Spectral properties of dissipative chaotic quantum maps

Chaos
Daniel Braun

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 variant Planck's over 2pi -->0. Numerically I find that even for finite variant Planck's over 2pi 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. (c) 1999 American Institute of Physics.

References

Jan 1, 1985·Physical Review A: General Physics·F WaldnerH Yamazaki
Jan 1, 1985·Physical Review. B, Condensed Matter·A HolzM Zuckermann
Feb 1, 1928·Proceedings of the National Academy of Sciences of the United States of America·J H Van Vleck

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Citations

Jun 4, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·B Georgeot, O Giraud
Feb 20, 2019·Physical Review. E·Gabriel G CarloMaría E Spina
Jul 13, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ignacio García-Mata, Marcos Saraceno
Aug 26, 2003·Physical Review Letters·Ignacio García-MataMaría Elena Spina
Jun 13, 2009·Physical Review Letters·Thomas Dittrich, Leonardo A Pachón

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