Spectral properties of Dissipative Chaotic Quantum Maps

Details Spectral properties of Dissipative Chaotic Quantum Maps Spectral properties of Dissipative Chaotic Quantum Maps

1999-03-29

arxiv.org/abs/chao-dyn/9904002v1

Nonlinear Sciences

Chaotic Dynamics

14 pages of revtex, including 6 ps-figures

Scientific paper

10.1063/1.166447

I examine spectral properties of a dissipative chaotic quantum map with the help of a recently discovered semiclassical trace formula. I show that in the presence of a small amount of dissipation the traces of any finite power of the propagator of the reduced density matrix, and traces of its classical counterpart, the Frobenius-Perron operator, are identical in the limit of $\hbar\to 0$. Numerically I find that even for finite $\hbar$ the agreement can be very good. This holds in particular if the classical phase space contains a strange attractor, as long as one stays clear of bifurcations. Traces of the quantum propagator for iterations of the map agree well with the corresponding traces of the Frobenius-Perron operator if the classical dynamics is dominated by a strong point attractor.

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