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Journal of Statistical Physics

, Volume 128, Issue 5, pp 1145–1152 | Cite as

Anomalous Dissipation in a Stochastically Forced Infinite-Dimensional System of Coupled Oscillators

  • Jonathan C. Mattingly
  • Toufic M. SuidanEmail author
  • Eric Vanden-Eijnden
Article

Abstract

We study a system of stochastically forced infinite-dimensional coupled harmonic oscillators. Although this system formally conserves energy and is not explicitly dissipative, we show that it has a nontrivial invariant probability measure. This phenomenon, which has no finite dimensional equivalent, is due to the appearance of some anomalous dissipation mechanism which transports energy to infinity. This prevents the energy from building up locally and allows the system to converge to the invariant measure. The invariant measure is constructed explicitly and some of its properties are analyzed.

Keywords

Invariant Measure Orthogonal Polynomial Covariance Structure Stat Phys Cantelli Lemma 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Szegö, G.: Orthogonal Polynomials, 4th edn. American Mathematical Society. Colloquium Publications, vol. 23. American Mathematical Society, Providence (1975) zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Jonathan C. Mattingly
    • 1
  • Toufic M. Suidan
    • 2
    Email author
  • Eric Vanden-Eijnden
    • 3
  1. 1.Duke UniversityDurhamUSA
  2. 2.University of CaliforniaSanta CruzUSA
  3. 3.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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