Dynamics of a large spin with weak dissipation

Abstract

We investigate the generalization of the spin-boson model to arbitrary spin size. The Born-Markov approximation is employed to derive a master equation in the regime of small coupling strengths to the environment. For spin one half, the master equation transforms into a set of Bloch equations, the solution of which is in good agreement with results of the spin-boson model for weak ohmic dissipation. For larger spins, we find a superradiance-like behavior known from the Dicke model. The influence of the nonresonant bosons of the dissipative environment can lead to the formation of a beat pattern in the dynamics of the $z$-component of the spin. The beat frequency is approximately proportional to the cutoff $ω_c$ of the spectral function.

11 pages, 3 figures, to appear in Chemical Physics Special Issue on the Spin-Boson Problem, ed. by H. Grabert and A. Nitzan