Semiclassical mechanics for time-dependent Wigner functions

Sam L Robinson

doi:10.1063/1.530112

Semiclassical mechanics for time-dependent Wigner functions

Sam L Robinson

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

An explicit and computable asymptotic integral representation is obtained for the time-dependent Wigner distribution associated with the initial quantum state ψ(x,0) = f(x) e^iS(x)/ℏ in the semiclassical (ℏ → 0) limit. The approximations are valid to arbitrarily high order in ℏ over any finite time interval. The leading order term is further analyzed to obtain a classically determined phase space function which is related to a classical probability density on phase space. The results hold for a large class of time-dependent potentials.

Original language	English (US)
Pages (from-to)	2185-2205
Number of pages	21
Journal	Journal of Mathematical Physics
Volume	34
Issue number	6
DOIs	https://doi.org/10.1063/1.530112
State	Published - Jan 1 1993
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.530112

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abstract = "An explicit and computable asymptotic integral representation is obtained for the time-dependent Wigner distribution associated with the initial quantum state ψ(x,0) = f(x) eiS(x)/ℏ in the semiclassical (ℏ → 0) limit. The approximations are valid to arbitrarily high order in ℏ over any finite time interval. The leading order term is further analyzed to obtain a classically determined phase space function which is related to a classical probability density on phase space. The results hold for a large class of time-dependent potentials.",

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N2 - An explicit and computable asymptotic integral representation is obtained for the time-dependent Wigner distribution associated with the initial quantum state ψ(x,0) = f(x) eiS(x)/ℏ in the semiclassical (ℏ → 0) limit. The approximations are valid to arbitrarily high order in ℏ over any finite time interval. The leading order term is further analyzed to obtain a classically determined phase space function which is related to a classical probability density on phase space. The results hold for a large class of time-dependent potentials.

AB - An explicit and computable asymptotic integral representation is obtained for the time-dependent Wigner distribution associated with the initial quantum state ψ(x,0) = f(x) eiS(x)/ℏ in the semiclassical (ℏ → 0) limit. The approximations are valid to arbitrarily high order in ℏ over any finite time interval. The leading order term is further analyzed to obtain a classically determined phase space function which is related to a classical probability density on phase space. The results hold for a large class of time-dependent potentials.

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Semiclassical mechanics for time-dependent Wigner functions

Abstract

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