Renormalized waves and thermalization of the Klein-Gordon equation
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Shirokoff-2011-Renormalized waves a.pdf
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Author(s)
Shirokoff, David George
Date Issued
April 2011
Journal
Physical Review E
Publisher
American Physical Society
Citation
Shirokoff, D. “Renormalized Waves and Thermalization of the Klein-Gordon Equation.” Physical Review E 83.4 (2011) : 046217 ©2011 American Physical Society
Version
Final published version
Abstract
We study the thermalization of the classical Klein-Gordon equation under a u[superscript 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.83.046217
