Dissipative Dynamics of a Two-State System, the Kondo Problem, and the Inverse-Square Ising Model

The dynamics of a two-state system coupled to an Ohmic continuum, the dissipative two-state system, is solved by exploiting its connection to the Kondo problem and the inverse-square Ising model. Such a system is known to possess a zero temperature quantum critical point. In the quantum disordered phase the asymptotic dynamics is always an incoherent power-law relaxation. At short times, the system can exhibit damped oscillations only over a limited range of parameters.