TY - JOUR
T1 - Homogenization of dissipative, noisy, Hamiltonian dynamics
AU - Birrell, Jeremiah
AU - Wehr, Jan
N1 - Funding Information:
J.W. was partially supported by NSF grants DMS 131271 and DMS 1615045 . Appendix A
Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2018/7
Y1 - 2018/7
N2 - We study the dynamics of a class of Hamiltonian systems with dissipation, coupled to noise, in a singular (small mass) limit. We derive the homogenized equation for the position degrees of freedom in the limit, including the presence of a noise-induced drift term. We prove convergence to the solution of the homogenized equation in probability and, under stronger assumptions, in an Lp-norm. Applications cover the overdamped limit of particle motion in a time-dependent electromagnetic field, on a manifold with time-dependent metric, and the dynamics of nuclear matter.
AB - We study the dynamics of a class of Hamiltonian systems with dissipation, coupled to noise, in a singular (small mass) limit. We derive the homogenized equation for the position degrees of freedom in the limit, including the presence of a noise-induced drift term. We prove convergence to the solution of the homogenized equation in probability and, under stronger assumptions, in an Lp-norm. Applications cover the overdamped limit of particle motion in a time-dependent electromagnetic field, on a manifold with time-dependent metric, and the dynamics of nuclear matter.
KW - Hamiltonian system
KW - Homogenization
KW - Noise-induced drift
KW - Small mass limit
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U2 - 10.1016/j.spa.2017.09.005
DO - 10.1016/j.spa.2017.09.005
M3 - Article
AN - SCOPUS:85030705246
VL - 128
SP - 2367
EP - 2403
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
IS - 7
ER -