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Functional integration approach to hysteresis.

G Bertotti1, I D Mayergoyz, V Basso

  • 1Istituto Elettrotecnico Nazionale Galileo Ferraris, Corso Massimo d'Azeglio 42, I-10125 Torino, Italy.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary

This study proposes a general scalar hysteresis formulation using generating functions and ensemble averaging. It shows how Markovian stochastic processes can precisely describe hysteresis, linking it to the Preisach model.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • Hysteresis is a complex phenomenon observed in various physical systems.
  • Existing models often lack a unified theoretical framework for diverse hysteresis behaviors.

Purpose of the Study:

  • To develop a general formulation for scalar hysteresis.
  • To connect ensemble hysteresis properties to stochastic processes and established models like the Preisach model.

Main Methods:

  • Associating a generating function with individual systems.
  • Defining a hysteresis evolution operator via envelope construction.
  • Expressing ensemble average response as a functional integral over generating functions.
  • Analyzing the formulation using continuous, Markovian stochastic processes.

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Main Results:

  • The formulation reduces ensemble hysteresis calculation to solving a level-crossing problem.
  • Homogeneous Markovian processes lead to exact description by the Preisach model.
  • The Preisach distribution is derived analytically from drift and diffusion parameters.

Conclusions:

  • The proposed formulation offers a unified approach to scalar hysteresis.
  • It provides a direct link between microscopic system dynamics and macroscopic hysteresis behavior.
  • Applications include magnetic and superconducting hysteresis interpretation.