  We present the results of studying the influence of different environmental
states on the coherence of quantum processes. We choose to discuss a simple
model which describe two electronic reservoirs connected through tunneling via
a resonant state. The model could, e.g., serve as an idealization of inelastic
resonant tunneling through a double barrier structure. We develop Schwinger's
closed time path formulation of non-equilibrium quantum statistical mechanics,
and show that the influence of the environment on a coherent quantum process
can be described by the value of a generating functional at a specific force
value, thereby allowing for a unified discussion of destruction of phase
coherence by various environmental states: thermal state, classical noise, time
dependent classical field, and a coherent state. The model allows an extensive
discussion of the influence of dissipation on the coherent quantum process, and
expressions for the transmission coefficient are obtained in the possible
limits.
