Fast GPU-based calculations in few-body quantum scattering

TL;DR

This paper introduces a novel GPU-based method for efficiently solving complex few-body quantum scattering problems by discretizing the continuum and leveraging parallel computations, enabling realistic three-body scattering calculations on standard desktops.

Contribution

The paper presents a new approach combining discretization of the continuum with GPU parallelization to solve few-particle quantum scattering problems efficiently.

Findings

Successfully solved three-body scattering above break-up threshold.

Achieved significant reduction in computational time using GPU.

Replaced integral equations with finite matrix equations for faster computation.

Abstract

A principally novel approach towards solving the few-particle (many-dimensional) quantum scattering problems is described. The approach is based on a complete discretization of few-particle continuum and usage of massively parallel computations of integral kernels for scattering equations by means of GPU. The discretization for continuous spectrum of a few-particle Hamiltonian is realized with a projection of all scattering operators and wave functions onto the stationary wave-packet basis. Such projection procedure leads to a replacement of singular multidimensional integral equations with linear matrix ones having finite matrix elements. Different aspects of the employment of a multithread GPU computing for fast calculation of the matrix kernel of the equation are studied in detail. As a result, the fully realistic three-body scattering problem above the break-up threshold is solved on an ordinary desktop PC with GPU for a rather small computational time.