Comparison of classical chaos with quantum chaos

Caron, Laurent; Huard, D.J.E.; Kröger, H.; Melkonyan, G.; Moriarty, K.J.M.; Nadeau, Louis

doi:10.1088/0305-4470/37/24/004

Cited by 5 publications

(5 citation statements)

References 28 publications

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“…In our opinion, the revival of KAM resonance 1 : 8 on the Husimi plots indicates the necessity of frequencydependent corrections to the standart ray approximation, when ray motion is strongly affected by small-scale features. A likely way of introducing such corrections is the construction of some effective sound-speed profile, using the homogenization procedures [39], or exploiting the quantum action [40]. We suppose that ray modeling with the effective sound-speed profile should be better consistent with wave pattern.…”

Section: Discussionmentioning

confidence: 99%

Recovery of ordered periodic orbits with increasing wavelength for sound propagation in a range-dependent waveguide

et al. 2007

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We consider sound wave propagation in a range-periodic acoustic waveguide in the deep ocean. It is demonstrated that vertical oscillations of a sound-speed perturbation, induced by ocean internal waves, influence near-axial rays in a resonant way, producing ray chaos and forming a wide chaotic sea in the underlying phase space. We study interplay between chaotic ray dynamics and wave motion with signal frequencies of 50-100 Hz. The Floquet modes of the waveguide are calculated and visualized by means of the Husimi plots. Despite of irregular phase space distribution of periodic orbits, the Husimi plots display the presence of ordered peaks within the chaotic sea. These peaks, not being supported by certain periodic orbits, draw the specific "chainlike" pattern, reminiscent of KAM resonance. The link between the peaks and KAM resonance is confirmed by ray calculations with lower amplitude of the sound-speed perturbation, when the periodic orbits are well-ordered. We associate occurrence of the peaks with the recovery of ordered periodic orbits, corresponding to KAM resonance, due to suppressing of wave-field sensitivity to small-scale features of the sound-speed profile that take place with increasing wavelength.

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Section: Discussionmentioning

confidence: 99%

Recovery of ordered periodic orbits with increasing wavelength for sound propagation in a range-dependent waveguide

et al. 2007

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“…3 General-type solutions 3.1 Dissipative and conservative solutions 1. In this section we study general solutions f (t, x, v) (satisfying (2.1)) of the Focker-Planck equation (1.1).…”

Section: )mentioning

confidence: 99%

“…The comparison of the energy and entropy in the classical and quantum cases is an important subject (see [1,[13][14][15][16][17]22] and references therein). Here, we compare these energy and entropy for the situation described by the Fokker-Planck equation.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Fokker–Planck Equation: Stability, Distance and the Corresponding Extremal Problem in the Spatially Inhomogeneous Case

Sakhnovich

2015

Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes

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We start with a global Maxwellian M k , which is a stationary solution, with the constant total density (ρ(t) ≡ ρ), of the Fokker-Planck equation. The notion of distance between the function M k and an arbitrary solution f (with the same total density ρ at the fixed moment t) of the Fokker-Planck equation is introduced. In this way, we essentially generalize the important Kullback-Leibler distance, which was studied before. Using this generalization, we show local stability of the global Maxwellians in the spatially inhomogeneous case. We compare also the energy and entropy in the classical and quantum cases.

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“…Quantum chaos is a quantum manifestation of classically chaotic systems whose quantum eigenstates have the statistics of Gaussian orthogonal ensemble (GOE) [5]. Quantum chaos studies how chaotic classical systems can be shown to be limits of quantum mechanical systems [6][7][8][9][10][11][12][13]. Quantum chaology is a well-established field with a well-defined notion of quantum chaos [14].…”

Section: Introductionmentioning

confidence: 99%

Chaos in compound hadrons in high-energy hadronic interactions

Ghosh¹,

Deb²,

Pal³

et al. 2010

Phys. Scr.

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In this paper, a detailed study of the chaotic behavior of compound hadrons (pions plus protons) in π−–AgBr interactions at 350 GeV c−1 has been performed with the help of the parameter ‘entropy index’ μq, which is a measure of the chaotic behavior in multipion production processes. This index describes the event-to-event fluctuation of factorial moments that measures the spatial fluctuation of multiplicity distribution. The analysis reveals a large value for the entropy index signifying the chaotic behavior of the produced compound hadrons in high-energy hadron–nucleus interactions. It was been observed that the multipion production process becomes less chaotic with increasing average multiplicity of the final states. The study has been further extended to pions, and the corresponding results are compared.

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Comparison of classical chaos with quantum chaos

Cited by 5 publications

References 28 publications

Recovery of ordered periodic orbits with increasing wavelength for sound propagation in a range-dependent waveguide

Recovery of ordered periodic orbits with increasing wavelength for sound propagation in a range-dependent waveguide

Nonlinear Fokker–Planck Equation: Stability, Distance and the Corresponding Extremal Problem in the Spatially Inhomogeneous Case

Chaos in compound hadrons in high-energy hadronic interactions

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