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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Quantum Hamiltonians with Weak Random Abstract Perturbation. II. Localization in the Expanded Spectrum
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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