Single-particle treatment of quantum stochastic resonance

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 ψn and eigenvalues En, 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 ψnʹs and Enʹs 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.