The dissipative dynamics of a quantum Brownian particle is studied for different types of environment. We derive analytic results for the time evolution of the mean energy of the system for Ohmic, sub-Ohmic, and super-Ohmic environments, without performing the Markovian approximation. Our results allow one to establish a direct link between the form of the environmental spectrum and the thermalization dynamics. This in turn leads to a natural explanation of the microscopic physical processes ruling the system time evolution both in the short-time non-Markovian region and in the long-time Markovian one. Our comparative study of thermalization for different environments sheds light on the physical contexts in which non-Markovian dissipation effects are dominant.
Paavola, J., Piilo, J., Suominen, K-A., & Maniscalco, S. (2009). Environment-dependent dissipation in quantum Brownian motion. Physical Review A, 79(5), . https://doi.org/10.1103/PhysRevA.79.052120