The thermal flux–flux correlation function and classical-quantum correspondence

Abstract

Exact quantum thermal flux–flux correlations are obtained for the inverted parabolic barrier and free particle by smearing and scaling corresponding two-surface classical correlations. The smearing width is identified as a dynamical uncertainty in x associated with imaginary time evolution by −iħβ/2. The scaling is just the ratio of the high temperature asymptotic form of this dynamical uncertainty to the dynamical uncertainty itself. It represents a sort of quantum amplification. This quantum adaptation of classical flux–flux correlation is generalized to generic one-dimensional barrier systems, and applied to the symmetric and asymmetric Eckart barriers. Good agreement between model and converged numerical results is obtained down to temperatures where tunnelling begins to predominate above-barrier transmission. The model does, however, fail further into the tunnelling regime.