Classical limit of master equation for a harmonic oscillator coupled to an oscillator bath with separable initial conditions

Banerjee, Subhashish ; Dhar, Abhishek (2006) Classical limit of master equation for a harmonic oscillator coupled to an oscillator bath with separable initial conditions Physical Review E - Statistical, Nonlinear and Soft Matter Physics, 73 (6). 067104_1-067104_3. ISSN 1539-3755

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Official URL: http://pre.aps.org/abstract/PRE/v73/i6/e067104

Related URL: http://dx.doi.org/10.1103/PhysRevE.73.067104

Abstract

The equation for the Wigner function describing the reduced dynamics of a single harmonic oscillator coupled to an oscillator bath, was obtained by Karrlein and Grabert [ Phys. Rev. E 55 153 (1997)]. It was shown that for some special correlated initial conditions the master equation reduces, in the classical limit, to the corresponding classical Fokker-Planck equation obtained by Adelman [ J. Chem Phys. 64 124 (1976)]. However, for separable initial conditions the Adelman equations were not recovered. We resolve this problem by showing that, for separable initial conditions, the classical Langevin equations are somewhat different from the one considered by Adelman. We obtain the corresponding Fokker-Planck equation and show that they exactly match the classical limit of the evolution of the Wigner function obtained from the master equation for separable initial conditions. We also discuss why thermal initial conditions correspond to Adelman's solution.

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:79682
Deposited On:28 Jan 2012 07:16
Last Modified:18 May 2016 21:57

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