推广的Heine-Stieltjes对应原理及其应用  

The extended Heine-Stieltjes correspondence and its applications

作　　者：潘峰[1] 关鑫[1] 史长亮[1] 刘轶彬[1] 

机构地区：[1]辽宁师范大学物理与电子技术学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2012年第2期174-177,共4页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(11175078);教育部博士点专项基金项目(20102136110002)

摘　　要：将Heine-Stieltjes对应原理推广为对应于Gaudin-Richardson模型Bethe假定方程的情形,并依此提出了这类量子多体问题的多项式求解方法.作为应用,讨论了从两格点Bose-Hubbard模型的解而得到的推广Heine-Stieltjes多项式以及标准对力模型严格解及与之相应的推广Heine-Stieltjes多项式的求解方法.The Heine-Stieltjes correspondence is extended to the cases corresponding to the Bethe an- satz equations of the Gaudin-Richardson models, with which a new polynomial approach to exact so- lutions of such quantum many-body problems is established. As examples of the application, the ex- tended Heine-Stieltjes polynomials resulting from the solution of the two-site Bose-Hubbard model and those for the standard nuclear pairing model are discussed. The new approach may be used to search for exact solutions of a large class of quantum many-body problems and to establish a new an- gular momentum projection technique.

关 键 词：推广的Heine-Stieltjes对应原理 量子多体问题 多项式解方法 

分 类 号：O41[理学—理论物理]