Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems
Quantum Physics
2014-11-13 v3 Mathematical Physics
math.MP
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].
Keywords
Cite
@article{arxiv.1301.7278,
title = {Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems},
author = {Mario Castagnino and Ignacio Gomez},
journal= {arXiv preprint arXiv:1301.7278},
year = {2014}
}