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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.

Authors:
 [1];  [2]
  1. Departments of Physics and Mathematics, Princeton University, Princeton, New Jersey 08544 (United States)
  2. Zentrum Mathematik, TU Munich, Boltzmannstr. 3, 85747 Garching (Germany)
Publication Date:
OSTI Identifier:
22093718
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 53; Journal Issue: 9; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FLUCTUATIONS; GRAPH THEORY; PARTICLES; QUANTUM MECHANICS; RANDOMNESS; RESONANCE; SCHROEDINGER EQUATION; SPECTRA

Citation Formats

Aizenman, Michael, and Warzel, Simone. Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs. United States: N. p., 2012. Web. doi:10.1063/1.4714617.
Aizenman, Michael, & Warzel, Simone. Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs. United States. doi:10.1063/1.4714617.
Aizenman, Michael, and Warzel, Simone. Sat . "Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs". United States. doi:10.1063/1.4714617.
@article{osti_22093718,
title = {Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs},
author = {Aizenman, Michael and Warzel, Simone},
abstractNote = {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.},
doi = {10.1063/1.4714617},
journal = {Journal of Mathematical Physics},
number = 9,
volume = 53,
place = {United States},
year = {Sat Sep 15 00:00:00 EDT 2012},
month = {Sat Sep 15 00:00:00 EDT 2012}
}