Low-temperature approximations for Feynman path integrals and their applications in quantum equilibrium and dynamical problems

Abstract

A new approximation for discretized equilibrium Feynman path integrals for both a single degree of freedom and for many coupled degrees of freedom is presented. The approximation is suitable for harmonic and anharmonic oscillators with discrete bound states, but not for free particles and scattering problems. It is capable of accounting for zero-point motion in an approximate way. When compared to the standard high-temperature approximation, the new approximation leads to more accurate results, especially in the limit of zero temperatures. When generalized to the computation of thermally symmetrized time correlation functions, this new approximation does not suffer from the usual phase cancellation problems and can be extended to time t≫βℏ/2 in some cases. The utility of this new approximation in equilibrium and dynamical problems is illustrated with several numerical examples.