Quantum Chaos in Terms of Entropy for a Periodically Kicked Top

Decoherence and Noise in Loschmidt Echo Experiments

“…The results confirm the expectation that the behavior of I 2 should be essentially the same as for the von Neumann entropy used previously in different examples [4,7]. This expectation is based on the Shannon−McMillan-Breiman theorem for classical systems [11] which translated to the quantum domain implies that for large N the density matrix [ÊÛ ⊗ 1 N ] n (|Ψ max Ψ max |) satisfies "microcanonical condition", i.e., all eigenvalues are practically equal (in logarithmic scale) or vanish.…”

“…Therefore for large enough N and the choice of the mapΛ such that ln K > h KS we can expect a linear increase in S[n] with the slope approximately equal to h KS up to the saturation point 2 ln N . Indeed such a short time semiclassical behavior has been observed in [7,4] for the von Neumann entropy.…”

Quantum chaos, random matrix theory, statistical mechanics in two dimensions, and the second law - a case study

“…In section 4, we unify the different streams of thought from quantum chaos, random matrix theory, and statistical mechanics by discussing entropy which is fundamental to all the three. We would like to mention that a recent work [19] is an interesting companion of this paper. We conclude the paper with a summary.…”

Completely mixing quantum open systems and quantum fractals

“…For example, they reveal significant differences in the character of their wave functions or the distribution of their energy levels [2]. Also the numerical analysis of some finite quantum systems shows quantitative differences in regular and chaotic regime [3]. It is obvious that on the quantum level the distinction between chaotic and quasiperiodic behavior must be blurred, nevertheless some relative measure of the degree of chaos should exist.…”