Abstract
An effective description is presented for a Brownian particle in a magnetized plasma. In order to systematically capture various corrections to linear Langevin equation, we construct effective action for the Brownian particle, to quartic order in its position. The effective action is first derived within nonequilibrium effective field theory formalism, and then confirmed via a microscopic holographic model consisting of an open string probing magnetic fifth-dimensional anti--de Sitter (${\mathrm{AdS}}_{5}$) black brane. For practical usage, the non-Gaussian effective action is converted into Fokker-Planck-type equation, which is an Euclidean analog of Schr\"odinger equation and describes time evolution of probability distribution for particle's position and velocity.
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