  The quantum Brownian motion paradigm provides a unified framework where one
can see the interconnection of some basic quantum statistical processes like
decoherence, dissipation, particle creation, noise and fluctuation. We treat
the case where the Brownian particle is coupled linearly to a bath of time
dependent quadratic oscillators. While the bath mimics a scalar field, the
motion of the Brownian particle modeled by a single oscillator could be used to
depict the behavior of a particle detector, a quantum field mode or the scale
factor of the universe. An important result of this paper is the derivation of
the influence functional encompassing the noise and dissipation kernels in
terms of the Bogolubov coefficients. This method enables one to trace the
source of statistical processes like decoherence and dissipation to vacuum
fluctuations and particle creation, and in turn impart a statistical mechanical
interpretation of quantum field processes. With this result we discuss the
statistical mechanical origin of quantum noise and thermal radiance from black
holes and from uniformly- accelerated observers in Minkowski space as well as
from the de Sitter universe discovered by Hawking, Unruh and Gibbons-Hawking.
We also derive the exact evolution operator and master equation for the reduced
density matrix of the system interacting with a parametric oscillator bath in
an initial squeezed thermal state. These results are useful for decoherence and
backreaction studies for systems and processes of interest in semiclassical
cosmology and gravity. Our model and results are also expected to be useful for
related problems in quantum optics. %\pacs
{05.40.+j,03.65.Sq,98.80.Cq,97.60.Lf}
