Fermion Monte Carlo
Prof. Malvin H. Kalos (Lawrence Livermore National Laboratory)

This talk will outline Monte Carlo methods that enable numerical solution of the many-body non-relativistic Schroedinger Equation. They permit computations with no uncontrolled approximations for the ground states of bosonic systems. Because the Pauli principle imposes a non-local constraint on the solution, extension to fermionic systems has proved much more difficult. The algorithmic barriers will be outlined, together with techniques that overcome them. These include the use of populations of pairs of random walkers that carry opposite algebraic signs; correlation of the diffusion of the pair; cancellation of pairs that become close; importance sampling; and the use of different dynamics whose choice depends on the signs of the walkers. The last breaks the "plus-minus symmetry" and thereby provably achieves statistical stability.