The equilibrium states of open quantum systems in the strong coupling regime

Published

December 26, 2012

Author(s)

Jacob M. Taylor, Yigit Subasi, Chris Fleming, Bei L. Hu

Abstract

In this work we investigate the late-time stationary states of open quantum systems coupled to a thermal reservoir in the strong coupling regime. This is because in general such systems do not necessarily relax to a Boltzmann distribution if the coupling to the thermal reservoir is non-vanishing or equivalently if the relaxation timescales are finite. Using a variety of non-equilibrium formalisms valid for non-Markovian processes, we show that starting from a product state of the closed system = system + environment, with the environment in its thermal state, the open system which results from coarse graining the environment will evolve towards an equilibrium state at late-times. This state can be expressed as the reduced state of the closed system thermal state at the temperature of the environment. For a linear (harmonic) system and environment, which is exactly solvable, we are able to show in a rigorous way that all multi-time correlations of the open system evolve towards those of the closed system thermal state. Multi-time correlations are especially relevant in the non- Markovian regime, since they cannot be generated by the dynamics of the single-time correlations. For more general systems, which cannot be exactly solved, we are able to provide a general proof that all single-time correlations of the open system evolve to those of the closed system thermal state, to first order in the relaxation rates. For the special case of a zero temperature reservoir, we are able to explicitly construct the reduced closed system thermal state in terms of the environmental correlations.

Citation

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

Pub Type

Journals

Download Paper

https://doi.org/10.1103/PhysRevE.86.061132

Keywords

Quantum foundations, thermalization

Citation

Taylor, J. , Subasi, Y. , Fleming, C. and Hu, B. (2012), The equilibrium states of open quantum systems in the strong coupling regime, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), [online], https://doi.org/10.1103/PhysRevE.86.061132 (Accessed April 30, 2024)