Transition between quantum coherence and incoherence

We show that a transformed Caldeira-Leggett Hamiltonian has two distinct families of fixed points rather than a single unique fixed point as often conjectured based on its connection to the anisotropic Kondo model. The two families are distinguished by a sharp qualitative difference in their quantum coherence properties and we argue that this distinction is best understood as the result of a transition in the model between degeneracy and nondegeneracy in the spectral function of the ``spin-flip'' operator.