The linear and nonlinear dynamical susceptibilities of a two level system are
calculated as it undergoes a transition to a decoherent state. Analogously to
the Glover-Tinkham-Ferrell sum rule of superconductivity, spectral weight in
the linear susceptibility is continuously transferred from a finite frequency
resonance to nearly zero frequency, corresponding to a broken symmetry in the
thermodynamic limit. For this reason, the behavior of the present model (the
Mermin model) differs significantly from the spin-boson model. The third order
nonlinear susceptibility, corresponding to two-photon absorption, has an
unexpected non-monotonic behavior as a function of the environmental coupling,
reaching a maximum within the decoherent phase of the model. Both linear and
nonlinear susceptibilities may be expressed in a universal form.Comment: 10 pages, 9 figure