Quantum correlations for two coupled oscillators interacting with two heat baths

We study a system of two coupled oscillators (the A-oscillator) each of the oscillators linearly interacts with its own heat bath consisting of a set of independent harmonic oscillators (the B-oscillators). The initial state of the A-oscillator is taken to be coherent while the B-oscillators are in thermal states. 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.The accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author