Highly optimized fourth-order short-time approximation for path integrals.
We derive a fourth-order short-time approximation for use in imaginary-time path-integral simulations. The short-time approximation converges for all continuous and bounded-from-below potentials, attains quartic order of convergence for sufficiently smooth potentials, and utilizes statistically independent random variables for its construction. These properties recommend the approximation as a natural replacement of the trapezoidal Trotter-Suzuki approximation for physical systems with continuous distributions.
Predescu
Cristian
C
Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720, USA. cpredescu@comcast.net