# Theory of Skyrmionic Diffusion: Hidden Diffusion Coeffcients and Breathing Diffusion

## TL;DR

This paper develops a new formalism for Skyrmionic diffusion involving PVCF, revealing hidden diffusion coefficients and oscillatory MSD behavior, with implications for correcting classical diffusion formulas.

## Contribution

It introduces a novel system of differential equations for PVCF in magnetic Skyrmions, uncovering hidden diffusion coefficients and oscillatory MSD dynamics.

## Key findings

- Identification of hidden diffusion coefficients in Skyrmionic systems
- Oscillatory behavior of MSD for small damping constants
- Correction of Ornstein-Fuerth formula considering initial PVCF values

## Abstract

Time evolution of the position-velocity correlation functions (PVCF) plays a key role in a new formalism of Brownian motion. A system of differential equations, which governs PVCF, is derived for magnetic Skyrmions on a 2-dimensional magnetic thin film with thermal agitation. In the formalism, a new type of diffusion coeffcient is introduced which does not come out in the usual diffusion equations. The mean-square displacement (MSD) is obtained from the PVCF and found that it oscillates in time when the damping constant is small. It is also shown, even for a structureless particle, that the famous Ornstein-Fuerth formula should be corrected taking a proper initial value of PVCF into account.