Title:	Classical limit of master equation for a harmonic oscillator coupled to an oscillator bath with separable initial conditions
Authors:	Banerjee, Subhashish Dhar, Abhishek
Issue Date:	30-Jun-2006
Publisher:	The American Physical Society
Citation:	Physical Review E, 2006, Vol.73, 067104
Abstract:	The Wigner transform of the master equation describing the reduced dynamics of the system, of a 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.
URI:	http://hdl.handle.net/2289/1431
ISSN:	1539-3755 1550-2376 (online)
Alternative Location:	http://link.aps.org/abstract/PRE/v73/e067104
Copyright:	(2006) by the American Physical Society
Appears in Collections:	Research Papers (TP)

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