Constructive fractional-moment criteria for localization in random operators
Identifieur interne : 000697 ( Main/Corpus ); précédent : 000696; suivant : 000698Constructive fractional-moment criteria for localization in random operators
Auteurs : Michael Aizenman ; Jeffrey H. Schenker ; Roland M. Friedrich ; Dirk HundertmarkSource :
- Physica A: Statistical Mechanics and its Applications [ 0378-4371 ] ; 2000.
Abstract
We present a family of finite-volume criteria which cover the regime of exponential decay for the fractional moments of Green functions of operators with random potentials. Such decay is a technically convenient characterization of localization for it is known to imply spectral localization, absence of level repulsion, dynamical localization and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. The constructive criteria also preclude fast power-law decay of the Green functions at mobility edges.
Url:
DOI: 10.1016/S0378-4371(00)00012-1
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Such decay is a technically convenient characterization of localization for it is known to imply spectral localization, absence of level repulsion, dynamical localization and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. The constructive criteria also preclude fast power-law decay of the Green functions at mobility edges.</div></front></TEI><istex><corpusName>elsevier</corpusName><author><json:item><name>Michael Aizenman</name><affiliations><json:string>E-mail: aizenman@princeton.edu</json:string><json:string>Physics Department, Princeton University, Jadwin Hall, Princeton, NJ 08544, USA</json:string></affiliations></json:item><json:item><name>Jeffrey H Schenker</name><affiliations><json:string>Mathematics Department, Princeton University, Fine Hall, Princeton, NJ 08544, USA</json:string></affiliations></json:item><json:item><name>Roland M Friedrich</name><affiliations><json:string>Student, Theoretische Physik, ETH-Zürich, CH–8093, Switzerland</json:string></affiliations></json:item><json:item><name>Dirk Hundertmark</name><affiliations><json:string>Department of Mathematics 253-37, Caltech, Pasadena, CA 91125, USA</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>Random operators</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Localization</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Constructive criteria</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Mobility edge</value></json:item></subject><language><json:string>eng</json:string></language><originalGenre><json:string>Full-length article</json:string></originalGenre><abstract>We present a family of finite-volume criteria which cover the regime of exponential decay for the fractional moments of Green functions of operators with random potentials. Such decay is a technically convenient characterization of localization for it is known to imply spectral localization, absence of level repulsion, dynamical localization and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. 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Fax: +1-609 258-6360</p></note><affiliation>Supported in part by the NSF Grant PHY-9971149.</affiliation><affiliation>Physics Department, Princeton University, Jadwin Hall, Princeton, NJ 08544, USA</affiliation></author><author xml:id="author-2"><persName><forename type="first">Jeffrey H</forename><surname>Schenker</surname></persName><note type="biography">Supported by an NSF Graduate Research Fellowship.</note><affiliation>Supported by an NSF Graduate Research Fellowship.</affiliation><affiliation>Mathematics Department, Princeton University, Fine Hall, Princeton, NJ 08544, USA</affiliation></author><author xml:id="author-3"><persName><forename type="first">Roland M</forename><surname>Friedrich</surname></persName><affiliation>Student, Theoretische Physik, ETH-Zürich, CH–8093, Switzerland</affiliation></author><author xml:id="author-4"><persName><forename type="first">Dirk</forename><surname>Hundertmark</surname></persName><note type="biography">Supported by the Deutsche Forschungsgemeinschaft Grant Hu 773/1-1.</note><affiliation>Supported by the Deutsche Forschungsgemeinschaft Grant Hu 773/1-1.