TY - JOUR

T1 - Anomalous dissipation in a stochastically forced infinite-dimensional system of coupled oscillators

AU - Mattingly, Jonathan C.

AU - Suidan, Toufic M.

AU - Vanden-Eijnden, Eric

N1 - Funding Information:
Acknowledgements We thank Percy Deift, Charles Fefferman, Stephanos Venakides, and Xin Zhou for useful conversations. J. Mattingly is supported in part by the Sloan Foundation and by an NSF CAREER award DMS04-49910. T. Suidan is supported in part by NSF grant DMS05-53403. E. Vanden-Eijnden is supported in part by NSF grants DMS02-09959 and DMS02-39625, and by ONR grant N00014-04-1-0565.

PY - 2007/9

Y1 - 2007/9

N2 - 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.

AB - 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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U2 - 10.1007/s10955-007-9351-8

DO - 10.1007/s10955-007-9351-8

M3 - Article

AN - SCOPUS:34547746889

SN - 0022-4715

VL - 128

SP - 1145

EP - 1152

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 5

ER -