Variational calculation of the dynamics of a two level system interacting with a bath

A variational calculation of the dynamics of a two level system interacting with a bath is presented. The effective tunneling matrix element is renormalized by the interaction with the bath. For the case of a bath with ohmic dissipation (or infrared divergence), the variational calculation gives a vanishing tunneling at T=0 for critical values of the coupling and gives a highly unusual temperature dependence for the tunneling rate for large kT, all of which agree with recent path integral calculations. The present method also yields results for intermediate temperatures and coupling. This indicates that a judicious choice of the zeroth order Hamiltonian to include the major part of the coupling can lead to correct results even in low order perturbation theory.