Anomalous dissipation in a stochastically forced infinite-dimensional system of coupled oscillators

Jonathan C. Mattingly, Toufic M. Suidan, Eric Vanden Eijnden

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1145-1152
Number of pages8
JournalJournal of Statistical Physics
Volume128
Issue number5
DOIs
StatePublished - Sep 2007

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Infinite-dimensional Systems
Coupled Oscillators
Invariant Measure
Anomalous
Dissipation
dissipation
oscillators
Energy Transport
Conserve
Energy
Harmonic Oscillator
infinity
harmonic oscillators
Probability Measure
energy
Infinity
Converge

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Anomalous dissipation in a stochastically forced infinite-dimensional system of coupled oscillators. / Mattingly, Jonathan C.; Suidan, Toufic M.; Vanden Eijnden, Eric.

In: Journal of Statistical Physics, Vol. 128, No. 5, 09.2007, p. 1145-1152.

Research output: Contribution to journalArticle

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