Memory Effects in Long-Time Lindblad Motion

TL;DR

This paper demonstrates that Lindblad equations can incorporate memory effects, leading to non-Markovian dynamics where expectation values depend on initial states, and extends these equations to systems with internal structure like Bose gases.

Contribution

It introduces a method to embed memory effects into Lindblad equations and extends their applicability to complex systems such as Bose gases.

Findings

Lindblad operators can produce memory effects in long-time dynamics.

Expectation values depend on initial states due to memory effects.

Systems evolve into equilibrium ensembles determined by Lindblad operators.

Abstract

It is shown that the Lindblad equation accounts for memory effects. That is to say, Lindblad operators can be constructed in a natural manner such that a memory term appears in the asymptotic (infinite time) region; at the same time the expectation values depend on the initial state. Furthermore a procedure to extend the Lindblad equation to an equation of motion for an ideal Bose 'gas' of 'particles', i.e.systems with non-trivial internal structure, is described. Initially in some quantum state, this collection of 'particles' will asymptotically turn into an equilibrium ensemble whose probability distribution is determined by the Lindblad operators building the dissipative part of the equation of motion.