FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 5, PAGES 65-74

**On the notion of quantum Lyapunov exponent**

M. F. Kondratieva

T. A. Osborn

Abstract

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Classical chaos refers to the property of trajectories to diverge
exponentially as time $t\; \to $¥.
It is characterized by a positive Lyapunov exponent.
There are many different descriptions of quantum chaos.
One description related to the notion of generalized (quantum)
Lyapunov exponent is based either on qualitative physical
considerations or on the so-called symplectic tomography map.
The purpose of this note is to show how the definition of quantum
Lyapunov exponent naturally arises in the framework of the Moyal phase
space formulation of quantum mechanics, and is based on the notions of
quantum trajectories and the family of quantizers.
The role of the Heisenberg uncertainty principle in the statement of
the criteria for quantum chaos is made explicit.

Location: http://mech.math.msu.su/~fpm/eng/k06/k065/k06506h.htm

Last modified: February 21, 2007