Lifschitz Tails for Random Schrödinger Operator in Bernoulli Distributed Potentials

Michael Bishop; Vita Borovyk; Jan Wehr

doi:10.1007/s10955-015-1242-9

Lifschitz Tails for Random Schrödinger Operator in Bernoulli Distributed Potentials

Michael Bishop, Vita Borovyk, Jan Wehr

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

2 Scopus citations

Abstract

This paper presents an elementary proof of Lifschitz tail behavior for random discrete Schrödinger operators with a Bernoulli-distributed potential. The proof approximates the low eigenvalues by eigenvalues of sine waves supported where the potential takes its lower value. This is motivated by the idea that the eigenvectors associated to the low eigenvalues react to the jump in the values of the potential as if the jump were infinite.

Original language	English (US)
Pages (from-to)	151-162
Number of pages	12
Journal	Journal of Statistical Physics
Volume	160
Issue number	1
DOIs	https://doi.org/10.1007/s10955-015-1242-9
State	Published - Jul 23 2015

Keywords

Bernoulli random variables
Lifschitz tail
Random Schrödinger operator

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-015-1242-9

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title = "Lifschitz Tails for Random Schr{\"o}dinger Operator in Bernoulli Distributed Potentials",

abstract = "This paper presents an elementary proof of Lifschitz tail behavior for random discrete Schr{\"o}dinger operators with a Bernoulli-distributed potential. The proof approximates the low eigenvalues by eigenvalues of sine waves supported where the potential takes its lower value. This is motivated by the idea that the eigenvectors associated to the low eigenvalues react to the jump in the values of the potential as if the jump were infinite.",

keywords = "Bernoulli random variables, Lifschitz tail, Random Schr{\"o}dinger operator",

author = "Michael Bishop and Vita Borovyk and Jan Wehr",

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AU - Borovyk, Vita

AU - Wehr, Jan

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N2 - This paper presents an elementary proof of Lifschitz tail behavior for random discrete Schrödinger operators with a Bernoulli-distributed potential. The proof approximates the low eigenvalues by eigenvalues of sine waves supported where the potential takes its lower value. This is motivated by the idea that the eigenvectors associated to the low eigenvalues react to the jump in the values of the potential as if the jump were infinite.

AB - This paper presents an elementary proof of Lifschitz tail behavior for random discrete Schrödinger operators with a Bernoulli-distributed potential. The proof approximates the low eigenvalues by eigenvalues of sine waves supported where the potential takes its lower value. This is motivated by the idea that the eigenvectors associated to the low eigenvalues react to the jump in the values of the potential as if the jump were infinite.

KW - Bernoulli random variables

KW - Lifschitz tail

KW - Random Schrödinger operator

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Lifschitz Tails for Random Schrödinger Operator in Bernoulli Distributed Potentials

Abstract

Keywords

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