  The act of measurement on a quantum state is supposed to "collapse" the state
into one of several eigenstates of the operator corresponding to the observable
being measured. This measurement process is sometimes described as outside
standard quantum-mechanical evolution and not calculable from Schr\"odinger's
equation. There are two general approaches to the study of wave-function
collapse: one called the "consistent" or "decoherent" histories approach and
the other, the "environmental decoherence" approach, which studies the effect
of the environment upon the quantum system, to explain wave-function collapse.
In the "environmental decoherence" approach, one usually studies a
Markovian-approximated Master equation to study the time-evolution of reduced
density matrix and obtains the long-term dependence of the off-diagonal
elements of this matrix. We do not make a Markovian assumption and study a
particularly simple and calculable example. We find, the short-time behavior of
a collapsing system, at least the one considered in this paper, is not
exponential, which is a new result (the long-term behavior is, of course, still
exponential). This allows one to connect the Fermi-golden rule
quadratic-in-time behavior of a transition probability to the exponential
long-time behavior of a collapsing wave-function.
