  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.
