Braun Daniel
FB7, Universitat-GHS Essen, 45 117 Essen, Germany.
Chaos. 1999 Sep;9(3):730-737. doi: 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 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.
我借助最近发现的半经典迹公式研究了一个耗散混沌量子映射的谱性质。我表明，在存在少量耗散的情况下，约化密度矩阵传播子的任何有限幂次的迹，以及其经典对应物弗罗贝尼乌斯 - 佩龙算子的迹，在普朗克常数除以(2\pi)趋于零的极限情况下是相同的。通过数值计算我发现，即使对于有限的普朗克常数除以(2\pi)，二者的一致性也可能非常好。如果经典相空间包含一个奇异吸引子，只要避开分岔点，这种情况尤其成立。如果经典动力学由一个强点吸引子主导，那么映射迭代的量子传播子的迹与弗罗贝尼乌斯 - 佩龙算子的相应迹吻合得很好。（c）1999美国物理研究所。
