Spectral localization for quantum Hamiltonians with weak random delta interaction

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F18%3A50014838" target="_blank" >RIV/62690094:18470/18:50014838 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.crma.2018.04.023" target="_blank" >http://dx.doi.org/10.1016/j.crma.2018.04.023</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.crma.2018.04.023" target="_blank" >10.1016/j.crma.2018.04.023</a>

Result language
angličtina
Original language name
Spectral localization for quantum Hamiltonians with weak random delta interaction
Original language description
We consider a negative Laplacian in multi-dimensional Euclidean space (or a multi-dimensional layer) with a weak disorder random perturbation. The perturbation consists of a sum of lattice translates of a delta interaction supported on a compact manifold of co-dimension one and modulated by coupling constants, which are independent identically distributed random variables times a small disorder parameter. We establish that the spectrum of the considered operator is almost surely a fixed set, characterize its minimum, give an initial length scale estimate and the Wegner estimate, and conclude that there is a small zone of a pure point spectrum containing the almost sure spectral bottom. The length of this zone is proportional to the small disorder parameter. (C) 2018 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
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
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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