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Comparative study of different discretizations of the phi(4) model
Ishani Roy1, Sergey V Dmitriev, Panayotis G Kevrekidis
1Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
Summary
Discretizing phi(4) field theory reveals that kink-antikink collisions become more elastic as discreteness increases. The classical discrete model shows the most inelastic collisions among those studied.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
- Computational Physics
Background:
- The phi(4) field theory is a fundamental model in quantum field theory.
- Discretization methods are crucial for numerical simulations and understanding non-perturbative effects.
- Investigating translationally invariant discretizations is important for preserving physical symmetries.
Purpose of the Study:
- To compare different translationally invariant discretizations of the phi(4) field theory.
- To analyze the behavior of kink-type solitary waves and their spectral properties.
- To study the scattering properties of kink-antikink pairs under varying degrees of discreteness.
Main Methods:
- Analysis of fundamental solutions and spectral properties of linearized equations.
- Numerical simulations of kink-antikink collisions for different lattice spacings.
- Comparison of collision elasticity and inelasticity across various discrete models.
Main Results:
- The elasticity of kink-antikink collisions increases with deviation from the continuum limit (h -> 0).
- The classical discrete phi(4) model exhibits the most inelastic collisions.
- The four translationally invariant discrete models show more elastic kink-antikink collisions compared to the classical discrete model.
Conclusions:
- Discreteness significantly modifies the dynamics of kink-antikink collisions in phi(4) theory.
- Translationally invariant discretizations offer a more elastic collision behavior than the classical discrete model.
- The choice of discretization scheme impacts fundamental properties like solitary wave interactions.
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