Finite-dimensional colored fluctuation-dissipation theorem for spin systems

TL;DR

This paper develops a finite-dimensional fluctuation-dissipation theorem for spin systems under non-Markovian noise, addressing complexities introduced by damping and non-linear noise-spin mappings.

Contribution

It introduces a new finite-dimensional fluctuation-dissipation theorem applicable to discretized spin dynamics with non-Markovian noise and damping effects.

Findings

The theorem applies to non-Markovian noise in spin systems.

It accounts for zero modes in the fluctuation-dissipation relation.

Subtleties with Gilbert damping and non-linear mappings are analyzed.

Abstract

When nano-magnets are coupled to random external sources, their magnetization becomes a random variable, whose properties are defined by an induced probability density, that can be reconstructed from its moments, using the Langevin equation, for mapping the noise to the dynamical degrees of freedom. When the spin dynamics is discretized in time, a general fluctuation-dissipation theorem, valid for non-Markovian noise, can be established, even when zero modes are present. We discuss the subtleties that arise, when Gilbert damping is present and the mapping between noise and spin degrees of freedom is non--linear.