Affordable Access

deepdyve-link deepdyve-link
Publisher Website

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

Authors
  • Banerjee, Subhashish
  • Dhar, Abhishek
Type
Published Article
Publication Date
Nov 28, 2005
Submission Date
Nov 28, 2005
Identifiers
DOI: 10.1103/PhysRevE.73.067104
arXiv ID: cond-mat/0511645
Source
arXiv
License
Unknown
External links

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, vol. 55, 153 (1997)]. It was shown that for some special correlated initial conditions the equation reduces, in the classical limit, to the corresponding classical Fokker-Planck equation obtained by Adelman [J. Chem Phys., vol. 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 equation obtained from the oscillator bath model is somewhat different from the one considered by Adelman. We obtain the corresponding Fokker-Planck equation and show that it exactly matches the classical limit of the equation for the Wigner function obtained from the master equation for separable initial conditions. We also discuss why the special correlated initial conditions correspond to Adelman's solution.

Report this publication

Statistics

Seen <100 times