Microscopic derivation of a class of non-linear dissipative schrödinger-like equations

The general formalism of master equations is used together with a projection which preserves the pure states to derive a class of non-linear Schrödinger-like equations. The result is applied to a spin- 1 2 coupled to a bath of two-level systems and the Bloch equations are recovered. Finally we make a connection with Sz-Nagy's theorem on the dilations of contracting semi-groups.