Harmonic oscillator in presence of nonequilibrium environment

Based on a microscopic Hamiltonian picture where the system is coupled with the nonequilibrium environment, comprising of a set of harmonic oscillators, the Langevin equation with proper microscopic specification of Langevin force is formulated analytically. In our case, the reservoir is perturbed by an external force, either executing rapid or showing periodic fluctuations, hence the reservoir is not in thermal equilibrium. In the presence of external fluctuating force, using Shapiro-Loginov procedure, we arrive at the linear coupled first order differential equations for the two-time correlations and examine the time evolution of the same considering the system as a simple harmonic oscillator. We study the stochastic resonance phenomena of a Kubo-type oscillator (assumed to be the system) when the bath is modulated by a periodic force. The result(s) obtained here is of general significance and can be used to analyze the signature of stochastic resonance.