Localization in a highly correlated potential landscape

A. Bunde; S. Havlin; J. W. Kantelhardt; S. Russ; I. Webman

doi:10.1016/S0167-7322(99)00136-1

Localization in a highly correlated potential landscape

A. Bunde, S. Havlin, J. W. Kantelhardt, S. Russ, I. Webman

Department of Physics

Research output: Contribution to journal › Conference article › peer-review

4 Scopus citations

Abstract

We discuss the localization behavior of quantum particles in a one-dimensional Anderson model with correlated and uncorrelated random potentials. We are interested in the question if a localization-delocalization transition in these systems can occur and what the conditions are that allow for such a transition between localized and extended states. For the particular case of self-affine potential landscapes we show that a localization-delocalization transition reported recently only occurs, if the variance of the potential fluctuations is kept fixed for all system sizes. If no constraints on the variance are imposed, a new type of `strong' localization occurs in self-affine systems. All states are strongly localized in a way different from the usual Anderson localized states.

Original language	English
Pages (from-to)	151-161
Number of pages	11
Journal	Journal of Molecular Liquids
Volume	86
Issue number	1
DOIs	https://doi.org/10.1016/S0167-7322(99)00136-1
State	Published - Jun 2000
Event	The Polish-Israeli-German Symposium 'Dynamical Processes in Condensed Molecular Systems' - Cracow, Pol Duration: 19 Jun 1999 → 23 Jun 1999

Bibliographical note

Funding Information:
We thank the German Israeli Foundation and the Minerva Foundation for financial support.

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10.1016/S0167-7322(99)00136-1

Cite this

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abstract = "We discuss the localization behavior of quantum particles in a one-dimensional Anderson model with correlated and uncorrelated random potentials. We are interested in the question if a localization-delocalization transition in these systems can occur and what the conditions are that allow for such a transition between localized and extended states. For the particular case of self-affine potential landscapes we show that a localization-delocalization transition reported recently only occurs, if the variance of the potential fluctuations is kept fixed for all system sizes. If no constraints on the variance are imposed, a new type of `strong' localization occurs in self-affine systems. All states are strongly localized in a way different from the usual Anderson localized states.",

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note = "Funding Information: We thank the German Israeli Foundation and the Minerva Foundation for financial support.; The Polish-Israeli-German Symposium 'Dynamical Processes in Condensed Molecular Systems' ; Conference date: 19-06-1999 Through 23-06-1999",

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AU - Havlin, S.

AU - Kantelhardt, J. W.

AU - Russ, S.

AU - Webman, I.

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AB - We discuss the localization behavior of quantum particles in a one-dimensional Anderson model with correlated and uncorrelated random potentials. We are interested in the question if a localization-delocalization transition in these systems can occur and what the conditions are that allow for such a transition between localized and extended states. For the particular case of self-affine potential landscapes we show that a localization-delocalization transition reported recently only occurs, if the variance of the potential fluctuations is kept fixed for all system sizes. If no constraints on the variance are imposed, a new type of `strong' localization occurs in self-affine systems. All states are strongly localized in a way different from the usual Anderson localized states.

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Localization in a highly correlated potential landscape

Abstract

Bibliographical note

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