The approach to thermal equilibrium in the Caldeira-Leggett model

We compare the long time behaviour and approach to thermal equilibrium of the one-dimensional Caldeira-Leggett model for the master equation in Lindblad and non-Lindblad forms. We first solve the explicit time evolution for the free particle and harmonic oscillator systems and show that our results agree with previous such attempts, and then show that Lindblad and non-Lindblad cases lead to the same evolution when we take the limitations of the Caldeira-Leggett model into account.