Parameter Scaling in the Decoherent Quantum-Classical Transition for Chaotic Systems

Pattanayak, Arjendu K.; Sundaram, Bala; Greenbaum, Benjamin

doi:10.1103/physrevlett.90.014103

Cited by 34 publications

(47 citation statements)

References 14 publications

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“…However that extrapolated limit is substantially smaller than the typical statistical errors for ensemble sizes of 1,000,000 to 2,000,000, and so is not significantly The maximum value of |qm − cl| 1 for the quantum and classical probability distributions must depend on the three parameters β, σ, and τ c . However, in agreement with arguments presented by Pattanayak et al [17], the data was found to collapse onto a single curve parameterized by ξ = β 2 /D (Fig. 23).…”

Section: A Environmental Effects In the Saturation Regimesupporting

confidence: 90%

Quantum mechanics of Hyperion

Wiebe

Ballentine

2005

Phys. Rev. A

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This paper is motivated by the suggestion [W. Zurek, Physica Scripta, T76, 186 (1998)] that the chaotic tumbling of the satellite Hyperion would become non-classical within 20 years, but for the effects of environmental decoherence. The dynamics of quantum and classical probability distributions are compared for a satellite rotating perpendicular to its orbital plane, driven by the gravitational gradient. The model is studied with and without environmental decoherence. Without decoherence, the maximum quantum-classical (QC) differences in its average angular momentum scale as 2/3 for chaotic states, and as 2 for non-chaotic states, leading to negligible QC differences for a macroscopic object like Hyperion. The quantum probability distributions do not approach their classical limit smoothly, having an extremely fine oscillatory structure superimposed on the smooth classical background. For a macroscopic object, this oscillatory structure is too fine to be resolved by any realistic measurement. Either a small amount of smoothing (due to the finite resolution of the apparatus) or a very small amount of environmental decoherence is sufficient ensure the classical limit. Under decoherence, the QC differences in the probability distributions scale as ( 2 /D) 1/6 , where D is the momentum diffusion parameter. We conclude that decoherence is not essential to explain the classical behavior of macroscopic bodies.

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Section: A Environmental Effects In the Saturation Regimesupporting

confidence: 90%

Quantum mechanics of Hyperion

Wiebe

Ballentine

2005

Phys. Rev. A

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“…1, we quantify the correlation between any two quantities f (θ, φ) and g(θ, φ) as a generalized Kullback-Liebler distance [14]. Here Tr denotes the trace or double integral over the variables (θ, φ).…”

Section: B Comparison Of Correlationsmentioning

confidence: 99%

Entanglement and its relationship to classical dynamics

2017

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We present an analysis of the entangling quantum kicked top focusing on the few qubit case and the initial condition dependence of the time-averaged entanglement SQ for spin-coherent states. We show a very strong connection between the classical phase space and the initial condition dependence of SQ even for the extreme case of two spin-1/2 qubits. This correlation is not related directly to chaos in the classical dynamics. We introduce a measure of the behavior of a classical trajectory which correlates far better with the entanglement and show that the maps of classical and quantum initial-condition dependence are both organized around the symmetry points of the Hamiltonian. We also show clear (quasi-)periodicity in entanglement as a function of number of kicks and of kick strength.

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“…For a classically chaotic, one-dimensional, time-dependent Hamiltonian, it was found that the interaction with a large (Markovian) environment would transform the dynamics of the Wigner function into that of the classical phase-space density, at least under some circumstances [19]. The study of the quantum-to-classical transition for phasespace densities under generic environmental interactions is often referred to as "decoherence" [20,21]. Heuristic arguments were devised to explain this phenomenon for classically chaotic systems [20] although, due to the complexity of the quantum and classical evolution equations for these systems, such arguments are not easy to make precise.…”

Section: Introductionmentioning

confidence: 99%

Conditions for the quantum-to-classical transition: Trajectories versus phase-space distributions

2007

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We contrast two sets of conditions that govern the transition in which classical dynamics emerges from the evolution of a quantum system. The first was derived by considering the trajectories seen by an observer (dubbed the "strong" transition) [Bhattacharya et al., Phys. Rev. Lett. 85 4852 (2000)], and the second by considering phase-space densities (the "weak" transition) [Greenbaum et al., Chaos 15, 033302 (2005)]. On the face of it these conditions appear rather different. We show, however, that in the semiclassical regime, in which the action of the system is large compared to , and the measurement noise is small, they both offer an essentially equivalent local picture. Within this regime, the weak conditions dominate while in the opposite regime where the action is not much larger than , the strong conditions dominate.

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Parameter Scaling in the Decoherent Quantum-Classical Transition for Chaotic Systems

Cited by 34 publications

References 14 publications

Quantum mechanics of Hyperion

Quantum mechanics of Hyperion

Entanglement and its relationship to classical dynamics

Conditions for the quantum-to-classical transition: Trajectories versus phase-space distributions

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