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We study the small mass limit of the equation describing planar motion of a charged particle of a small mass $mu$ in a force field, containing a magnetic component, perturbed by a stochastic term. We regularize the problem by adding a small friction of intensity $e>0$. We show that for all small but fixed frictions the small mass limit of $q_{mu, e}$ gives the solution $q_e$ 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 $q_e$ 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.
We apply Bogolyubovs averaging theorem to the motion of an electron of an atom driven by a linearly polarized laser field in the Kramers-Henneberger frame. We provide estimates of the differences between the original trajectories and the trajectories
The Smoluchowski equation is a system of partial differential equations modelling the diffusion and binary coagulation of a large collection of tiny particles. The mass parameter may be indexed either by positive integers, or by positive reals, these
The classical relationship between the Tutte polynomial of graph theory and the Potts model of statistical mechanics has resulted in valuable interactions between the disciplines. Unfortunately, it does not include the external magnetic fields that a
We study the impact of a finite magnetic field on the deconfinement phase transition for heavy quarks by computing the fluctuations of the Polyakov loops. It is demonstrated that the explicit Z(3) breaking field increases with the magnetic field, lea
We investigate a motion of a colloid in a harmonic trap driven out of equilibrium by an external non-conservative force producing a torque in the presence of a uniform magnetic field. We find that steady state exists only for a proper range of parame