Dynamical Localization for Random Band Matrices Up to W≪N1/4

Giorgio Cipolloni; Ron Peled; Jeffrey Schenker; Jacob Shapiro

doi:10.1007/s00220-024-04948-1

Dynamical Localization for Random Band Matrices Up to W≪N1/4

Giorgio Cipolloni, Ron Peled, Jeffrey Schenker, Jacob Shapiro

Mathematics

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

Abstract

We prove that a large class of N×N Gaussian random band matrices with band width W exhibits dynamical Anderson localization at all energies when W≪N^1/4. The proof uses the fractional moment method (Aizenman and Molchanov in Commun Math Phys 157(2):245–278, 1993. https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-157/issue-2/Localizationat-large-disorder-and-at-extreme-energies–an/cmp/1104253939.full) and an adaptive Mermin–Wagner style shift.

Original language	English (US)
Article number	82
Journal	Communications In Mathematical Physics
Volume	405
Issue number	3
DOIs	https://doi.org/10.1007/s00220-024-04948-1
State	Published - Mar 2024

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "We prove that a large class of N×N Gaussian random band matrices with band width W exhibits dynamical Anderson localization at all energies when W≪N1/4. The proof uses the fractional moment method (Aizenman and Molchanov in Commun Math Phys 157(2):245–278, 1993. https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-157/issue-2/Localizationat-large-disorder-and-at-extreme-energies–an/cmp/1104253939.full) and an adaptive Mermin–Wagner style shift.",

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AU - Peled, Ron

AU - Schenker, Jeffrey

AU - Shapiro, Jacob

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.

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AB - We prove that a large class of N×N Gaussian random band matrices with band width W exhibits dynamical Anderson localization at all energies when W≪N1/4. The proof uses the fractional moment method (Aizenman and Molchanov in Commun Math Phys 157(2):245–278, 1993. https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-157/issue-2/Localizationat-large-disorder-and-at-extreme-energies–an/cmp/1104253939.full) and an adaptive Mermin–Wagner style shift.

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Dynamical Localization for Random Band Matrices Up to W≪N1/4

Abstract

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