Renormalized waves and thermalization of the Klein-Gordon equation

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We study the thermalization of the classical Klein-Gordon equation under a u4 interaction. We numerically show that even in the presence of strong nonlinearities, the local thermodynamic equilibrium state exhibits a weakly nonlinear behavior in a renormalized wave basis. The renormalized basis is defined locally in time by a linear transformation and the requirement of vanishing wave-wave correlations. We show that the renormalized waves oscillate around one frequency, and that the frequency dispersion relation undergoes a nonlinear shift proportional to the mean square field. In addition, the renormalized waves exhibit a Planck-like spectrum. Namely, there is equipartition of energy in the low-frequency modes described by a Boltzmann distribution, followed by a linear exponential decay in the high-frequency modes.

Original languageEnglish (US)
Article number046217
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number4
StatePublished - Apr 25 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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