Geometric phase for a two-level atom immersed in a thermal bath in the global monopole space-time

In the framework of open quantum systems, and combining with the quantum field theory in curved space-time, we study the geometric phase for a static two-level atom immersed in a thermal bath of a massless scalar field in the background of global monopole space-time. We show that the correction to geometric phase of the atom results from combined effects of both thermal radiation of the thermal bath at finite temperature and the topological property of global monopole. We also discuss the modified geometric phases for this two-level atom purely due to thermal fluctuation of the thermal bath at an effective temperature in Minkowski space-time and also purely resulting from the effect of global monopole space-time. In addition, the numerical results of correction to the geometric phase induced by the effects of thermal environment and the global monopole is presented and discussed. It is clearly seen that the corrections depend crucially on the temperature T of environment and the position r of the atom relative to the global monopole.