</affiliation><affiliation>Department of Mathematics 253-37, Caltech, Pasadena, CA 91125, USA</affiliation></author></analytic><monogr><title level="j">Physica A: Statistical Mechanics and its Applications</title><title level="j" type="abbrev">PHYSA</title><idno type="pISSN">0378-4371</idno><idno type="PII">S0378-4371(00)X0126-4</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="2000"></date><biblScope unit="volume">279</biblScope><biblScope unit="issue">1–4</biblScope><biblScope unit="page" from="369">369</biblScope><biblScope unit="page" to="377">377</biblScope></imprint></monogr><idno type="istex">50AE8E608E766F0E26193C8E586D655FAFE190D8</idno><idno type="DOI">10.1016/S0378-4371(00)00012-1</idno><idno type="PII">S0378-4371(00)00012-1</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2000</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>We present a family of finite-volume criteria which cover the regime of exponential decay for the fractional moments of Green functions of operators with random potentials. Such decay is a technically convenient characterization of localization for it is known to imply spectral localization, absence of level repulsion, dynamical localization and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. The constructive criteria also preclude fast power-law decay of the Green functions at mobility edges.</p></abstract><textClass><keywords scheme="keyword"><list><head>Keywords</head><item><term>Random operators</term></item><item><term>Localization</term></item><item><term>Constructive criteria</term></item><item><term>Mobility edge</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2000">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><original>false</original><mimetype>text/plain</mimetype><extension>txt</extension><uri>https://api.istex.fr/document/50AE8E608E766F0E26193C8E586D655FAFE190D8/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Elsevier, elements deleted: body; tail"><istex:xmlDeclaration>version="1.0" encoding="utf-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//ES//DTD journal article DTD version 4.5.2//EN//XML" URI="art452.dtd" name="istex:docType"></istex:docType><istex:document><converted-article version="4.5.2" docsubtype="fla"><item-info><jid>PHYSA</jid><aid>5280</aid><ce:pii>S0378-4371(00)00012-1</ce:pii><ce:doi>10.1016/S0378-4371(00)00012-1</ce:doi><ce:copyright type="unknown" year="2000"></ce:copyright></item-info><head><ce:title>Constructive fractional-moment criteria for localization in random operators</ce:title><ce:dedication>To Joel L. Lebowitz, on the occasion of his 70th birthday</ce:dedication><ce:author-group><ce:author><ce:given-name>Michael</ce:given-name><ce:surname>Aizenman</ce:surname><ce:cross-ref refid="FN1"><ce:sup>1</ce:sup></ce:cross-ref><ce:cross-ref refid="AFF1"><ce:sup>a</ce:sup></ce:cross-ref><ce:cross-ref refid="AFF2"><ce:sup>b</ce:sup></ce:cross-ref><ce:cross-ref refid="CORR1">*</ce:cross-ref><ce:e-address>aizenman@princeton.edu</ce:e-address></ce:author><ce:author><ce:given-name>Jeffrey H</ce:given-name><ce:surname>Schenker</ce:surname><ce:cross-ref refid="FN2"><ce:sup>2</ce:sup></ce:cross-ref><ce:cross-ref refid="AFF2"><ce:sup>b</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>Roland M</ce:given-name><ce:surname>Friedrich</ce:surname><ce:cross-ref refid="AFF3"><ce:sup>c</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>Dirk</ce:given-name><ce:surname>Hundertmark</ce:surname><ce:cross-ref refid="FN3"><ce:sup>3</ce:sup></ce:cross-ref><ce:cross-ref refid="AFF4"><ce:sup>d</ce:sup></ce:cross-ref></ce:author><ce:affiliation id="AFF1"><ce:label>a</ce:label><ce:textfn>Physics Department, Princeton University, Jadwin Hall, Princeton, NJ 08544, USA</ce:textfn></ce:affiliation><ce:affiliation id="AFF2"><ce:label>b</ce:label><ce:textfn>Mathematics Department, Princeton University, Fine Hall, Princeton, NJ 08544, USA</ce:textfn></ce:affiliation><ce:affiliation id="AFF3"><ce:label>c</ce:label><ce:textfn>Student, Theoretische Physik, ETH-Zürich, CH–8093, Switzerland</ce:textfn></ce:affiliation><ce:affiliation id="AFF4"><ce:label>d</ce:label><ce:textfn>Department of Mathematics 253-37, Caltech, Pasadena, CA 91125, USA</ce:textfn></ce:affiliation><ce:correspondence id="CORR1"><ce:label>*</ce:label><ce:text>Corresponding author. Fax: +1-609 258-6360</ce:text></ce:correspondence><ce:footnote id="FN1"><ce:label>1</ce:label><ce:note-para>Supported in part by the NSF Grant PHY-9971149.