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Memory driven Ginzburg-Landau model.

Steffen Trimper1, Knud Zabrocki, Michael Schulz

  • 1Fachbereich Physik, Martin-Luther-Universität, D-06099 Halle, Germany. trimper@physik.uni-halle.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
PubMed
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This study explores a bistable Ginzburg-Landau model with memory. Negative memory strength can enable the system to switch between stationary states, a phenomenon not observed with positive memory.

Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • Bistable systems exhibit two stable states.
  • Ginzburg-Landau models describe phase transitions.
  • Non-Markovian memory introduces history dependence.

Purpose of the Study:

  • Investigate the impact of non-Markovian memory on a bistable Ginzburg-Landau model.
  • Analyze the control of stationary solution branches by initial conditions and memory strength.
  • Determine conditions for state switching between solution branches.

Main Methods:

  • Analytical solutions for the Ginzburg-Landau model.
  • Numerical simulations of the time evolution.
  • Phase diagram analysis in the P(0)-lambda plane.

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Main Results:

  • Stationary solution branches are controlled by initial condition sign and memory strength (lambda).
  • Positive lambda reduces stationary solutions.
  • Negative lambda (<0) can increase solutions and induce switching between branches within a critical range (-u < lambda < lambda(c)).

Conclusions:

  • The non-Markovian memory term significantly alters the behavior of the bistable Ginzburg-Landau model.
  • Negative memory strength is crucial for achieving state switching.
  • A critical memory strength (lambda(c)) defines the boundary for this switching behavior.