A TOPOLOGICAL APPROACH TO PHASE OF QUANTUM CHAOS

摘要

We explain the underlying ideas in our study of the relationship between quantum chaos and statistical mechanics.rnThis study consists of the following two steps. The first is to focus attention to topological defects of phase in the Husimi representation for quantum dynamics corresponding to chaos. This reveals characteristic features of quantum chaos corresponding to the folding of horseshoe dynamics in classical chaos. The second is to investigate the phase retrieval problem of quantum chaos. This shows a close connection between the difficulty of phase retrieval and the characteristics of topological defects of quantum chaos.rnBased on these results, we suggest that the difficulty of phase retrieval is crucial for the loss of phase information in quantum statistical mechanics, when we take into account not only measurement but also information processes on statistical ensembles.