Dynamics of driven Brownian inverted oscillator

Abstract In this paper, we derive the quantum Langevin equation for a driven Brownian inverted oscillator in the framework of the Heisenberg picture for the Caldeira-Leggett model. We describe the influence of an arbitrary time-dependent force on an open inverted oscillator dynamics. We take into account environment through the integral operator of relaxation and the force correlation function. The resulting behavior of the system is represented as a combination the time evolution of the position expectation and the variance, being induced simultaneously by spreading the wave packet and the chaotic Brownian motion. We discuss the possibility of stabilization of an open inverted oscillator, when applying external alternating force.