Schrödinger operators with an electric field and random or deterministic potentials

F. Bentosela; R. Carmona; P. Duclos; B. Simon; B. Souillard; R. Weder

doi:10.1007/BF01213215

Schrödinger operators with an electric field and random or deterministic potentials

F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, R. Weder

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Abstract

We prove that the Schrödinger operator H=-d²/dx²+V(x)+F·x has purely absolutely continuous spectrum for arbitrary constant external field F, for a large class of potentials; this result applies to many periodic, almost periodic and random potentials and in particular to random wells of independent depth for which we prove that when F=0, the spectrum is almost surely pure point with exponentially decaying eigenfunctions.

Original language	English (US)
Pages (from-to)	387-397
Number of pages	11
Journal	Communications In Mathematical Physics
Volume	88
Issue number	3
DOIs	https://doi.org/10.1007/BF01213215
State	Published - Sep 1983
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01213215

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title = "Schr{\"o}dinger operators with an electric field and random or deterministic potentials",

abstract = "We prove that the Schr{\"o}dinger operator H=-d2/dx2+V(x)+F·x has purely absolutely continuous spectrum for arbitrary constant external field F, for a large class of potentials; this result applies to many periodic, almost periodic and random potentials and in particular to random wells of independent depth for which we prove that when F=0, the spectrum is almost surely pure point with exponentially decaying eigenfunctions.",

author = "F. Bentosela and R. Carmona and P. Duclos and B. Simon and B. Souillard and R. Weder",

year = "1983",

month = sep,

doi = "10.1007/BF01213215",

language = "English (US)",

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pages = "387--397",

journal = "Communications In Mathematical Physics",

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T1 - Schrödinger operators with an electric field and random or deterministic potentials

AU - Bentosela, F.

AU - Carmona, R.

AU - Duclos, P.

AU - Simon, B.

AU - Souillard, B.

AU - Weder, R.

PY - 1983/9

Y1 - 1983/9

N2 - We prove that the Schrödinger operator H=-d2/dx2+V(x)+F·x has purely absolutely continuous spectrum for arbitrary constant external field F, for a large class of potentials; this result applies to many periodic, almost periodic and random potentials and in particular to random wells of independent depth for which we prove that when F=0, the spectrum is almost surely pure point with exponentially decaying eigenfunctions.

AB - We prove that the Schrödinger operator H=-d2/dx2+V(x)+F·x has purely absolutely continuous spectrum for arbitrary constant external field F, for a large class of potentials; this result applies to many periodic, almost periodic and random potentials and in particular to random wells of independent depth for which we prove that when F=0, the spectrum is almost surely pure point with exponentially decaying eigenfunctions.

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ER -

Schrödinger operators with an electric field and random or deterministic potentials

Abstract

All Science Journal Classification (ASJC) codes

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