2011/06/26 by Feng Pan, Xin Guan, Kristina D. Launey +3 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Ansatz #Atomic and Molecular Physics #Bethe ansatz #Combinatorics #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Nuclear physics research studies #Pairing #Physics #Polynomial #Projection (relational algebra) #Pure mathematics #Quantum mechanics #cond-mat.str-el #math-ph #math.MP #nucl-th #quant-ph
paper · pdf · doi:10.1103/physrevc.86.024313
ReVTeX, 4 pages, no figure
arxiv created 2011/06/26 · openalex publication_date 2012/08/28 · arxiv updated 2015/05/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A new approach for solving the Bethe ansatz (Gaudin-Richardson) equations of the standard pairing problem is established based on the Heine-Stieltjes correspondence. For k pairs of valence nucleons on n different single-particle levels, it is found that solutions of the Bethe ansatz equations can be obtained from one (k+1)\ifmmode×\else\texttimes\fi(k+1) and one (n\ensuremath-1)\ifmmode×\else\texttimes\fi(k+1) matrices, which are associated with the extended Heine-Stieltjes and Van Vleck polynomials, respectively. Since the coefficients in these polynomials are free from divergence with variations in contrast to the original Bethe ansatz equations, the approach provides an efficient and systematic way to solve the problem, which by extension, can also be used to solve a large class of Gaudin-type quantum many-body problems, including an efficient angular momentum projection method for multiparticle systems.