Upper bounds on wavepacket spreading for random Jacobi matrices
Jitomirskaya S, Schulz-Baldes H (2007)
Publication Type: Journal article
Publication year: 2007
Journal
Publisher: Springer Verlag (Germany)
Book Volume: 273
Pages Range: 601-618
URI: http://de.arxiv.org/abs/math-ph/0607029
DOI: 10.1007/s00220-007-0252-0
Abstract
A method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix. As an application, one obtains sharp upper bounds on the diffusion exponents for random polymer models, coinciding with the lower bounds obtained in a prior work. The second application is an elementary argument (not using multiscale analysis or the Aizenman-Molchanov method) showing that under the condition of uniformly positive Lyapunov exponents, the moments of the position operator grow at most logarithmically in time. © Springer-Verlag 2007.
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APA:
Jitomirskaya, S., & Schulz-Baldes, H. (2007). Upper bounds on wavepacket spreading for random Jacobi matrices. Communications in Mathematical Physics, 273, 601-618. https://dx.doi.org/10.1007/s00220-007-0252-0
MLA:
Jitomirskaya, Svetlana, and Hermann Schulz-Baldes. "Upper bounds on wavepacket spreading for random Jacobi matrices." Communications in Mathematical Physics 273 (2007): 601-618.
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