Effective classical partition functions with an improved time-dependent reference potential.
The original Feynman-Kleinert [Phys. Rev. A 34, 5080 (1986)] variational approach to Euclidean path integrals is improved by introducing a reference harmonic potential whose center is allowed to change with time. The motion of the center of the potential is varied such that the "effective potential" of Feynman and Kleinert is minimized and leads to an equation of motion for the classical path in the reference system that closely reproduces the "exact" average path. The formalism is applied to the double-well potential V(x)=-x(2)/2 + gx(4)/4+1/4g. This modification improves the accuracy of the approximate quantum-mechanical distribution function and, to a larger extent, the density matrix.
Palmieri
Benoit
B
Department of Chemistry, McGill University, 801 Sherbrooke Ouest, Montréal, Québec, Canada H3A 2K6.
Ronis
David
D