Expansion method for nonlinear quantum master equations

M.A. Despósito

Physica A: Statistical Mechanics and its Applications, 1994, vol. 209, issue 1, 237-248

Abstract: We are interested in the solutions of those master equations which appear when we consider a nonlinear coupling between an oscillator and an arbitrary thermal bath. For this purpose we implement a power series expansion in the parameter Ω = kT/h̵ω0. After observing that the master equation is of the diffusion type, we obtain a nonlinear Fokker-Planck equation for the probability density. Solving this equation we find that the relaxation becomes non-exponential. Going beyond lowest order in the expansion we deal again with a nonlinear Fokker-Plank equation which is equivalent to the obtained equation to first order in the case of a linear-plus-quadratic coupling. Finally, we transform the obtained equations to Schrödinger's ones and analyze the corresponding eigenvalue spectrum.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:209:y:1994:i:1:p:237-248

DOI: 10.1016/0378-4371(94)90057-4

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