Single-particle treatment of quantum stochastic resonance

Abstract

We first consider a test particle subjected to the simultaneous influence of a double-well mean field, thermal velocity distribution, external white noise and sinusoidal modulation. Within a path-integral framework the resulting power spectrum along with the signal-to-noise ratio (SNR) are expressed perturbatively in terms of the unperturbed eigenfunctions ψ_n and eigenvalues E_n, permitting us to demonstrate the existence of the phenomenon of quantum stochastic resonance (SR) in the dissipationless case. Next, we show that with the help of suitable transformations (viz., a complex Fourier frequency or a scaled-up potential) systems with weak friction or strong damping can be approximately mapped onto the dissipationless case. This yields a convenient method for studying frictional SR because the ψ_n's and E_n's can still be generated through a short-time propagator. Our formulation is illustrated numerically by displaying the variation of the SNR with the external noise strength and comparing the results vis-á-vis those obtained from classical stochastic simulation and quantum bath models. The usefulness of the single-particle approach to analyze the quantum SR phenomenon is emphasized.