HYSTERESIS LOSS AND STOCHASTIC RESONANCE - A NUMERICAL STUDY OF A DOUBLE-WELL POTENTIAL

A Langevin dynamic simulation is carried out in order to understand th e phenomena of hysteresis in a double-well system represented by a Lan dau (m(4)) potential, where m is the order parameter, with a symmetric al sawtooth-type periodic external field. The calculation of a hystere sis loop is based on the statistics of first-passage time to make a tr ansition from one well to the other across the potential barrier as th e external field (of symmetrical sawtooth type) is swept in time. The basic construction of our model used to understand hysteresis rules ou t any dynamical (symmetry breaking) phase transition predicted by othe r workers in Ising- and O(N-->infinity)-model systems. Also, we do not find any universal scaling relationship between the hysteresis loss a nd the field-sweep ''frequency.'' Our treatment, however, makes close contact with a recently observed phenomenon of stochastic resonance: t he hysteresis loss shows a stochastic resonant behavior with respect t o the noise strength. We discuss the recent experiment on the observat ion of the Kramers rate and stochastic resonance by Simon and Libchabe r [Phys. Rev. Lett. 68, 3375 (1992)] in light of our results.