TY - GEN
T1 - A homogenization theorem for langevin systems with an application to hamiltonian dynamics
AU - Birrell, Jeremiah
AU - Wehr, Jan
N1 - 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 -