The approach to equilibrium of a nondegenerate quantum system involves the
damping of microscopic population oscillations, and, additionally, the bringing
about of detailed balance, i.e. the achievement of the correct Boltzmann
factors relating the populations. These two are separate effects of interaction
with a reservoir. One stems from the randomization of phases and the other from
phase space considerations. Even the meaning of the word `phase' differs
drastically in the two instances in which it appears in the previous statement.
In the first case it normally refers to quantum phases whereas in the second it
describes the multiplicity of reservoir states that corresponds to each system
state. The generalized master equation theory for the time evolution of such
systems is here developed in a transparent manner and both effects of reservoir
interactions are addressed in a unified fashion. The formalism is illustrated
in simple cases including in the standard spin-boson situation wherein a
quantum dimer is in interaction with a bath consisting of harmonic oscillators.
The theory has been constructed for application in energy transfer in molecular
aggregates and in photosynthetic reaction centers
