Dynamics of a Pair of Interacting Spins Coupled to an Environmental Sea

TL;DR

This paper analytically explores the complex dynamics of two interacting spins coupled to an environment, revealing regimes of locking, correlated relaxation, and mutual coherence, applicable to various quantum and microscopic systems.

Contribution

It provides the first comprehensive analytic solution for the dynamics of two spins coupled to an environment across multiple regimes.

Findings

Identification of three distinct dynamical regimes

Analytic expressions for spin behavior in each regime

Applicable to diverse physical systems with coupled spins

Abstract

We solve for the dynamics of a pair of spins, coupled to each other and also to an environmental sea of oscillators. The environment mediates an indirect interaction between the spins, causing both mutual coherence effects and dissipation. This model describes a wide variety of physical systems, ranging from 2 coupled microscopic systems (eg., magnetic impurities, bromophores, etc), to 2 coupled macroscopic quantum systems. We obtain analytic results for 3 regimes, viz., (i) The locked regime, where the 2 spins lock together; (ii) The correlated relaxation regime (mutually correlated incoherent relaxation); and (iii) The mutual coherence regime, with correlated damped oscillations. These results cover most of the parameter space of the system.