Hysteresis loss and stochastic resonance: A numerical study of a double-well potential.

Abstract

A Langevin dynamic simulation is carried out in order to understand the phenomena of hysteresis in a double-well system represented by a Landau (${\mathit{m}}^{4}$) potential, where m is the order parameter, with a symmetrical sawtooth-type periodic external field. The calculation of a hysteresis loop is based on the statistics of first-passage time to make a transition from one well to the other across the potential barrier as the external field (of symmetrical sawtooth type) is swept in time. The basic construction of our model used to understand hysteresis rules out any dynamical (symmetry breaking) phase transition predicted by other workers in Ising- and O(N\ensuremath{\rightarrow}\ensuremath{\infty})-model systems. Also, we do not find any universal scaling relationship between the hysteresis loss and the field-sweep ``frequency.'' Our treatment, however, makes close contact with a recently observed phenomenon of stochastic resonance: the hysteresis loss shows a stochastic resonant behavior with respect to the noise strength. We discuss the recent experiment on the observation of the Kramers rate and stochastic resonance by Simon and Libchaber [Phys. Rev. Lett. 68, 3375 (1992)] in light of our results.