Brownian parametric quantum oscillator with dissipation.

Abstract

We study the quantum fluctuational properties of a parametric oscillator with and without coupling to an Ohmic environment. After considering the momentum and coordinate variances as a function of initial squeezing for the undamped dynamics, we invoke the functional integral method to derive the fully exact reduced density matrix for parametric dissipative quantum Brownian motion, covering the whole temperature regime from T=0 up to the classical limit at room temperatures. Moreover, we present the exact result for the quantum master equation for both the density matrix and the corresponding Wigner function. The time evolution of the covariance matrix elements of damped quantum fluctuations is studied numerically. These variances undergo within the regime of global stability asymptotic, periodic oscillations. As an interesting result, we find that the minima of these oscillations fall below the corresponding thermal equilibrium values.