EVALUATION OF COHERENT-STATE PATH-INTEGRALS IN STATISTICAL-MECHANICS BY MATRIX MULTIPLICATION

The numerical evaluation of coherent-state path-integral representatio ns for partition functions and other quantities in equilibrium quantum statistical mechanics is discussed. Several coherent-state path-integ ral schemes are introduced, which differ from each other by the order of approximation and by the operator ordering employed in the high-tem perature approximation of the density operator. Simple one-dimensional systems are used to test these schemes. For the harmonic oscillator, finite-dimensional approximations to the coherent-state path integral are calculated analytically and compared to each other and to the real -space path integral. For anharmonic systems, integrations must be app roximated by quadrature formulas. This leads to a matrix multiplicatio n scheme which is tested for the double-well potential. The results ob tained are accurate from zero temperatures way up into the high-temper ature regime where quantum effects become negligible. This is a signif icant advantage over traditional real-space path integral schemes whic h break down at low temperatures. (C) 1998 American Institute of Physi cs.