Functional integration approach to hysteresis

A general formulation of scalar hysteresis is proposed. This formulation is based on two steps. First, a generating function g(x) is associated with a n individual system, and a hysteresis evolution operator is defined by an a ppropriate envelope construction applied to g(x), inspired by the overdampe d dynamics of systems evolving in multistable free-energy landscapes. Secon d, the average hysteresis response of an ensemble of such systems is expres sed as a functional integral over the space G of all admissible generating functions, under the assumption that an appropriate measure mu has been int roduced in G. The consequences of the formulation are analyzed in detail in the case where the measure mu is generated by a continuous, Markovian stoc hastic process. The calculation of the hysteresis properties of the ensembl e is reduced to the solution of the level-crossing problem for the stochast ic process. In particular, it is shown that, when the process is translatio nally invariant (homogeneous), the ensuing hysteresis properties can be exa ctly described by the Preisach model of hysteresis, and the associated Prei sach distribution is expressed in closed analytic form in terms of the drif t and diffusion parameters of the Markovian process. Possible applications of the formulation are suggested, concerning the interpretation of magnetic hysteresis due to domain wall motion in quenched-in disorder and the inter pretation of critical state models of superconducting hysteresis. [S1063-65 1X(99)06308-4].