Classical limit of the harmonic oscillator Wigner functions in the Bargmann representation

Ripamonti, Nicolò

doi:10.1088/0305-4470/29/16/031

Cited by 11 publications

(11 citation statements)

References 16 publications

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“…In this limit one indeed recovers the classical microcanonical distribution function of the harmonic oscillator, as it was proven in Ref. 23 using the closely related method of Wigner functions.…”

Section: Examples Of Classical Limitssupporting

confidence: 70%

Remark on a Group-Theoretical Formalism for Quantum Mechanics and the Quantum-to-Classical Transition

Korbicz

Lewenstein

2007

Found Phys

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We sketch a group-theoretical framework, based on the Heisenberg-Weyl group, encompassing both quantum and classical statistical descriptions of unconstrained, non-relativistic mechanical systems. We redefine in group-theoretical terms a kinematical arena and a space of statistical states of a system, achieving a unified quantum-classical language and an elegant version of the quantum-toclassical transition. We briefly discuss the structure of observables and dynamics within our framework.

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Section: Examples Of Classical Limitssupporting

confidence: 70%

Remark on a Group-Theoretical Formalism for Quantum Mechanics and the Quantum-to-Classical Transition

Korbicz

Lewenstein

2007

Found Phys

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“…This limit only holds in the sense of distributions, against integration of appropriate functions (see [36] for a detailed analysis of this limit in the case of the harmonic oscillator). In fact, the Wigner function approaches a delta function in a highly non-trivial way: it decays very fast outside the classical curve, it has a peak approximately at the classical curve, and it oscillates very rapidly around zero inside the curve.…”

Section: Classical and Quantum Geometry In Fermi Gasesmentioning

confidence: 99%

Quantum curves as quantum distributions

Mariño

Zakany

2019

J. High Energ. Phys.

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Topological strings on toric Calabi-Yau threefolds can be defined non-perturbatively in terms of a non-interacting Fermi gas of N particles. Using this approach, we propose a definition of quantum mirror curves as quantum distributions on phase space. The quantum distribution is obtained as the Wigner transform of the reduced density matrix of the Fermi gas. We show that the classical mirror geometry emerges in the strongly coupled, large N limit in which ∼ N . In this limit, the Fermi gas has effectively zero temperature, and the Wigner distribution becomes sharply supported on the interior of the classical mirror curve. The quantum fluctuations around the classical limit turn out to be captured by an improved version of the universal scaling form of Balazs and Zipfel.

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“…where W nm (ζ) are the Weyl symbols of the projectors |ψ n ψ m |/2π (the factors of 2π are to keep the notation consistent with standard practice for Wigner functions in the case n = m). For the asymptotically harmonic potential in (1) the functions W nm (ζ) are known analytically (see [24] for example). The Weyl symbol WR(ζ, E) ofR(E) provides a remarkably transparent means of visualising the quantum transmission problem and of relating the scattering matrix to the geometry of classical phase space.…”

Section: Representing the Scattering Matrix In Phase Spacementioning

confidence: 99%

Uniform approximation of barrier penetration in phase space

2005

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A method to approximate transmission probabilities for a nonseparable multidimensional barrier is applied to a waveguide model. The method uses complex barrier-crossing orbits to represent reaction probabilities in phase space and is uniform in the sense that it applies at and above a threshold energy at which classical reaction switches on. Above this threshold the geometry of the classically reacting region of phase space is clearly reflected in the quantum representation. Two versions of the approximation are applied. A harmonic version which uses dynamics linearised around an instanton orbit is valid only near threshold but is easy to use. A more accurate and more widely applicable version using nonlinear dynamics is also described

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Classical limit of the harmonic oscillator Wigner functions in the Bargmann representation

Cited by 11 publications

References 16 publications

Remark on a Group-Theoretical Formalism for Quantum Mechanics and the Quantum-to-Classical Transition

Remark on a Group-Theoretical Formalism for Quantum Mechanics and the Quantum-to-Classical Transition

Quantum curves as quantum distributions

Uniform approximation of barrier penetration in phase space

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