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

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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.

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References

  1. Abramowitz, M., Stegun, I. (ed.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York (1992), reprint of the 1972 edition

    Google Scholar 

  2. Deift, P.A.: Orthogonal Polynomials and Random Matrices: a Riemann–Hilbert Approach. Courant Lecture Notes in Mathematics, vol. 3. New York University Press, New York (1999)

    Google Scholar 

  3. Mattingly, J.C., Suidan, T.M., Vanden-Eijnden, E.: Simple systems with anomalous dissipation and energy cascade. arxiv.org/abs/math-ph/0607047

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

    MATH  Google Scholar 

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Authors and Affiliations

  1. Duke University, Box 90320, Durham, NC, 27708-0320, USA

    Jonathan C. Mattingly

  2. University of California, Santa Cruz, CA, 95064, USA

    Toufic M. Suidan

  3. Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY, 10012, USA

    Eric Vanden-Eijnden

Authors
  1. Jonathan C. Mattingly
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  2. Toufic M. Suidan
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  3. Eric Vanden-Eijnden
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Correspondence to Toufic M. Suidan.

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Mattingly, J.C., Suidan, T.M. & Vanden-Eijnden, E. Anomalous Dissipation in a Stochastically Forced Infinite-Dimensional System of Coupled Oscillators. J Stat Phys 128, 1145–1152 (2007). https://doi.org/10.1007/s10955-007-9351-8

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  • DOI: https://doi.org/10.1007/s10955-007-9351-8

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