Walter Thirring
What are the Quantum Mechanical Lyapunov Exponents
The paper is published: in: H. Grosse et. al. (eds) "Low-dimensional models in statistical physics and quantum field theory. Proceedings of the 34. Internationale Universitaetswochen fuer Kern- und Teilchenphysik, Schladming, Austria, March 4-11, 1995", Lect. Notes Phys. 469, Springer-Verlag 1996, 223-237

MSC:

28D20 Entropy and other invariants

46L55 Noncommutative dynamical systems, See also {28Dxx, 54H20,

81R99 None of the above but in this section

Abstract: The origin of chaotic behaviour of a dynamical system in the sense of
sensitive dependence on initial conditions is the action of a certain
group. We are used to the importance of a group from the theory of
relativity and in fact this group happens to be a subgroup of the
Poincare group. Physical consequences like sensitive dependence on
initial conditions or exponential decay of time correlations can be
deduced if we add some continuity requirements on the action of this
group. This will be illustrated by examples from classical mechanics,
quantum mechanics and quantum field theory.


Keywords: dynamical system, entropy, quantum mechanics, quantum field theory, Lyapunov exponents