The Approach to Ergodicity in the Quantum Baker's Map

Details The Approach to Ergodicity in the Quantum Baker's Map The Approach to Ergodicity in the Quantum Baker's Map

2001-08-14

arxiv.org/abs/nlin/0108024v2

Nonlinear Sciences

Chaotic Dynamics

14 pages, 3 figures; minor typos corrected in v2

Scientific paper

We study the quantum mechanics of a generalized version of the baker's map. We show that the Ruelle resonances (which govern the approach to ergodicity of classical distributions on phase space) also appear in the quantum correlation functions of observables at different times, and hence control the statistical variance of matrix elements of observables (in the basis of eigenstates of the quantum time evolution operator). We illustrate this with numerical results.

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