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arXiv:1604.02743

Dynamical complexity in the quantum to classical transition

Bibek Pokharel, Peter Duggins, Moses Misplon, Walter Lynn, Kevin Hallman, Dustin Anderson, Arie Kapulkin, Arjendu K. Pattanayak

Published Apr 10, 2016• 4 citations
arXivHTMLPDF

Abstract

We study the dynamical complexity of an open quantum driven double-well oscillator, mapping its dependence on effective Planck's constant $\hbar_{eff}\equivβ$ and coupling to the environment, $Γ$. We study this using stochastic Schrodinger equations, semiclassical equations, and the classical limit equation. We show that (i) the dynamical complexity initially increases with effective Hilbert space size (as $β$ decreases) such that the most quantum systems are the least dynamically complex. (ii) If the classical limit is chaotic, that is the most dynamically complex (iii) if the classical limit is regular, there is always a quantum system more dynamically complex than the classical system. There are several parameter regimes where the quantum system is chaotic even though the classical limit is not. While some of the quantum chaotic attractors are of the same family as the classical limiting attractors, we also find a quantum attractor with no classical counterpart. These phenomena occur in experimentally accessible regimes.

DOI
10.48550/arxiv.1604.02743

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The relationship between classically chaotic dynamics and the entanglement properties of the corresponding quantum system is examined in the semiclassical limit. Numerical results are computed for a modified kicked top, keeping the classical dynamics constant while investigating the entanglement for several versions of the corresponding quantum system characterized by a different value of the effective Planck constant ℏ eff. Our findings indicate that as ℏ eff → 0, the apparent signatures of classical chaos in the entanglement properties, such as characteristic oscillations in the time-dependence of the linear entropy, can also be obtained in the regular regime. These results suggest that entanglement is not a universal marker of chaotic dynamics of the corresponding classical system.
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We study how decoherence rules the quantum-classical transition of the kicked harmonic oscillator. The system presents classical dynamics that ranges from regular to strong chaotic behavior depending on the amplitude of the kicks. We show that for regular and mixed classical dynamics, and in the presence of noise, the distance between the classical and quantum phase space distributions is proportional to a single parameter chi identical to K Planck's (eff)(2)/4D(3/2) , which relates the effective Planck constant, Planck's (eff), to the kicking strength, K, and the diffusion constant, D. This relation between classical and quantum distributions is valid when chi<1 , a case that is always attainable in the semiclassical regime, independent of the value of the strength of noise given by D. Our results extend a recent study performed in the chaotic regime.