Relaxation spectrum of quantum harmonic motion in the presence of nonlinear dissipative-diffusive couplings

We analyze the behavior of a damped quantum harmonic oscillator immersed in a heat bath with a nonlinear coupling. For this purpose, we construct a generalized master equation (GME) for the reduced density of the oscillator. We specialize the results for a quadratic coupling in the presence of a bos...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Despósito, Marcelo Arnaldo, Hernández, Ester Susana
Publicado: 1992
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10502947_v46_n12_p7510_Desposito
http://hdl.handle.net/20.500.12110/paper_10502947_v46_n12_p7510_Desposito
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_10502947_v46_n12_p7510_Desposito
record_format dspace
spelling paper:paper_10502947_v46_n12_p7510_Desposito2023-06-08T16:01:36Z Relaxation spectrum of quantum harmonic motion in the presence of nonlinear dissipative-diffusive couplings Despósito, Marcelo Arnaldo Hernández, Ester Susana We analyze the behavior of a damped quantum harmonic oscillator immersed in a heat bath with a nonlinear coupling. For this purpose, we construct a generalized master equation (GME) for the reduced density of the oscillator. We specialize the results for a quadratic coupling in the presence of a bosonic reservoir and an Ohmic dissipation model, analyzing the evolution equation for the mean value of the oscillator coordinate. In the asymptotic case we obtain a gain-loss master equation whose transition rates are polynomials in the number of quanta. No explicit solutions other than the equilibrium one can be written, since the standard methods do not apply. The equilibrium solution is investigated and the eigenvalues of the corresponding spectral problem are numerically computed to study the effect of the nonlinearity on the evolution of the system. By means of the Wigner transformation of the GME, we extract a third-order partial derivative equation that represents the semiclassical evolution of the damped oscillator. In the classical limit this is a nonlinear Fokker-Planck equation. © 1992 The American Physical Society. Fil:Despósito, M.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Hernández, E.S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1992 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10502947_v46_n12_p7510_Desposito http://hdl.handle.net/20.500.12110/paper_10502947_v46_n12_p7510_Desposito
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We analyze the behavior of a damped quantum harmonic oscillator immersed in a heat bath with a nonlinear coupling. For this purpose, we construct a generalized master equation (GME) for the reduced density of the oscillator. We specialize the results for a quadratic coupling in the presence of a bosonic reservoir and an Ohmic dissipation model, analyzing the evolution equation for the mean value of the oscillator coordinate. In the asymptotic case we obtain a gain-loss master equation whose transition rates are polynomials in the number of quanta. No explicit solutions other than the equilibrium one can be written, since the standard methods do not apply. The equilibrium solution is investigated and the eigenvalues of the corresponding spectral problem are numerically computed to study the effect of the nonlinearity on the evolution of the system. By means of the Wigner transformation of the GME, we extract a third-order partial derivative equation that represents the semiclassical evolution of the damped oscillator. In the classical limit this is a nonlinear Fokker-Planck equation. © 1992 The American Physical Society.
author Despósito, Marcelo Arnaldo
Hernández, Ester Susana
spellingShingle Despósito, Marcelo Arnaldo
Hernández, Ester Susana
Relaxation spectrum of quantum harmonic motion in the presence of nonlinear dissipative-diffusive couplings
author_facet Despósito, Marcelo Arnaldo
Hernández, Ester Susana
author_sort Despósito, Marcelo Arnaldo
title Relaxation spectrum of quantum harmonic motion in the presence of nonlinear dissipative-diffusive couplings
title_short Relaxation spectrum of quantum harmonic motion in the presence of nonlinear dissipative-diffusive couplings
title_full Relaxation spectrum of quantum harmonic motion in the presence of nonlinear dissipative-diffusive couplings
title_fullStr Relaxation spectrum of quantum harmonic motion in the presence of nonlinear dissipative-diffusive couplings
title_full_unstemmed Relaxation spectrum of quantum harmonic motion in the presence of nonlinear dissipative-diffusive couplings
title_sort relaxation spectrum of quantum harmonic motion in the presence of nonlinear dissipative-diffusive couplings
publishDate 1992
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10502947_v46_n12_p7510_Desposito
http://hdl.handle.net/20.500.12110/paper_10502947_v46_n12_p7510_Desposito
work_keys_str_mv AT despositomarceloarnaldo relaxationspectrumofquantumharmonicmotioninthepresenceofnonlineardissipativediffusivecouplings
AT hernandezestersusana relaxationspectrumofquantumharmonicmotioninthepresenceofnonlineardissipativediffusivecouplings
_version_ 1768544605817536512

Ejemplares similares