A non-perturbative analytic expression of signal amplification factor in stochastic resonance

We put forward a non-perturbative scheme to calculate the response of an overdamped bistable system driven by a Gaussian white noise and perturbed by a weak monochromatic force (signal) analytically. The formalism takes into account infinite number of perturbation terms of a perturbation series with amplitude of the signal as an expansion parameter. The contributions of infinite number of relaxation modes of the stochastic dynamics to the response are also taken into account in this formalism. A closed form analytic expression of the response is obtained. Only the knowledge of the first non-trivial eigenvalue and the lowest eigenfunction of the un-perturbed Fokker-Planck operator are needed to evaluate the response. The response calculated from the derived analytic expression matches fairly well with the numerical results.