Adiabatic Evolution of an Open Quantum System in its Instantaneous Steady State

Abstract

In this paper, we derive an adiabatic condition for an quantum system subject to environment. The adiabaticity defined here dicates that the open quantum system prepared initially in its steady state would adiabatically follow its instantaneous steady state. We find that if the driving on the open system does not induce transition between the eigenstates of the instantaneous steady state, the open system can evolve adiabatically. In order to examine the validity of the adiabatic condition, a two-band model is exemplified. The results show that the topological quantum phase transition presented in the two-band model is caused by the competition between the effect of decay and the spoiling of the adiabaticity. The geometric phase is also calculated and discussed when the adiabatic condition is satisfied.