Lindblad dynamics of a quantum spherical spin

Abstract

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