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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
Summary
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.
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.
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