Magnetism of a system interacting with a common environment

Abstract

We consider a system and environment governed by the Markovian process. The density matrix (the reduced density matrix) of the system satisfies the Kossakowski-Lindblad equation. We calculate the z-direction magnetization in the system for various types of initial states and interactions between the system and the environment. In all cases, the values of the magnetization asymptotically approached the same value in spite of the different initial states. However, for the different types of interactions between the system and the environment, the asymptotic values differed with the initial state.