Non-adiabatic geometric phases and dephasing in an open quantum system
  We analyze the influence of a dissipative environment on geometric phases in a quantum system subject to non-adiabatic evolution. We find dissipative contributions to the acquired phase and modification of dephasing, considering the cases of weak short-correlated noise as well as of slow quasi-stationary noise. Motivated by recent experiments, we find the leading non-adiabatic corrections to the results, known for the adiabatic limit. 
A.E. Svetogorov and Yu. Makhlin
quant-ph cond-mat.mes-hall