Semiquantal corrections to stochastic resonance

Stochastic resonance occurs when a nonlinear dynamical system is periodically modulated in the presence of noise. We study in this paper the effect of including quantal corrections on the thermal transition rates of such a system, by using the Gaussian effective potential. We demonstrate that these corrections sharpen the peak of the signal-to-noise ratio and shift it toward a lower noise variance, in general. By studying the symmetric double-well system over a range of parameters, we are also able to show that the extreme quantal case of this system demonstrates no stochastic resonance, in agreement with recent calculations.