The Approach to Ergodicity in the Quantum Baker's Map

2001/08/14 by Andrew N. Jordan, Andrew Jordan, Jordan, Andrew +2
Computer Science · Mathematics · Physics and Astronomy · #Advanced Algebra and Logic #Advanced Mathematical Identities #Chaotic Dynamics (nlin.CD) #Condensed Matter (cond-mat) #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #cond-mat #nlin.CD #quant-ph

paper · pdf · doi:10.48550/arxiv.nlin/0108024

14 pages, 3 figures; minor typos corrected in v2

openalex publication_date 2001/08/14 · arxiv created 2001/08/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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