Quantum Hamiltonians with Weak Random Abstract Perturbation. II. Localization in the Expanded Spectrum

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F21%3A50017893" target="_blank" >RIV/62690094:18470/21:50017893 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s10955-020-02683-0" target="_blank" >https://link.springer.com/article/10.1007/s10955-020-02683-0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10955-020-02683-0" target="_blank" >10.1007/s10955-020-02683-0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Quantum Hamiltonians with Weak Random Abstract Perturbation. II. Localization in the Expanded Spectrum

Popis výsledku v původním jazyce

We consider multi-dimensional Schrodinger operators with a weak random perturbation distributed in the cells of some periodic lattice. In every cell the perturbation is described by the translate of a fixed abstract operator depending on a random variable. The random variables, indexed by the lattice, are assumed to be independent and identically distributed according to an absolutely continuous probability density. A small global coupling constant tunes the strength of the perturbation. We treat analogous random Hamiltonians defined on multi-dimensional layers, as well. For such models we determine the location of the almost sure spectrum and its dependence on the global coupling constant. In this paper we concentrate on the case that the spectrum expands when the perturbation is switched on. Furthermore, we derive a Wegner estimate and an initial length scale estimate, which together with Combes-Thomas estimate allow to invoke the multi-scale analysis proof of localization. We specify an energy region, including the bottom of the almost sure spectrum, which exhibits spectral and dynamical localization. Due to our treatment of general, abstract perturbations our results apply at once to many interesting examples both known and new.

Název v anglickém jazyce

Quantum Hamiltonians with Weak Random Abstract Perturbation. II. Localization in the Expanded Spectrum

Popis výsledku anglicky

We consider multi-dimensional Schrodinger operators with a weak random perturbation distributed in the cells of some periodic lattice. In every cell the perturbation is described by the translate of a fixed abstract operator depending on a random variable. The random variables, indexed by the lattice, are assumed to be independent and identically distributed according to an absolutely continuous probability density. A small global coupling constant tunes the strength of the perturbation. We treat analogous random Hamiltonians defined on multi-dimensional layers, as well. For such models we determine the location of the almost sure spectrum and its dependence on the global coupling constant. In this paper we concentrate on the case that the spectrum expands when the perturbation is switched on. Furthermore, we derive a Wegner estimate and an initial length scale estimate, which together with Combes-Thomas estimate allow to invoke the multi-scale analysis proof of localization. We specify an energy region, including the bottom of the almost sure spectrum, which exhibits spectral and dynamical localization. Due to our treatment of general, abstract perturbations our results apply at once to many interesting examples both known and new.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

JOURNAL OF STATISTICAL PHYSICS

ISSN

0022-4715

e-ISSN

—

Svazek periodika

182

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

48

Strana od-do

"Article Number: 1"

Kód UT WoS článku

000604097400001

EID výsledku v databázi Scopus

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