Programs in Physics & Physical Chemistry
|[Licence| Download | New Version Template] aetd_v1_0.tar.gz(38 Kbytes)|
|Manuscript Title: Numerical algorithm for the standard pairing problem based on the Heine-Stieltjes correspondence and the polynomial approach|
|Authors: Xin Guan, Kristina D. Launey, Mingxia Xie, Lina Bao, Feng Pan, Jerry P. Draayer|
|Program title: exactPairingHS|
|Catalogue identifier: AETD_v1_0|
Distribution format: tar.gz
|Journal reference: Comput. Phys. Commun. 185(2014)2714|
|Programming language: Mathematica.|
|Computer: Laptop, workstation.|
|Operating system: Tested with MATHEMATICA version 9.0 on Mac OS X and Windows 7.|
|RAM: Less than 10MB|
|Keywords: Exact pairing problem, Heine-Stieltjes polynomial approach, Second-order Fuchsian equation, Richardson-Gaudin theory, Bethe ansatz equations, Newton-Raphson algorithm, Monte Carlo sampling procedure.|
|PACS: 21.60.Cs, 03.65.Fd, 71.10.Li, 02.60.Cb.|
Nature of problem:
The program calculates exact pairing energies based on the Heine-Stieltjes polynomial approach. Existing conventional exact-pairing approaches require solving systems of highly nonlinear equations, which are difficult and often impossible to solve beyond the simplest of the quantum-mechanical many-particle systems. In this study, the Heine-Stieltjes polynomial approach is employed to provide solutions for more than one or two pairs of particles residing in many energy levels.
The new Heine-Stieltjes polynomial approach transforms the pairing problem to one that involves the handling of only two matrix equations. This, combined with an efficient numerical algorithm implemented by the fast Newton-Raphson method with a Monte Carlo sampling procedure for the initial guesses, makes exact pairing solutions feasible even when more energy levels or heavy nuclei (many pairs) are considered.
Less than a hundred seconds using a 2.80 GHz processor. The notebook takes approximately 23 minutes to complete.
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