Nonlinear effective dynamics of Brownian particle in magnetized plasma

TL;DR

This paper develops a nonlinear effective description of a Brownian particle in a magnetized plasma, incorporating corrections beyond the linear Langevin equation using effective field theory and holographic models.

Contribution

It introduces a systematic method to derive a nonlinear effective action for the Brownian particle, capturing quartic corrections and translating it into a Fokker-Planck type equation.

Findings

Derived a quartic-order effective action for the particle.

Confirmed the effective action using a holographic model.

Presented a Fokker-Planck equation describing probability evolution.

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 non-equilibrium effective field theory formalism, and then confirmed via a microscopic holographic model consisting of an open string probing magnetic 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$\ddot{\rm o}$dinger equation and describes time evolution of probability distribution for particle's position and velocity.