Abstract
This chapter provides a review of a new method of addressing problems in diffusion Monte Carlo: the Green’s function first-passage method (GFFP). In particular, we address four new strands of thought and their interaction with the GFFP method: the use of angle-averaging methods to reduce vector or tensor Laplace equations to scalar Laplace equations; the use of the simulation-tabulation (ST) method to dramatically expand the range of the GFFP method; the use of the Feynman-Kac formula, combined with GFFP to actually perform path integrals, one patch at a time; and the development of last-passage diffusion methods; these drastically improve the efficiency of diffusion Monte Carlo methods. All of these techniques are described in detail, with specific examples.
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Given, J.A., Hwang, CO., Mascagni, M. (2004). First- and Last-Passage Algorithms in Diffusion Monte Carlo. In: Wille, L.T. (eds) New Directions in Statistical Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-08968-2_4
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DOI: https://doi.org/10.1007/978-3-662-08968-2_4
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