Continuously Measured Chaotic Quantum Systems

Abstract

In this lecture we wish to examine how a dynamical quantum system which is chaotic in its classical limit, will be influenced by continuous observation in time with a certain limited accuracy and time resolution. In particular, we study in how far dynamical localization, a coherence effect responsible for the suppression of chaotic dynamics in certain quantum systems, remains effective if the system is continuously observed. First we explain the (conventional) view of the measurement process we adopt here; then we consider the quantum dynamics of a system continuously observed in time and analyse the response of the macroscopic measuring device (‘meter’). Thereby, we derive a general inequality relating its accuracy, its optimum time resolution, and the time scale of the observed system. As an application of this general analysis, we consider the continuous measurement of the angular-momentum distribution of a kicked quantum rotor as an application, and present the results of some numerical experiments. Finally we summarize some of our conclusions. A large part of this lecture is based on our work published in Refs. [1, 2].