Exponential Dephasing of Oscillators in the Kinetic Kuramoto Model

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• 作者：Dario Benedetto ; Emanuele Caglioti ; Umberto Montemagno
• 关键词：Kuramoto model ; Dephasing ; Landau damping ; Abstract Cauchy–Kowalewskaya theorem ; 35A10 ; 35Q92 ; 74A25 ; 76N10 ; 92B25
• 刊名：Journal of Statistical Physics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：162
• 期：4
• 页码：813-823
• 全文大小：419 KB
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• 作者单位：Dario Benedetto (1)
  Emanuele Caglioti (1)
  Umberto Montemagno (1)
  
  1. Dipartimento di Matematica, Sapienza Università di Roma, P.zle A. Moro, 5, 00185, Rome, Italy
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Statistical Physics
  Mathematical and Computational Physics
  Physical Chemistry
  Quantum Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9613

文摘

We study the kinetic Kuramoto model for coupled oscillators with coupling constant below the synchronization threshold. We manage to prove that, for any analytic initial datum, if the interaction is small enough, the order parameter of the model vanishes exponentially fast, and the solution is asymptotically described by a free flow. This behavior is similar to the phenomenon of Landau damping in plasma physics. In the proof we use a combination of techniques from Landau damping and from abstract Cauchy–Kowalewskaya theorem. Keywords Kuramoto model Dephasing Landau damping Abstract Cauchy–Kowalewskaya theorem