Second Order Corrections to the Variational Approximation to Frolich's Polaron Model.

Using Feynman's path integral variational principle with a general quadratic trial action, we obtain equations for the absorption function of Frolich's polaron model. We evaluate numerically this absorption function in several cases. To test the accuracy of the variational absorption function, we develop formulas for the second order corrections to the absorption function and evaluate these numerically. Rather than evaluating the correction directly in the double path integral formalism, we make analytic continuations in time which reduce the amount of labor involved in deriving the expressions for the corrections. The method of analytic continuation in time is generalized in such a way as to allow application of the variational principle to nonlinear transport problems and time dependent problems. Finally, we present the variational equations and the second order corrections to them for a somewhat more realistic model of an electron in a crystal.