</ce:note-para></ce:footnote><ce:footnote id="FN2"><ce:label>2</ce:label><ce:note-para>Supported by an NSF Graduate Research Fellowship.</ce:note-para></ce:footnote><ce:footnote id="FN3"><ce:label>3</ce:label><ce:note-para>Supported by the Deutsche Forschungsgemeinschaft Grant Hu 773/1-1.</ce:note-para></ce:footnote></ce:author-group><ce:abstract><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para>We present a family of finite-volume criteria which cover the regime of exponential decay for the fractional moments of Green functions of operators with random potentials. Such decay is a technically convenient characterization of localization for it is known to imply spectral localization, absence of level repulsion, dynamical localization and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. The constructive criteria also preclude fast power-law decay of the Green functions at mobility edges.</ce:simple-para></ce:abstract-sec></ce:abstract><ce:keywords class="keyword"><ce:section-title>Keywords</ce:section-title><ce:keyword><ce:text>Random operators</ce:text></ce:keyword><ce:keyword><ce:text>Localization</ce:text></ce:keyword><ce:keyword><ce:text>Constructive criteria</ce:text></ce:keyword><ce:keyword><ce:text>Mobility edge</ce:text></ce:keyword></ce:keywords></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>Constructive fractional-moment criteria for localization in random operators</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Constructive fractional-moment criteria for localization in random operators</title></titleInfo><name type="personal"><namePart type="given">Michael</namePart><namePart type="family">Aizenman</namePart><affiliation>E-mail: aizenman@princeton.edu</affiliation><affiliation>Physics Department, Princeton University, Jadwin Hall, Princeton, NJ 08544, USA</affiliation><description>Corresponding author. 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Such decay is a technically convenient characterization of localization for it is known to imply spectral localization, absence of level repulsion, dynamical localization and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. The constructive criteria also preclude fast power-law decay of the Green functions at mobility edges.</abstract><subject><genre>Keywords</genre><topic>Random operators</topic><topic>Localization</topic><topic>Constructive criteria</topic><topic>Mobility edge</topic></subject><relatedItem type="host"><titleInfo><title>Physica A: Statistical Mechanics and its Applications</title></titleInfo><titleInfo type="abbreviated"><title>PHYSA</title></titleInfo><genre type="journal">journal</genre><originInfo><dateIssued encoding="w3cdtf">20000501</dateIssued></originInfo><identifier type="ISSN">0378-4371</identifier><identifier type="PII">S0378-4371(00)X0126-4</identifier><part><date>20000501</date><detail type="volume"><number>279</number><caption>vol.</caption></detail><detail type="issue"><number>1–4</number><caption>no.</caption></detail><extent unit="issue pages"><start>1</start><end>486</end></extent><extent unit="pages"><start>369</start><end>377</end></extent></part></relatedItem><identifier type="istex">50AE8E608E766F0E26193C8E586D655FAFE190D8</identifier><identifier type="DOI">10.1016/S0378-4371(00)00012-1</identifier><identifier type="PII">S0378-4371(00)00012-1</identifier><recordInfo><recordContentSource>ELSEVIER</recordContentSource></recordInfo></mods></metadata><enrichments><istex:catWosTEI uri="https://api.istex.fr/document/50AE8E608E766F0E26193C8E586D655FAFE190D8/enrichments/catWos"><teiHeader><profileDesc><textClass><classCode scheme="WOS">PHYSICS</classCode><classCode scheme="WOS">PHYSICS, MULTIDISCIPLINARY</classCode></textClass></profileDesc></teiHeader></istex:catWosTEI></enrichments><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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