Quantum correlations for two coupled oscillators interacting with two heat baths

We study a system of two coupled oscillators (A oscillators), each of which linearly interact with their own heat bath consisting of a set of independent harmonic oscillators (B oscillators). The initial state of the A oscillator is taken to be coherent while the B oscillator is in a thermal state. We analyze the time-dependent state of the A oscillator, which is a two-mode Gaussian state. By making use of Simon's separability criterion, we show that this state is separable for all times. We consider the equilibrium state of the A oscillator in detail and calculate its Wigner function. (author)