On the Lindblad equation for open quantum systems: Rényi entropy rate and weak invariants

Abstract

© Published under licence by IOP Publishing Ltd. A brief review of two recent topics on the Lindblad equation is presented. One is concerned with time evolution of the quantum Ré nyi entropy under the equation. The lower bound of the entropy rate is derived in a compact form. The other is about the concept of weak invariants, which generalize the Lewis-Riesenfeld invariant and are defined in such a way that they are not constant but their expectation values remain invariant in time. The Lindbladian operator describing the time-dependent damped quantum oscillator is identified, and the corresponding weak invariant is explicitly constructed as an example.