Solving spin quantum-master equations with matrix continued-fraction methods: application to superparamagnets

TL;DR

This paper introduces a continued-fraction method to solve quantum master equations for spins, enabling exact calculations of the full density matrix including relaxation, coherence, and dynamical properties in superparamagnets.

Contribution

The authors develop a novel continued-fraction approach to exactly solve quantum master equations for arbitrary spins coupled to thermal baths, capturing both relaxation and coherent dynamics.

Findings

Exact solutions for spin density matrices including coherence and relaxation.

Analysis of static response and dynamical susceptibility in superparamagnets.

Demonstration of spin resonance phenomena in transverse fields.

Abstract

We implement continued-fraction techniques to solve exactly quantum master equations for a spin with arbitrary S coupled to a (bosonic) thermal bath. The full spin density matrix is obtained, so that along with relaxation and thermoactivation, coherent dynamics is included (precession, tunnel, etc.). The method is applied to study isotropic spins and spins in a bistable anisotropy potential (superparamagnets). We present examples of static response, the dynamical susceptibility including the contribution of the different relaxation modes, and of spin resonance in transverse fields.