Theoretical Nuclear Physics

Texas A&M Research Foundation, College Station TX

Investigators

Abstract

The PI and his collaborators have shown that the method of factorizing the operator exp[-dt(T+V)] to fourth order with purely positive coefficients, which has produced superior symplectic integrators for solving classical dynamical problems, has also yielded excellent numerical algorithms for solving the time-dependent Schroedinger equation, the Fokker-Plank equation, the Kramers equation, and the imaginary time Schroedinger equation. The latter has resulted in a number of new fourth order Diffusion Monte Carlo algorithms. These new algorithms require knowing the potential and the gradient of the potential. The fourth order error coefficients of these new algorithms are orders of magnitude smaller then those of the existing split operator (second-order) method and can produce converged results using time steps 10-50 times as large. This operator factorization approach suggests a new class of more efficient algorithms for solving diverse quantum many-body and dynamical problems in nuclear, condensed matter and atomic physics. This proposal seeks to develop further fourth order algorithms for solving large scale, grid based, Hartree-Fock, Kohn-Sham and Gross-Pitaevskii equations in arbitrary three-dimensional geometry.