Magnetic field induced anomalous distribution of particles

TL;DR

This paper demonstrates that a fluctuating magnetic field can induce anomalous, non-Boltzmann particle distributions even in linear stochastic systems, and explores complex distributions in nonlinear systems with potential implications for semiconductor physics.

Contribution

It reveals that magnetic field-induced anomalies in particle distributions can occur in linear stochastic systems, expanding understanding beyond nonlinear noise-induced transitions.

Findings

Magnetic field alters stationary particle distribution shape.

Distribution can become non-monotonic and deviate from Boltzmann.

Complex distributions with multiple islands can emerge in nonlinear systems.

Abstract

It seems that a stochastic system must be a nonlinear one to observe the phenomenon, noise induced transition. But in the present paper, we have demonstrated that the phenomenon may be observed even in a linear stochastic process where both deterministic and stochastic parts are linear functions of the relevant phase space variables. The shape of the stationary distribution of particles (which are confined in a harmonic potential) may change on increasing the strength of the applied fluctuating magnetic field. The probability density may vary non monotonically with an increase in the coordinate of a Brownian particle. Thus the distribution of particles may deviate strongly from the Boltzmann one and it is a unique signature of the fluctuating magnetic field. Then we are motivated strongly to study the distribution of particles in a nonlinear stochastic system where the Brownian particles are confined in a bi-stable potential energy field in the presence of the fluctuating magnetic field. With a relatively large strength of the fluctuating field, the distribution of particles may be a strange one where many islands may appear which are not expected from the given potential energy field. It may offer an explanation to describe the phenomenon, the reduction of the current in a semiconductor in the presence of a time dependent magnetic field.