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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todo:paper_03784371_v209_n1-2_p237_Desposito2023-10-03T15:32:26Z Expansion method for nonlinear quantum master equations Despósito, M.A. 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. Fil:Despósito, M.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03784371_v209_n1-2_p237_Desposito |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
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. |
| format |
JOUR |
| author |
Despósito, M.A. |
| spellingShingle |
Despósito, M.A. Expansion method for nonlinear quantum master equations |
| author_facet |
Despósito, M.A. |
| author_sort |
Despósito, M.A. |
| title |
Expansion method for nonlinear quantum master equations |
| title_short |
Expansion method for nonlinear quantum master equations |
| title_full |
Expansion method for nonlinear quantum master equations |
| title_fullStr |
Expansion method for nonlinear quantum master equations |
| title_full_unstemmed |
Expansion method for nonlinear quantum master equations |
| title_sort |
expansion method for nonlinear quantum master equations |
| url |
http://hdl.handle.net/20.500.12110/paper_03784371_v209_n1-2_p237_Desposito |
| work_keys_str_mv |
AT despositoma expansionmethodfornonlinearquantummasterequations |
| _version_ |
1807322885295964160 |