Nonlinear Anderson Localized States at Arbitrary Disorder
Given an Anderson model H = - Δ + V in arbitrary dimensions, and assuming the model satisfies localization, we construct quasi-periodic in time (and localized in space) solutions for the nonlinear random Schrödinger equation i ∂ u ∂ t = - Δ u + V u + δ | u | 2 p u for small δ . Our approach combines...
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| Veröffentlicht in: | Communications in mathematical physics 2024-11, Vol.405 (11), Article 272 |
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| container_title | Communications in mathematical physics |
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| creator | Liu, Wencai Wang, W.-M. |
| description | Given an Anderson model
H
=
-
Δ
+
V
in arbitrary dimensions, and assuming the model satisfies localization, we construct quasi-periodic in time (and localized in space) solutions for the nonlinear random Schrödinger equation
i
∂
u
∂
t
=
-
Δ
u
+
V
u
+
δ
|
u
|
2
p
u
for small
δ
. Our approach combines probabilistic estimates from the Anderson model with the Craig–Wayne–Bourgain method for studying quasi-periodic solutions of nonlinear PDEs. |
| doi_str_mv | 10.1007/s00220-024-05150-z |
| format | Article |
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H
=
-
Δ
+
V
in arbitrary dimensions, and assuming the model satisfies localization, we construct quasi-periodic in time (and localized in space) solutions for the nonlinear random Schrödinger equation
i
∂
u
∂
t
=
-
Δ
u
+
V
u
+
δ
|
u
|
2
p
u
for small
δ
. Our approach combines probabilistic estimates from the Anderson model with the Craig–Wayne–Bourgain method for studying quasi-periodic solutions of nonlinear PDEs.</description><identifier>ISSN: 0010-3616</identifier><identifier>EISSN: 1432-0916</identifier><identifier>DOI: 10.1007/s00220-024-05150-z</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Classical and Quantum Gravitation ; Complex Systems ; Mathematical and Computational Physics ; Mathematical Physics ; Nonlinear differential equations ; Parabolic differential equations ; Partial differential equations ; Physics ; Physics and Astronomy ; Quantum Physics ; Relativity Theory ; Schrodinger equation ; Theoretical</subject><ispartof>Communications in mathematical physics, 2024-11, Vol.405 (11), Article 272</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c200t-1a564006527a7b4ea89e8ca0bcb89f355152fe41f7acae8fe9dc33e4cb7c620f3</cites><orcidid>0000-0001-5154-6474</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00220-024-05150-z$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00220-024-05150-z$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,781,785,27929,27930,41493,42562,51324</link.rule.ids></links><search><creatorcontrib>Liu, Wencai</creatorcontrib><creatorcontrib>Wang, W.-M.</creatorcontrib><title>Nonlinear Anderson Localized States at Arbitrary Disorder</title><title>Communications in mathematical physics</title><addtitle>Commun. Math. Phys</addtitle><description>Given an Anderson model
H
=
-
Δ
+
V
in arbitrary dimensions, and assuming the model satisfies localization, we construct quasi-periodic in time (and localized in space) solutions for the nonlinear random Schrödinger equation
i
∂
u
∂
t
=
-
Δ
u
+
V
u
+
δ
|
u
|
2
p
u
for small
δ
. Our approach combines probabilistic estimates from the Anderson model with the Craig–Wayne–Bourgain method for studying quasi-periodic solutions of nonlinear PDEs.</description><subject>Classical and Quantum Gravitation</subject><subject>Complex Systems</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Physics</subject><subject>Nonlinear differential equations</subject><subject>Parabolic differential equations</subject><subject>Partial differential equations</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Schrodinger equation</subject><subject>Theoretical</subject><issn>0010-3616</issn><issn>1432-0916</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kLtOxDAQRS0EEmHhB6giURvGduwkZbQ8pQgKoLYcZ4yyCvFiZwv26zEEiY5qmnPvXB1CzhlcMoDyKgJwDhR4QUEyCXR_QDJWCE6hZuqQZAAMqFBMHZOTGDcAUHOlMlI_-mkcJjQhb6YeQ_RT3nprxmGPff48mxljbua8Cd0wBxM-8-sh-pDIU3LkzBjx7PeuyOvtzcv6nrZPdw_rpqWWA8yUGakKACV5acquQFPVWFkDne2q2gmZ1nKHBXOlsQYrh3VvhcDCdqVVHJxYkYuldxv8xw7jrDd-F6b0UgvGQUrBZZUovlA2-BgDOr0Nw3vaqxnob0V6UaSTIv2jSO9TSCyhmODpDcNf9T-pL86JaXY</recordid><startdate>20241101</startdate><enddate>20241101</enddate><creator>Liu, Wencai</creator><creator>Wang, W.-M.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-5154-6474</orcidid></search><sort><creationdate>20241101</creationdate><title>Nonlinear Anderson Localized States at Arbitrary Disorder</title><author>Liu, Wencai ; Wang, W.-M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-1a564006527a7b4ea89e8ca0bcb89f355152fe41f7acae8fe9dc33e4cb7c620f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Classical and Quantum Gravitation</topic><topic>Complex Systems</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Physics</topic><topic>Nonlinear differential equations</topic><topic>Parabolic differential equations</topic><topic>Partial differential equations</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Schrodinger equation</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Wencai</creatorcontrib><creatorcontrib>Wang, W.-M.</creatorcontrib><collection>CrossRef</collection><jtitle>Communications in mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Wencai</au><au>Wang, W.-M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Nonlinear Anderson Localized States at Arbitrary Disorder</atitle><jtitle>Communications in mathematical physics</jtitle><stitle>Commun. Math. Phys</stitle><date>2024-11-01</date><risdate>2024</risdate><volume>405</volume><issue>11</issue><artnum>272</artnum><issn>0010-3616</issn><eissn>1432-0916</eissn><abstract>Given an Anderson model
H
=
-
Δ
+
V
in arbitrary dimensions, and assuming the model satisfies localization, we construct quasi-periodic in time (and localized in space) solutions for the nonlinear random Schrödinger equation
i
∂
u
∂
t
=
-
Δ
u
+
V
u
+
δ
|
u
|
2
p
u
for small
δ
. Our approach combines probabilistic estimates from the Anderson model with the Craig–Wayne–Bourgain method for studying quasi-periodic solutions of nonlinear PDEs.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00220-024-05150-z</doi><orcidid>https://orcid.org/0000-0001-5154-6474</orcidid></addata></record> |
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| ispartof | Communications in mathematical physics, 2024-11, Vol.405 (11), Article 272 |
| issn | 0010-3616 1432-0916 |
| language | eng |
| recordid | cdi_proquest_journals_3120553258 |
| source | SpringerNature Journals |
| subjects | Classical and Quantum Gravitation Complex Systems Mathematical and Computational Physics Mathematical Physics Nonlinear differential equations Parabolic differential equations Partial differential equations Physics Physics and Astronomy Quantum Physics Relativity Theory Schrodinger equation Theoretical |
| title | Nonlinear Anderson Localized States at Arbitrary Disorder |
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