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Kink dynamics in a topological straight phi4 lattice.

A B Adib1, C A Almeida

  • 1Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, 60455-760 Fortaleza, Ceará, Brazil. adib@fisica.ufc.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 3, 2001
PubMed
Summary

Topological discrete systems accurately model free kinks but struggle with dynamic kink problems. Their accuracy for kink-antikink scattering is limited to fine lattices, making them unsuitable for general kink dynamics.

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Area of Science:

  • Nonlinear dynamics
  • Computational physics
  • Field theory

Background:

  • Topological discrete systems preserve topological lower bounds on kink energy.
  • These systems were proposed as suitable for numerical studies of continuum kink dynamics.

Purpose of the Study:

  • To numerically investigate kink-antikink scattering and breather formation in topological lattices.
  • To assess the accuracy of topological discrete systems for kink dynamics.

Main Methods:

  • Focus on the straight phi(4) theory.
  • Numerical simulations of kink-antikink scattering and breather formation.
  • Analysis of accuracy across different lattice discretizations (h).

Main Results:

Related Experiment Videos

  • Topological discrete systems are accurate for free kinks in coarse lattices.
  • Accuracy for kink-antikink scattering is restricted to fine lattices (h ≈ 0.1).
  • Bogomol'nyi bound breaking during interactions limits accuracy.

    • Conclusions:

    • Topological discrete systems are not ideal for general kink dynamics.
    • Standard discretizations offer similar accuracy at fine resolutions.
    • The breaking of the Bogomol'nyi bound during interactions is a key limitation.