<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-04225842</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-21T07:07:00+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Schrödinger equation driven by the square of a Gaussian field: instanton analysis in the large amplification limit</title>
            <author role="aut">
              <persName>
                <forename type="first">Philippe</forename>
                <surname>Mounaix</surname>
              </persName>
              <email type="md5">4e3a15ed029eb63d166976315604f0d8</email>
              <email type="domain">polytechnique.edu</email>
              <idno type="idhal" notation="numeric">1078629</idno>
              <idno type="halauthorid" notation="string">624517-1078629</idno>
              <affiliation ref="#struct-10"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Philippe</forename>
                <surname>Mounaix</surname>
              </persName>
              <email type="md5">4e3a15ed029eb63d166976315604f0d8</email>
              <email type="domain">polytechnique.edu</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2023-10-03 10:49:42</date>
              <date type="whenModified">2025-08-20 10:51:15</date>
              <date type="whenReleased">2023-10-03 13:26:28</date>
              <date type="whenProduced">2023</date>
              <date type="whenEndEmbargoed">2023-10-03</date>
              <ref type="file" target="https://hal.science/hal-04225842v1/document">
                <date notBefore="2023-10-03"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-04225842v1/file/https%3Aarxiv.org%3Apdf%3A2301.13000.pdf" id="file-4225842-3686529">
                <date notBefore="2023-10-03"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/2301.13000v2"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="775660">
                <persName>
                  <forename>Philippe</forename>
                  <surname>Mounaix</surname>
                </persName>
                <email type="md5">4e3a15ed029eb63d166976315604f0d8</email>
                <email type="domain">polytechnique.edu</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04225842</idno>
            <idno type="halUri">https://hal.science/hal-04225842</idno>
            <idno type="halBibtex">mounaix:hal-04225842</idno>
            <idno type="halRefHtml">&lt;i&gt;Journal of Physics A: Mathematical and Theoretical&lt;/i&gt;, 2023, 56 (30), pp.305001. &lt;a target="_blank" href="https://dx.doi.org/10.1088/1751-8121/ace0e8"&gt;&amp;#x27E8;10.1088/1751-8121/ace0e8&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Journal of Physics A: Mathematical and Theoretical, 2023, 56 (30), pp.305001. &amp;#x27E8;10.1088/1751-8121/ace0e8&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-4225842-3686529"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="X">École polytechnique</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="X-CPHT" corresp="X">Centre de Physique Théorique (CPHT)</idno>
            <idno type="stamp" n="X-DEP-PHYS">Département de physique de l’École polytechnique</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="IP_PARIS">Institut Polytechnique de Paris</idno>
            <idno type="stamp" n="DEPARTEMENT-DE-MATHEMATIQUES">Collection du Département de Mathématiques</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Schrödinger equation driven by the square of a Gaussian field: instanton analysis in the large amplification limit</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Philippe</forename>
                    <surname>Mounaix</surname>
                  </persName>
                  <email type="md5">4e3a15ed029eb63d166976315604f0d8</email>
                  <email type="domain">polytechnique.edu</email>
                  <idno type="idhal" notation="numeric">1078629</idno>
                  <idno type="halauthorid" notation="string">624517-1078629</idno>
                  <affiliation ref="#struct-10"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">16018</idno>
                <idno type="issn">1751-8113</idno>
                <idno type="eissn">1751-8121</idno>
                <title level="j">Journal of Physics A: Mathematical and Theoretical</title>
                <imprint>
                  <publisher>IOP Publishing</publisher>
                  <biblScope unit="volume">56</biblScope>
                  <biblScope unit="issue">30</biblScope>
                  <biblScope unit="pp">305001</biblScope>
                  <date type="datePub">2023</date>
                </imprint>
              </monogr>
              <idno type="arxiv">2301.13000v2</idno>
              <idno type="doi">10.1088/1751-8121/ace0e8</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">stochastic partial differential equations</term>
                <term xml:lang="en">instanton analysis</term>
                <term xml:lang="en">extreme event statistics</term>
                <term xml:lang="en">laser-plasma interactions</term>
              </keywords>
              <classCode scheme="halDomain" n="phys.mphy">Physics [physics]/Mathematical Physics [math-ph]</classCode>
              <classCode scheme="halDomain" n="math.math-ap">Mathematics [math]/Analysis of PDEs [math.AP]</classCode>
              <classCode scheme="halDomain" n="phys.qphy">Physics [physics]/Quantum Physics [quant-ph]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We study the tail of p ( U ), the probability distribution of U = | ψ ( 0 , L ) | 2 , for ln U ≫ 1 , ψ ( x , z ) being the solution to ∂ z ψ − i 2 m ∇ ⊥ 2 ψ = g | S | 2 ψ , where S ( x , z ) is a complex Gaussian random field, z and x respectively are the axial and transverse coordinates, with 0 ⩽ z ⩽ L , and both m ≠ 0 and g &gt; 0 are real parameters. We perform the first instanton analysis of the corresponding Martin-Siggia-Rose action, from which it is found that the realizations of S concentrate onto long filamentary instantons, as ln U → + ∞ . The tail of p ( U ) is deduced from the statistics of the instantons. The value of g above which ⟨ U ⟩ diverges coincides with the one obtained by the completely different approach developed in Mounaix et al (2006 Commun. Math. Phys. 264 741). Numerical simulations clearly show a statistical bias of S towards the instanton for the largest sampled values of ln U . The high maxima—or ‘hot spots’—of | S ( x , z ) | 2 for the biased realizations of S tend to cluster in the instanton region.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-10" status="VALID">
          <idno type="IdRef">034052526</idno>
          <idno type="ISNI">0000000121659021</idno>
          <idno type="RNSR">199719343T</idno>
          <idno type="ROR">https://ror.org/02bsd9p69</idno>
          <idno type="Wikidata">Q16008925</idno>
          <orgName>Centre de Physique Théorique</orgName>
          <orgName type="acronym">CPHT</orgName>
          <date type="start">1997-01-01</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.cpht.polytechnique.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300340" type="direct"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation name="UMR7644" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300340" status="VALID">
          <idno type="IdRef">027309320</idno>
          <idno type="ISNI">0000000121581279</idno>
          <idno type="ROR">https://ror.org/05hy3tk52</idno>
          <idno type="Wikidata">Q273626</idno>
          <orgName>École polytechnique</orgName>
          <orgName type="acronym">X</orgName>
          <date type="start">1794-03-11</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.polytechnique.edu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-563936" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-563936" status="VALID">
          <idno type="IdRef">238327159</idno>
          <idno type="ISNI">0000000502717600</idno>
          <idno type="ROR">https://ror.org/042tfbd02</idno>
          <idno type="Wikidata">Q48759778</idno>
          <orgName>Institut Polytechnique de Paris</orgName>
          <orgName type="acronym">IP Paris</orgName>
          <date type="start">2019-06-02</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91120 Palaiseau Cedex, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ip-paris.fr</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>