# Domain wall dynamics in the Landau--Lifshitz magnet and the classical-quantum correspondence for spin transport

## TL;DR

This paper analyzes the classical Landau--Lifshitz magnet to reveal three distinct spin transport regimes and demonstrates a strong classical-quantum correspondence in spin dynamics, aligning with quantum Heisenberg chain results.

## Contribution

It provides an exact analytical study of spin transport regimes in the classical Landau--Lifshitz model and links these findings to quantum spin chain behavior.

## Key findings

- Ballistic spin expansion in the easy-plane regime
- No spin transport in the easy-axis regime
- Logarithmic diffusion in the isotropic case

## Abstract

We investigate the dynamics of spin in the axially anisotropic Landau--Lifshitz field theory with a magnetic domain wall initial condition. Employing the analytic scattering technique, we obtain the exact scattering data and reconstruct the time-evolved profile. We identify three qualitatively distinct regimes of spin transport, ranging from ballistic expansion in the easy-plane regime, absence of transport in the easy-axis regime and log-modified diffusion for the isotropic interaction. Our results are in perfect qualitative agreement with those found in the anisotropic quantum Heisenberg spin-$1/2$ chain, indicating a remarkable classical-quantum correspondence for macroscopic spin transport.