Localization in one dimensional random media: A scattering theoretic approach

Robert Sims; Günter Stolz

doi:10.1007/s002200000251

Localization in one dimensional random media: A scattering theoretic approach

Robert Sims, Günter Stolz

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

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Abstract

We use scattering theoretic methods to prove exponential localization for random displacement models in one dimension. The operators we consider model both quantum and classical wave propagation. Our main tools are the reflection and transmission coefficients for compactly supported single site perturbations. We show that randomly displaced, non-reflectionless single sites lead to localization.

Original language	English (US)
Pages (from-to)	575-597
Number of pages	23
Journal	Communications in Mathematical Physics
Volume	213
Issue number	3
DOIs	https://doi.org/10.1007/s002200000251
State	Published - Oct 2000
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s002200000251

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title = "Localization in one dimensional random media: A scattering theoretic approach",

abstract = "We use scattering theoretic methods to prove exponential localization for random displacement models in one dimension. The operators we consider model both quantum and classical wave propagation. Our main tools are the reflection and transmission coefficients for compactly supported single site perturbations. We show that randomly displaced, non-reflectionless single sites lead to localization.",

author = "Robert Sims and G{\"u}nter Stolz",

year = "2000",

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doi = "10.1007/s002200000251",

language = "English (US)",

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journal = "Communications in Mathematical Physics",

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AU - Sims, Robert

AU - Stolz, Günter

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N2 - We use scattering theoretic methods to prove exponential localization for random displacement models in one dimension. The operators we consider model both quantum and classical wave propagation. Our main tools are the reflection and transmission coefficients for compactly supported single site perturbations. We show that randomly displaced, non-reflectionless single sites lead to localization.

AB - We use scattering theoretic methods to prove exponential localization for random displacement models in one dimension. The operators we consider model both quantum and classical wave propagation. Our main tools are the reflection and transmission coefficients for compactly supported single site perturbations. We show that randomly displaced, non-reflectionless single sites lead to localization.

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EP - 597

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -

Localization in one dimensional random media: A scattering theoretic approach

Abstract

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