Analytical solutions for a charged particle with white, thermal, and active noises in the presence of a uniform magnetic field

TL;DR

This paper derives analytical solutions for the probability density of a charged particle influenced by various noises in a magnetic field, enhancing understanding of its stochastic dynamics.

Contribution

It provides the first analytical solutions for the joint probability density of a charged particle under combined white, thermal, and active noises in a magnetic field.

Findings

Analytical solutions obtained for different time domains.

Enhanced understanding of stochastic behavior of charged particles.

Framework applicable to complex noise environments.

Abstract

We study the two-dimensional equations of motion for a charged particle subjected to white, thermal, and active noises in uniform a magnetic field. By deriving the corresponding Fokker Planck equation, analytical solutions for the joint probability density are obtained in different time domains.