Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems

Ignacio Gomez and Mario Castagnino

Physica A: Statistical Mechanics and its Applications, 2014, vol. 393, issue C, 112-131

Abstract: In this paper we translate the two higher levels of the Ergodic Hierarchy [11], the Kolmogorov level and the Bernoulli level, to quantum language. Moreover, this paper can be considered as the second part of [3]. As in [3], we consider the formalism where the states are positive functionals on the algebra of observables and we use the properties of the Wigner transform [12]. We illustrate the physical relevance of the Quantum Ergodic Hierarchy with two emblematic examples of the literature: the Casati–Prosen model [13,14] and the kicked rotator [6–8].

Keywords: Ergodic; Mixing; Kolmogorov; Bernoulli; EH; QEH (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:393:y:2014:i:c:p:112-131

DOI: 10.1016/j.physa.2013.08.070

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