Upper quantum Lyapunov exponent and parametric oscillators

We introduce a definition of upper Lyapunov exponent for quantum systems in the Heisenberg representation, and apply it to parametric quantum oscillators. We provide a simple proof that the upper quantum Lyapunov exponent ranges from zero to a positive value, as the parameters range from the classic...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical physics 2004-11, Vol.45 (11), p.4377-4385
Main Authors: Jauslin, H. R., Sapin, O., Guérin, S., Wreszinski, W. F.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical analysis
Mathematical methods in physics
Mathematics
Mechanics
Oscillators
Physics
Quantum theory
Sciences and techniques of general use
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We introduce a definition of upper Lyapunov exponent for quantum systems in the Heisenberg representation, and apply it to parametric quantum oscillators. We provide a simple proof that the upper quantum Lyapunov exponent ranges from zero to a positive value, as the parameters range from the classical system’s region of stability to the instability region. It is also proved that in the instability region the parametric quantum oscillator satisfies the discrete quantum Anosov relations defined by Emch, Narnhofer, Sewell, and Thirring.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1803926