Quantum Mechanics Simulated as Branching Process
Abstract
Description
Diffusion processes with branching play an important role in statistical dynamics. They are a common approach to the computing of quantum mechanical groundstates, and serve as models for population dynamics and as physical pictures for biological evolution.
On a computer the efficiency of this simulation method is limited by the approach to the infinitesimal time step, which is necessary to perform alternating diffusion and branching steps.
In this paper, a method is described, which eliminates the infinitesimal time step for a certain class of branching processes, if the process of interest can be ``embedded'' into another process, which is solvable by other analytic and/or numerical methods. The simplest choice for the embbeding process is given by a process with a constant branching rate, which dominates the rate of the embedded process.
4 pages, RevTex, epsf, 3 pictures, submitted to Phys. Rev. Let., revision of minor Latex bug fixes
4 pages, RevTex, epsf, 3 pictures, submitted to Phys. Rev. Let., revision of minor Latex bug fixes