  We study two continuous variable systems (or two harmonic oscillators) and
investigate their entanglement evolution under the influence of non-Markovian
thermal environments. The continuous variable systems could be two modes of
electromagnetic fields or two nanomechanical oscillators in the quantum domain.
We use quantum open system method to derive the non-Markovian master equations
of the reduced density matrix for two different but related models of the
continuous variable systems. The two models both consist of two interacting
harmonic oscillators. In model A, each of the two oscillators is coupled to its
own independent thermal reservoir, while in model B the two oscillators are
coupled to a common reservoir. To quantify the degrees of entanglement for the
bipartite continuous variable systems in Gaussian states, logarithmic
negativity is used. We find that the dynamics of the quantum entanglement is
sensitive to the initial states, the oscillator-oscillator interaction, the
oscillator-environment interaction and the coupling to a common bath or to
different, independent baths.
