SEMICLASSICAL DENSITY-MATRIX NEAR THE TOP OF A POTENTIAL BARRIER

Employing the path integral approach, we calculate the semiclassical e quilibrium density matrix of a particle moving in a nonlinear potentia l field for coordinates near the top of a potential barrier As the tem perature is decreased, near a critical temperature T-c the harmonic ap proximation for the fluctuation path integral fails. This is due to a caustic arising at a bifurcation point of the classical paths. We prov ide a selfconsistent scheme to treat the large quantum fluctuations le ading to a nonlinear fluctuation potential. The procedure differs from methods used near caustics of the real time propagator. The semiclass ical density matrix is determined explicitly for the case of asymmetri c barriers from high temperatures down to temperatures somewhat below T-c.