINXE.COM

Document Zbl 07783771 - zbMATH Open