ArticleChaos out of order: Quantum mechanics, the correspondence principle and chaos
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Stable regularities without governing laws?
2019, Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern PhysicsCitation Excerpt :Following Werndl (2009), define chaos in terms of strong mixing. ( Likewise, the present argument holds equally for the previous characterization by Belot and Earman (1997), where chaos is defined in terms of the higher Kolmogorov level, and for the characterization by Brading and Castellani (2013), who advocate seeing chaos as a matter of degree, quantified according to the position within the hierarchy: whatever the specific degree chosen, the present argument holds.) As we can see in the hierarchy, it follows that a Bernoulli system possesses the property of mixing; hence, it possesses the properties of a chaotic system.
KS–entropy and logarithmic time scale in quantum mixing systems
2018, Chaos, Solitons and FractalsCitation Excerpt :This remark is crucial in order to obtain the characteristic timescales of quantum chaos where the classically behavior and the chaotic one overlap each other [17–19]. On the other hand, many chaotic systems of interest are mixing, i.e. the subsets of phase space have a correlation decay such that any two subsets are statistically independent for large times [2,20–22]. This property is one of the most useful concepts to describe phenomena such as chaos, approach to equilibrium and relaxation in dynamical systems theory [7].
A Quantum Version of Spectral Decomposition Theorem of dynamical systems, quantum chaos hierarchy: Ergodic, mixing and exact
2015, Chaos, Solitons and FractalsOn the classical limit of quantum mechanics, fundamental graininess and chaos: Compatibility of chaos with the correspondence principle
2014, Chaos, Solitons and FractalsCitation Excerpt :As we mentioned in the introduction the key is to average a point-test-distribution function on minimal rectangular boxes of the phase space. The motivation of this approach lies in the fact that we can obtain a classical limit (and its limitations) searching the trajectories of the rectangular boxes (and later of the cells) we will consider as “points”, integrating the Heisenberg equation, and then studying the deformations of the cells under the motion (as in [10]). The Henon–Heiles system and the high energy problem
Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems
2014, Physica A: Statistical Mechanics and its ApplicationsCitation Excerpt :This way to define the quantum version of the Ergodic Hierarchy, based in the classical one, is the one that we will also use in this paper (see Table 2). As a consequence, following the ideas of Ref. [1] and the preceding paper [3], we will study the problem of quantum chaos hierarchy directly from the quantum description of the chaotic classical limit. So as in paper [3], that we consider as the first part of this paper, we have defined the quantum chaos in the two first levels of the ergodic hierarchy (EH): ergodic and mixing.
Towards a definition of the quantum ergodic hierarchy: Ergodicity and mixing
2009, Physica A: Statistical Mechanics and its Applications