Wang J, Lai CH, Gu Y. Ergodicity and scars of the quantum cat map in the semiclassical regime.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001;
63:056208. [PMID:
11414991 DOI:
10.1103/physreve.63.056208]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2000] [Revised: 12/14/2000] [Indexed: 05/23/2023]
Abstract
We study the quantum localization effect of the cat map manifested in the motions of statistical ensembles. Specifically, the coarse-grained entropy and time-averaged phase space distributions are investigated. For this purpose, an amended version of the Wigner function on the discretized phase torus is presented. We find that the time average of the coarse-grained Wigner function is scarred (antiscarred) along some short periodic orbits, and the heights (depths) of these scars (antiscars) decrease in a linear way with the Planck constant when the semiclassical limit is approached. The relationship between the scars observed here and those exhibited in the quasienergy eigenstates is discussed.
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