A nonlinear drift which leads to $\kappa$-generalized distributions

TL;DR

This paper introduces a novel nonlinear drift in a Fokker-Planck system that results in a steady-state distribution described by a $$-generalized Gaussian, featuring non-Gaussian power-law tails.

Contribution

It presents a new momentum-dependent drift in the Fokker-Planck equation leading to $$-generalized Gaussian steady states, expanding understanding of non-Gaussian distributions.

Findings

Steady-state distribution is a $$-generalized Gaussian.

The drift coefficient asymptotically decreases as -1/p.

The resulting distribution has power-law tails.

Abstract

We consider a system described by a Fokker-Planck equation with a new type of momentum-dependent drift coefficient which asymptotically decreases as $-1/p$ for a large momentum $p$. It is shown that the steady-state of this system is a $\kappa$-generalized Gaussian distribution, which is a non-Gaussian distribution with a power-law tail.