TY - GEN

T1 - A homogenization theorem for langevin systems with an application to hamiltonian dynamics

AU - Birrell, Jeremiah

AU - Wehr, Jan

N1 - Funding Information:
J. W. was partially supported by NSF grants DMS 131271 and
Funding Information:
J. W. was partially supported by NSF grants DMS 131271 and DMS 1615045.
Publisher Copyright:
© Springer Nature Singapore Pte Ltd 2019.

PY - 2019

Y1 - 2019

N2 - This paper studies homogenization of stochastic differential systems. The standard example of this phenomenon is the small mass limit of Hamiltonian systems. We consider this case first from the heuristic point of view, stressing the role of detailed balance and presenting the heuristics based on a multiscale expansion. This is used to propose a physical interpretation of recent results by the authors, as well as to motivate a new theorem proven here. Its main content is a sufficient condition, expressed in terms of solvability of an associated partial differential equation (“the cell problem”), under which the homogenization limit of an SDE is calculated explicitly. The general theorem is applied to a class of systems, satisfying a generalized detailed balance condition with a position-dependent temperature.

AB - This paper studies homogenization of stochastic differential systems. The standard example of this phenomenon is the small mass limit of Hamiltonian systems. We consider this case first from the heuristic point of view, stressing the role of detailed balance and presenting the heuristics based on a multiscale expansion. This is used to propose a physical interpretation of recent results by the authors, as well as to motivate a new theorem proven here. Its main content is a sufficient condition, expressed in terms of solvability of an associated partial differential equation (“the cell problem”), under which the homogenization limit of an SDE is calculated explicitly. The general theorem is applied to a class of systems, satisfying a generalized detailed balance condition with a position-dependent temperature.

KW - Hamiltonian system

KW - Homogenization

KW - Noise-induced drift

KW - Small mass limit

KW - Stochastic differential equation

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U2 - 10.1007/978-981-15-0294-1_4

DO - 10.1007/978-981-15-0294-1_4

M3 - Conference contribution

AN - SCOPUS:85077715059

SN - 9789811502934

T3 - Springer Proceedings in Mathematics and Statistics

SP - 89

EP - 122

BT - Sojourns in Probability Theory and Statistical Physics - I - Spin Glasses and Statistical Mechanics, A Festschrift for Charles M. Newman

A2 - Sidoravicius, Vladas

PB - Springer

T2 - International Conference on Probability Theory and Statistical Physics, 2016

Y2 - 25 March 2016 through 27 March 2016

ER -