Relaxation of two coupled quantum oscillators to quasi-equilibrium states based on path integrals

Abstract

The paper addresses the problem of relaxation of open quantum systems. Using the path integral methods we found an analytical expression for time-dependent density matrix of two coupled quantum oscillators interacting with different baths of oscillators. The expression for density matrix was found in the linear regime with respect to the coupling constant between selected oscillators. Time-dependent spatial variances and covariance were investigated analytically and numerically. It was shown that asymptotic variances in the long-time limit are always in accordance with the fluctuation dissipation theorem despite on their initial values. In the weak coupling approach there is good reason to believe that subsystems asymptotically in equilibrium at their own temperatures even despite of the arbitrary difference in temperatures within the whole system.

31 pages, 6 figures

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Cited by in corpus (4)

• Quasi-equilibrium relaxation of two identical quantum oscillators with arbitrary coupling strength
• Dynamics and stationarity of two coupled arbitrary oscillators interacting with separate reservoirs
• Dynamics of two externally driven coupled quantum oscillators interacting with separate baths based on path integrals
• Quantum correlations for two coupled oscillators interacting with two heat baths