The Brownian dynamics of the density operator for a quantum system int
eracting with a classical heat bath is described using a stochastic, n
on-linear Liouville equation obtained from a variational principle. Th
e rate of the noise-induced transitions is expressed as a function of
the environmental spectral density, and is discussed for the case of w
hite noise and blackbody radiation. The time-scales of decoherence and
dissipation are investigated numerically for a system of two quantum
states. These are the ground and first excited state of the center of
mass vibrations for a single ion confined in a harmonic trap. (C) 1998
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