FERMION DIFFUSION AND THE FEYNMAN-KAC FUNCTIONAL FOR INTERACTING FERMIONS

The fermion diffusion process, which we recently introduced, is confro nted with quantum Monte-Carlo calculations for an interacting fermion system with harmonic interactions. The study of this model illustrates that fermion diffusion in general leads to either the exact groundsta te energy or to an exact excited state of the system, whereas a quantu m Monte-Carlo calculation based on the nodal surface leads to an upper bound for the groundstate energy. We discovered how a class of totall y positive determinants relevant for our process allows us to construc t sample paths with a rejection technique. It is then obvious that the stochastic implementation of the anti-commutation relations introduce s no extra noise. Both conceptually and practically are therefore have developed a methodology which; does not suffer from the so-called sig n problem for fermions.