Anderson localization for time periodic random Schrödinger operators

Avy Soffer; Wei Min Wang

doi:10.1081/PDE-120019385

Anderson localization for time periodic random Schrödinger operators

Avy Soffer, Wei Min Wang

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We prove that at large disorder, Anderson localization in Z^d is stable under localized time-periodic perturbations by proving that the associated quasi-energy operator has pure point spectrum. The formulation of this problem is motivated by questions of Anderson localization for non-linear Schrödinger equations.

Original language	English (US)
Pages (from-to)	333-347
Number of pages	15
Journal	Communications in Partial Differential Equations
Volume	28
Issue number	1-2
DOIs	https://doi.org/10.1081/PDE-120019385
State	Published - 2003

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Keywords

Anderson localization
Floquet operator
Quasi-energy operator

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10.1081/PDE-120019385

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title = "Anderson localization for time periodic random Schr{\"o}dinger operators",

abstract = "We prove that at large disorder, Anderson localization in Zd is stable under localized time-periodic perturbations by proving that the associated quasi-energy operator has pure point spectrum. The formulation of this problem is motivated by questions of Anderson localization for non-linear Schr{\"o}dinger equations.",

keywords = "Anderson localization, Floquet operator, Quasi-energy operator",

author = "Avy Soffer and Wang, {Wei Min}",

note = "Funding Information: We thank J. Bourgain, M. Combescure, J. Lebowitz, T. Spencer, and M. Weinstein for useful conversations. W.-M. Wang thanks Rutgers University, where part of this work was done, for its hospitality. This work is partially supported by Rutgers center for non-linear analysis and NSF grants DMS-0100490 and DMR-9813268.",

year = "2003",

doi = "10.1081/PDE-120019385",

language = "English (US)",

volume = "28",

pages = "333--347",

journal = "Communications in Partial Differential Equations",

issn = "0360-5302",

publisher = "Taylor and Francis Ltd.",

number = "1-2",

}

TY - JOUR

T1 - Anderson localization for time periodic random Schrödinger operators

AU - Soffer, Avy

AU - Wang, Wei Min

N1 - Funding Information: We thank J. Bourgain, M. Combescure, J. Lebowitz, T. Spencer, and M. Weinstein for useful conversations. W.-M. Wang thanks Rutgers University, where part of this work was done, for its hospitality. This work is partially supported by Rutgers center for non-linear analysis and NSF grants DMS-0100490 and DMR-9813268.

PY - 2003

Y1 - 2003

N2 - We prove that at large disorder, Anderson localization in Zd is stable under localized time-periodic perturbations by proving that the associated quasi-energy operator has pure point spectrum. The formulation of this problem is motivated by questions of Anderson localization for non-linear Schrödinger equations.

AB - We prove that at large disorder, Anderson localization in Zd is stable under localized time-periodic perturbations by proving that the associated quasi-energy operator has pure point spectrum. The formulation of this problem is motivated by questions of Anderson localization for non-linear Schrödinger equations.

KW - Anderson localization

KW - Floquet operator

KW - Quasi-energy operator

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UR - http://www.scopus.com/inward/citedby.url?scp=0038134845&partnerID=8YFLogxK

U2 - 10.1081/PDE-120019385

DO - 10.1081/PDE-120019385

M3 - Article

AN - SCOPUS:0038134845

SN - 0360-5302

VL - 28

SP - 333

EP - 347

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 1-2

ER -

Anderson localization for time periodic random Schrödinger operators

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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