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Solvable model of driven matter with pinning.

Gourab Kumar Sar1, Dibakar Ghosh1, Kevin O'Keeffe2

  • 1Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India.

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|May 17, 2024
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Summary

We developed a solvable model for driven matter with impurities, revealing complex dynamics like chaos and hysteresis. This model accurately reflects magnetic domain wall behavior, offering new insights into condensed matter systems.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • Driven matter systems with impurities exhibit complex behaviors.
  • Minimal models are crucial for understanding emergent phenomena.
  • Experimental observations of magnetic domain walls show rich dynamics.

Purpose of the Study:

  • To introduce a simple, solvable model for driven matter in a 1D medium with pinning impurities.
  • To analyze the rich dynamics and phase transitions within this model.
  • To validate the model's predictions against experimental data, particularly for magnetic domain walls.

Main Methods:

  • Development of a minimal, analytically solvable model for driven matter.
  • Derivation of the complete phase diagram for small system sizes (N).
  • Derivation of expressions for order parameters and bifurcation curves for large N.

Main Results:

  • The model exhibits diverse dynamical behaviors: hysteresis, reentrance, quasiperiodicity, and two routes to chaos.
  • The phase diagram is fully characterized for small N.
  • Analytical expressions for macroscopic properties and critical phenomena are obtained for large N.
  • The model's collective states closely replicate experimental observations of magnetic domain walls.

Conclusions:

  • The presented model offers a tractable yet realistic framework for studying driven matter systems.
  • The model successfully captures complex dynamics and phase transitions observed in physical systems.
  • This work provides a theoretical basis for understanding phenomena in magnetic domain walls and related systems.