STOCHASTIC RESONANCE - NONPERTURBATIVE CALCULATION OF POWER SPECTRA AND RESIDENCE-TIME DISTRIBUTIONS

We examine the response of a finite-temperature two-state system to pe riodic driving using time-dependent transition rate theory. This syste m can exhibit the phenomenon of stochastic resonance, where raising th e temperature increases the signal-to-noise ratio of the response. We obtain the power spectrum and the distribution of residence times nonp erturbatively for any transition rates that are periodic in time. Give n the drive period T(s), the power spectrum is the Fourier transform o f the sum of ''signal,'' which is periodic in time with period T(s), a nd ''noise,'' which is the product of an exponential and a function pe riodic with period T(s). The residence-time distribution is the produc t of an exponential and a function that is periodic with period T(s). Both the power spectrum and the residence-time distribution can be cal culated exactly given the dependence of the transition rates on the co ntrol parameter (e.g., asymmetry or temperature). We calculate the cha racteristics of stochastic resonance for a two-state system with activ ated transition rates and for a quantum-mechanical dissipative two-lev el system.