2 Imaginary Phases in Two - Level Model with Spontaneous Decay

We study a two-level model coupled to the electromagnetic vacuum and to a weak external electric field with fixed frequency. The amplitude of the external electrical field is supposed to vary very slowly in time. The coupling of the two-level system with the environment (vacuum) introduces decreasing exponentials in the probability of the two-level system to be in its upper level. Garrison and Wright (Phys. Lett. A128 (1988) 177) used the non-hermitian Hamiltonian approach to study the adiabatic limit of this model and concluded that the decreasing exponential is an imaginary geometric phase. Using the master equation for describing the time evolution of the two-level system at finite temperature we obtain that the imaginary phase due to dissipative effects is time dependent, in opposition to Garrison and Wright result.