Spectral properties of Dissipative Chaotic Quantum Maps

Abstract

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 $\hslash \to 0$. Numerically I find that even for finite $\hslash$ 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.

14 pages of revtex, including 6 ps-figures

References in corpus (3)

• Decoherence Free Subspaces for Quantum Computation
• Decoherence, Chaos, and the Correspondence Principle
• WKB for a damped spin

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• Time-domain scars: resolving the spectral form factor in phase space
• 3D classical and quantum stable structures of dissipative systems
• Chaos simplifies quantum friction
• Quantum computing of semiclassical formulas
• Classical projected phase space density of billiards and its relation to the quantum Neumann spectrum
• Quantum metrology with a non-linear kicked Mach-Zehnder interferometer
• Correspondence principle, dissipation, and Ginibre ensemble