Dynamical Entropy in Quantum Theory

摘要

The theory of dynamical systems was initiated by the attempt of physicists to understand the approach to equilibrium. In the mean time it has become a highly developed field, but its application to physical problems is somewhat limited, because it is based on measure theory and therefore restricted to classical systems, whereas we know that nature, at least on a microscopic level, has to be described by quantum laws. Therefore it will be our aim to translate concepts of measure theory that have turned out to be useful, into the quantum language. One of these concepts is the so-called dynamical entropy of flows that on one hand gives a qualitative characterization of those automorphisms with the best mixing behaviour, and in addition is also a quantitative measure how fast the system is mixed. We have been able to define a corresponding quantity also for quantum systems with a number of promising properties. To gain as much information about the system from this dynamical entropy as it was possible in the classical situation will be a challenge for the future. 19 refs. (Atomindex citation 20:006785)