Berryʹs phase in the presence of a dissipative medium

We consider the spin model coupled to a slowly varying magnetic field in the presence of a weak damping represented by a Lindblad-form operators. We show that Berryʹs geometrical phase remains unaltered by the two dissipation mechanism considered. Dissipation effects are twofold: a shrinking in the modulus of the Blochʹs vector, which characterizes coherence loss and a time-dependent (dissipation related) precession angle. We show that the line broadening of the Fourier transformation of the components of magnetization is only due to the presence of dissipation