Quantum Mechanics Simulated as Branching Process

Thomas Fricke

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arXiv · cond-mat/9507128

Quantum Mechanics Simulated as Branching Process

Thomas Fricke

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Abstract

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.

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Thomas Fricke. 1995-07-31. Quantum Mechanics Simulated as Branching Process. https://arxiv.org/abs/cond-mat/9507128

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