Ergodicity and scars of the quantum cat map in the semiclassical regime.
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.
Wang
J
J
Department of Physics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore.
Lai
C H
CH
Gu
Y
Y