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arXiv · 1404.5253

New general approach in few-body scattering calculations: Solving discretized Faddeev equations on a graphics processing unit

V. N. Pomerantsev·V. I. Kukulin·O. A. Rubtsova
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Abstract

Background: The numerical solution of few-body scattering problems with realistic interactions is a difficult problem that normally must be solved on powerful supercomputers, taking a lot of computer time. This strongly limits the possibility of accurate treatments for many important few-particle problems in different branches of quantum physics. Purpose: To develop a new general highly effective approach for the practical solution of few-body scattering equations that can be implemented on a graphics processing unit. Methods: The general approach is realized in three steps: (i) the reformulation of the scattering equations using a convenient analytical form for the channel resolvent operator; (ii) a complete few-body continuum discretization and projection of all operators and wave functions onto a $L_2$ basis constructed from stationary wave packets and (iii) the ultra-fast solution of the resulting matrix equations using graphics processor. Results: The whole approach is illustrated by a calculation of the neutron-deuteron elastic scattering cross section below and above the three-body breakup threshold with a realistic $NN$ potential which is performed on a standard PC using a graphics processor with an extremely short runtime. Conclusions: The general technique proposed in this paper opens a new way for a fast practical solution of quantum few-body scattering problems both in non-relativistic and relativistic formulations in hadronic, nuclear and atomic physics.

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V. N. Pomerantsev, V. I. Kukulin, O. A. Rubtsova. 2014-07-01. New general approach in few-body scattering calculations: Solving discretized Faddeev equations on a graphics processing unit. https://doi.org/10.1103/physrevc.89.064008

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