SEMICLASSICAL CANONICAL RATE THEORY

The exact quantum rate may be represented as a phase space trace of a product of two operators: the symmetrized thermal flux operator and a projection operator onto the product space. A semiclassical analysis o f the phase space representation of these two operators is presented a nd used to explain recent results found for a quantum thermodynamic ra te theory. For low temperatures, the central object that is responsibl e for the oscillatory nature of the Bur operator is a periodic orbit o n the upside down potential surface whose period is 2 (h) over bar/k(B )T. The semiclassical analysis of the flux distribution explains why a variation of the dividing surface leads to improved thermodynamic rar e estimates in asymmetric systems. The semiclassical limit (stationary phase limit) of the projection operator is shown to be identical to t he classical projection operator. A semi-classical rate theory is obta ined using the product of the semiclassical flux distribution and eith er the parabolic barrier or the classical projection operator and comp ared with the exact rate and approximate quantum thermodynamic estimat es. [S1063-651X(98)13310-X].