Stable and unstable periodic orbits in the one-dimensional lattice φ4 theory

研究成果: Article査読

4 被引用数 (Scopus)


Periodic orbits for the classical φ4 theory on the one-dimensional lattice are systematically constructed by extending the normal modes of the harmonic theory, for periodic, free and fixed boundary conditions. Through the process, we investigate which normal modes of the linear theory can or cannot be extended to the full nonlinear theory and why. We then analyze the stability of these orbits, clarifying the link between the stability, parametric resonance, and Lyapunov spectra for these orbits. The construction of the periodic orbits and the stability analysis is applicable to theories governed by Hamiltonians with quadratic intersite potentials and a general on-site potential. We also apply the analysis to theories with on-site potentials that have qualitatively different behavior from the φ4 theory, with some concrete examples.

ジャーナルPhysical Review E
出版ステータスPublished - 2016 10 13

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 統計学および確率
  • 凝縮系物理学


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