Lindblad dynamics of a quantum spherical spin

TL;DR

This paper investigates the quantum dynamics of a constrained bosonic spin system coupled to a heat bath, revealing distinct regimes of relaxation and a re-entrant phase diagram akin to classical fluctuation-induced order.

Contribution

It provides an exact solution to the Lindblad dynamics of a quantum spherical spin and explores its relation to the Dicke model, highlighting novel quantum fluctuation and dissipation effects.

Findings

Identification of weak and strong coupling regimes affecting relaxation.

Exact solutions for quantum observables' equations of motion.

Discovery of a re-entrant quantum phase diagram with fluctuation-induced order.

Abstract

The coherent quantum dynamics of a single bosonic spin variable, subject to a constraint derived from the quantum spherical model of a ferromagnet, and coupled to an external heat bath, is studied through the Lindblad equation for the reduced density matrix. Closed systems of equations of motion for several quantum observables are derived and solved exactly. The relationship to the single-mode Dicke model from quantum optics is discussed. The analysis of the interplay of the quantum fluctuation and the dissipation and their influence on the relaxation of the time-dependent magnetisation leads to the distinction of qualitatively different regimes of weak and strong quantum couplings. Considering the model's behaviour in an external field as a simple mean-field approximation of the dynamics of a quantum spherical ferromagnet, the magnetic phase diagramme appears to be re-entrant and presents a quantum analogue of well-established classical examples of fluctuation-induced order.