Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs

Michael Aizenman; Simone Warzel

doi:10.1063/1.4714617

Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs

Michael Aizenman
, Simone Warzel

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

26 Scopus citations

Abstract

We discuss the dynamical implications of the recent proof that for a quantum particle in a random potential on a regular tree graph absolutely continuous (ac) spectrum occurs non-perturbatively through rare fluctuation-enabled resonances. The main result is spelled in the title.

Original language	English (US)
Article number	095205
Journal	Journal of Mathematical Physics
Volume	53
Issue number	9
DOIs	https://doi.org/10.1063/1.4714617
State	Published - Sep 28 2012

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.4714617

Cite this

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title = "Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs",

abstract = "We discuss the dynamical implications of the recent proof that for a quantum particle in a random potential on a regular tree graph absolutely continuous (ac) spectrum occurs non-perturbatively through rare fluctuation-enabled resonances. The main result is spelled in the title.",

author = "Michael Aizenman and Simone Warzel",

note = "Funding Information: We are grateful for the National Science Foundation (NSF) support of the research presented here, which was supported in part by Grant Nos. PHY-1104596 (M.A.) and DMS-0701181 (S.W.).",

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AU - Warzel, Simone

N1 - Funding Information: We are grateful for the National Science Foundation (NSF) support of the research presented here, which was supported in part by Grant Nos. PHY-1104596 (M.A.) and DMS-0701181 (S.W.).

PY - 2012/9/28

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N2 - We discuss the dynamical implications of the recent proof that for a quantum particle in a random potential on a regular tree graph absolutely continuous (ac) spectrum occurs non-perturbatively through rare fluctuation-enabled resonances. The main result is spelled in the title.

AB - We discuss the dynamical implications of the recent proof that for a quantum particle in a random potential on a regular tree graph absolutely continuous (ac) spectrum occurs non-perturbatively through rare fluctuation-enabled resonances. The main result is spelled in the title.

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Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs

Abstract

All Science Journal Classification (ASJC) codes

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