Effective dephasing for a qubit interacting with a transverse classical   field
  We address the dynamics of a qubit interacting with a quasi static random classical field having both a longitudinal and a transverse component and described by a Gaussian stochastic process. In particular, we analyze in details the conditions under which the dynamics may be effectively approximated by a unitary operation or a pure dephasing without relaxation. 
Claudia Benedetti and Matteo G. A. Paris
quant-ph