Expansion method for nonlinear quantum master equations
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/ h {combining short stroke overlay}ω0. After observing t...
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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03784371_v209_n1-2_p237_Desposito |
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| Sumario: | 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/ h {combining short stroke overlay}ω0. 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. © 1994. |
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