Renormalized waves and thermalization of the Klein-Gordon equation
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 renormaliz...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2011
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| Online Access: | http://hdl.handle.net/1721.1/65874 |
| _version_ | 1826201522277449728 |
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| author | Shirokoff, David George |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Shirokoff, David George |
| author_sort | Shirokoff, David George |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:52:45Z |
| format | Article |
| id | mit-1721.1/65874 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:52:45Z |
| publishDate | 2011 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/658742022-10-01T06:40:04Z Renormalized waves and thermalization of the Klein-Gordon equation Shirokoff, David George Massachusetts Institute of Technology. Department of Mathematics Shirokoff, David George Shirokoff, David George 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. Natural Sciences and Engineering Research Council of Canada (NSERC) National Science Foundation (U.S.) (grant DMS-0813648) 2011-09-16T18:04:15Z 2011-09-16T18:04:15Z 2011-04 2010-11 Article http://purl.org/eprint/type/JournalArticle 1539-3755 1550-2376 http://hdl.handle.net/1721.1/65874 Shirokoff, D. “Renormalized Waves and Thermalization of the Klein-Gordon Equation.” Physical Review E 83.4 (2011) : 046217 ©2011 American Physical Society en_US http://dx.doi.org/10.1103/PhysRevE.83.046217 Physical Review E 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. application/pdf American Physical Society APS |
| spellingShingle | Shirokoff, David George Renormalized waves and thermalization of the Klein-Gordon equation |
| title | Renormalized waves and thermalization of the Klein-Gordon equation |
| title_full | Renormalized waves and thermalization of the Klein-Gordon equation |
| title_fullStr | Renormalized waves and thermalization of the Klein-Gordon equation |
| title_full_unstemmed | Renormalized waves and thermalization of the Klein-Gordon equation |
| title_short | Renormalized waves and thermalization of the Klein-Gordon equation |
| title_sort | renormalized waves and thermalization of the klein gordon equation |
| url | http://hdl.handle.net/1721.1/65874 |
| work_keys_str_mv | AT shirokoffdavidgeorge renormalizedwavesandthermalizationofthekleingordonequation |