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arXiv · 1301.7278

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

Mario Castagnino·Ignacio Gomez
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Abstract

In this paper we translate the two higher levels of the Ergodic Hierarchy [1], the Kolmogorov level and the Bernoulli level, to quantum language. Moreover, this paper can be considered as the second part of [2]. As in paper [2], we consider the formalism where the states are positive functionals on the algebra of observables and we use the properties of the Wigner transform [3]. We illustrate the physical relevance of the Quantum Ergodic Hierarchy with two emblematic examples of the literature: the Casati-Prosen model [4], [5] and the kicked rotator [6], [7], [8].

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Mario Castagnino, Ignacio Gomez. 2013-09-16. Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems. https://doi.org/10.1016/j.physa.2013.08.070

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