Bloch-Redfield theory of high-temperature magnetic fluctuations in interacting spin systems

TL;DR

This paper derives an effective diffusion model for high-temperature magnetic fluctuations in interacting spin systems, showing how magnetic field gradients and external noise influence spin relaxation and diffusion.

Contribution

It introduces a microscopic derivation of spin dynamics leading to a diffusion equation with a variable diffusion coefficient based on magnetic field gradients.

Findings

Diffusion coefficient depends on magnetic field gradient and spin interactions

External noise affects relaxation times and diffusion behavior

Effective equations of motion accurately describe high-temperature spin fluctuations

Abstract

We study magnetic fluctuations in a system of interacting spins on a lattice at high temperatures and in the presence of a spatially varying magnetic field. Starting from a microscopic Hamiltonian we derive effective equations of motion for the spins and solve these equations self-consistently. We find that the spin fluctuations can be described by an effective diffusion equation with a diffusion coefficient which strongly depends on the ratio of the magnetic field gradient to the strength of spin-spin interactions. We also extend our studies to account for external noise and find that the relaxation times and the diffusion coefficient are mutually dependent.