Dynamical complexity in the quantum to classical transition

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

doi:10.48550/arxiv.1604.02743

Cited by 5 publications

(13 citation statements)

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“…There were recent reports of emergence of chaos in the quantum regime in absence of classical chaos. 77,78 In these works, the quantum versus classical "weights" of the system is controlled by the effective Planck constant, where the classical limit is reached when the constant approaches zero. In our system, the parameter g 0 plays the same role.…”

Section: Remark 1: Transient Chaos In Quantum Systems -What Does It M...mentioning

confidence: 99%

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics

Wang¹,

Lai²,

Grebogi³

2016

Sci Rep

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Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law.

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Section: Remark 1: Transient Chaos In Quantum Systems -What Does It M...mentioning

confidence: 99%

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics

Wang¹,

Lai²,

Grebogi³

2016

Sci Rep

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“…In particular, the study of the effects of the coupling details on the chaotic behaviour [11] and of puzzling results in optomechanics [12] have provided with very interesting advances. In this context, quantum chaotic attractors with apparently no classical counterpart have been found in the open dissipative quantum Duffing system [13]. On the other hand, despite known discrepancies [16,25] for some limited cases and surviving quantum effects, effective classical maps with Gaussian noise have been proposed as a direct replacement to obtain the main features of quantum dissipative systems.…”

Section: Discussionmentioning

confidence: 99%

“…Finally, it was recently claimed that quantum chaotic attractors (i.e. complex quantum equilibrium states typically associated to classical chaotic attractors) with no classical * carlo@tandar.cnea.gov.ar counterpart exist in the open dissipative quantum Duffing system [13].…”

Section: Introductionmentioning

confidence: 99%

Classical counterparts of quantum attractors in generic dissipative systems

et al. 2017

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In the context of dissipative systems, we show that for any quantum chaotic attractor a corresponding classical chaotic attractor can always be found. We provide a general way to locate them, rooted in the structure of the parameter space (which is typically bidimensional, accounting for the forcing strength and dissipation parameters). In cases where an approximate pointlike quantum distribution is found, it can be associated with exceptionally large regular structures. Moreover, supposedly anomalous quantum chaotic behavior can be very well reproduced by the classical dynamics plus Gaussian noise of the size of an effective Planck constant ℏ_{eff}. We give support to our conjectures by means of two paradigmatic examples of quantum chaos and transport theory. In particular, a dissipative driven system becomes fundamental in order to extend their validity to generic cases.

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“…In the former case, the evolution approaches that of the probability density in phase space for the equivalent classical system as the action is increased [4,7,15]. Continuous observation turns this probability density into individual trajectories that follow the nonlinear classical motion with the requisite Lyapunov exponents [12,15,17,18].…”

mentioning

confidence: 98%

“…There has been a great deal of interest in purely quantum systems, displaying unitary evolution, and non-unitary open quantum systems. This paper is concerned with open quantum systems whose classical counterparts are chaotic and make a transition to chaotic behavior as their size (more precisely their action) is increased so as to be large compared to [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. This transition is enabled by their interaction with the environment or when they are subjected to continuous observation.…”

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confidence: 99%

Observing quantum chaos with noisy measurements and highly mixed states

2017

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PHYSICAL REVIEW A 95, 012135 (2017) Observing quantum chaos with noisy measurements and highly mixed states A fundamental requirement for the emergence of classical behavior from an underlying quantum description is that certain observed quantum systems make a transition to chaotic dynamics as their action is increased relative to . While experiments have demonstrated some aspects of this transition, the emergence of quantum trajectories with a positive Lyapunov exponent has never been observed directly. Here, we remove a major obstacle to achieving this goal by showing that, for the Duffing oscillator, the transition to a positive Lyapunov exponent can be resolved clearly from observed trajectories even with measurement efficiencies as low as 20%. We also find that the positive Lyapunov exponent is robust to highly mixed, low-purity states and to variations in the parameters of the system.

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Dynamical complexity in the quantum to classical transition

Cited by 5 publications

References 0 publications

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics

Classical counterparts of quantum attractors in generic dissipative systems

Observing quantum chaos with noisy measurements and highly mixed states

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