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

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

2006-10-25

arxiv.org/abs/math-ph/0610066v2

Physics

Mathematical Physics

Updated version. Small changes included in finial version to be published in The Journal of Statistical Physics (JSP)

Scientific paper

10.1007/s10955-007-9351-8

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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