  In the framework of the theory of open systems based on completely positive
quantum dynamical semigroups, we determine the degree of quantum decoherence of
a harmonic oscillator interacting with a thermal bath. It is found that the
system manifests a quantum decoherence which is more and more significant in
time. We also calculate the decoherence time and show that it has the same
scale as the time after which thermal fluctuations become comparable with
quantum fluctuations. Then we solve the master equation for two independent
harmonic oscillators interacting with an environment in the asymptotic
long-time regime. We give a description of the continuous-variable asymptotic
entanglement in terms of the covariance matrix of the quantum states of the
considered system for an arbitrary Gaussian input state. Using the Peres-Simon
necessary and sufficient condition for separability of two-mode Gaussian
states, we show that the two non-interacting systems immersed in a common
environment become asymptotically entangled for certain environments, so that
in the long-time regime they manifest non-local quantum correlations.
