Lifshitz asymptotics and localization for random quantum waveguides (Q2730406)
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scientific article; zbMATH DE number 1631104
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lifshitz asymptotics and localization for random quantum waveguides |
scientific article; zbMATH DE number 1631104 |
Statements
7 August 2001
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quantum waveguides
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domain perturbations
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random Schrödinger operator
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localization
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Lifshitz tails
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Lifshitz asymptotics and localization for random quantum waveguides (English)
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The paper is devoted to an investigation of ``quantum waveguide'', i.e. the two-dimensional motion of electrons in small channels which is mathematically represented by a family of Dirichlet Laplacians on randomly dented or bulged strips in \({\mathbb R}^2\). The principal tool is an abstract form of multi-scale analysis from [\textit{P. Stollmann}, Caught by disorder. Bound states in random media, Progress in Mathematical Physics, 20, Boston, Birkhäuser (2001; Zbl 0983.82016)] which allows to obtain Lifshitz asymptotics of the integrated density of states and to study domain perturbations of the Laplacian.
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