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Domain wall propagation and nucleation in a metastable two-level system
Hans C Fogedby1, John Hertz, Axel Svane
1Institute of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark. fogedby@phys.au.dk
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 5, 2004
Summary
We describe nonequilibrium transitions in a noisy Ginzburg-Landau equation using a novel phase space method. This reveals domain wall dynamics crucial for understanding system switching and energy barriers.
Area of Science:
- Statistical mechanics
- Nonlinear dynamics
- Condensed matter physics
Background:
- Nonequilibrium transitions are fundamental in complex systems.
- The noisy one-dimensional Ginzburg-Landau equation models various physical phenomena.
- Understanding transition pathways requires advanced analytical techniques.
Purpose of the Study:
- To provide a dynamical description of nonequilibrium transitions.
- To analyze the role of domain walls in system switching.
- To develop a theoretical framework for weak noise systems.
Main Methods:
- Canonical phase space formulation (Freidlin-Wentzel/Martin-Siggia-Rose methods).
- Derivation of nonlinear domain wall (soliton) solutions.
- Analysis of transition pathways via nucleation and propagation.
Main Results:
- Identified propagating nonlinear domain wall solutions.
- Characterized transition pathways by domain wall nucleation and propagation.
- Modeled the switching scenario as a dilute gas of domain walls.
- Evaluated the Arrhenius factor using associated action.
Conclusions:
- The weak noise canonical phase space formulation provides an effective description of nonequilibrium transitions.
- Domain wall dynamics are central to understanding switching phenomena.
- Theoretical predictions show excellent agreement with numerical studies.