Universal destabilization and slowing of spin-transfer functions by a bath of spins

We investigate the effect of a spin bath on the spin-transfer functions of a permanently coupled spin system. When each spin is coupled to a separate environment, the effect on the transfer functions in the first excitation sector is amazingly simple: the group velocity is slowed down by a factor of 2, and the fidelity is destabilized by a modulation of vertical bar cos Gt vertical bar, where G is the mean square coupling to the environment.