We study the small mass limit of the equation describing planar motion of a charged particle of a small mass µ in a force field, containing a magnetic component, perturbed by a stochastic term. We regularize the problem by adding a small friction of intensity ǫ > 0. We show that for all small but fixed frictions the small mass limit of qµ,ǫ gives the solution qǫ to a stochastic first order equation, containing a noise-induced drift term. Then, by using a generalization of the classical averaging theorem for Hamiltonian systems by Freidlin and Wentzell, we take the limit of the slow component of the motion qǫ and we prove that it converges weakly to a Markov process on the graph obtained by identifying all points in the same connected components of the level sets of the magnetic field intensity function.
|Original language||English (US)|
|State||Published - Mar 4 2020|
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