title: Renormalized waves and thermalization of the Klein-Gordon equation.
abstract: We study the thermalization of the classical Klein-Gordon equation under a u(4) 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.
authors: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. shirokof@math.mit.edu
authors: D
authors: D
authors: Shirokoff