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Source Identities and Kernel Functions for Deformed (Quantum) Ruijsenaars Models
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
2014 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 104, no 7, 811-835 p.Article in journal (Refereed) Published
Abstract [en]

We consider the relativistic generalization of the quantum A (N-1) Calogero-Sutherland models due to Ruijsenaars, comprising the rational, hyperbolic, trigonometric and elliptic cases. For each of these cases, we find an exact common eigenfunction for a generalization of Ruijsenaars analytic difference operators that gives, as special cases, many different kernel functions; in particular, we find kernel functions for Chalykh-Feigin-Veselov-Sergeev-type deformations of such difference operators which generalize known kernel functions for the Ruijsenaars models. We also discuss possible applications of our results.

Place, publisher, year, edition, pages
2014. Vol. 104, no 7, 811-835 p.
Keyword [en]
exactly solvable models, Ruijsenaars models, Chalykh-Feigin-Veselov-Sergeev type deformation, kernel functions
National Category
Other Physics Topics Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-147020DOI: 10.1007/s11005-014-0690-5ISI: 000336412300002Scopus ID: 2-s2.0-84901603241OAI: oai:DiVA.org:kth-147020DiVA: diva2:728896
Funder
Swedish Research Council, 621-2010-3708
Note

QC 20140625

Available from: 2014-06-25 Created: 2014-06-23 Last updated: 2017-12-05Bibliographically approved
In thesis
1. A kernel function approach to exact solutions of Calogero-Moser-Sutherland type models
Open this publication in new window or tab >>A kernel function approach to exact solutions of Calogero-Moser-Sutherland type models
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This Doctoral thesis gives an introduction to the concept of kernel functionsand their signicance in the theory of special functions. Of particularinterest is the use of kernel function methods for constructing exact solutionsof Schrodinger type equations, in one spatial dimension, with interactions governedby elliptic functions. The method is applicable to a large class of exactlysolvable systems of Calogero-Moser-Sutherland type, as well as integrable generalizationsthereof. It is known that the Schrodinger operators with ellipticpotentials have special limiting cases with exact eigenfunctions given by orthogonalpolynomials. These special cases are discussed in greater detail inorder to explain the kernel function methods with particular focus on the Jacobipolynomials and Jack polynomials.

Place, publisher, year, edition, pages
Stockholm: Kungliga Tekniska högskolan, 2016. 57 p.
Series
TRITA-FYS, ISSN 0280-316X ; 2016:58
Keyword
Kernel functions, Calogero-Moser-Sutherland models, Ruijsenaarsvan Diejen models, Elliptic functions, Exact solutions, Source Identities, Chalykh- Feigin-Sergeev-Veselov type deformations, non-stationary Heun equation
National Category
Other Physics Topics
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-193322 (URN)978-91-7729-132-9 (ISBN)
Public defence
2016-10-27, Oskar Kleins auditorium FR4, Roslagstullsbacken 21, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20161003

Available from: 2016-10-04 Created: 2016-09-30 Last updated: 2016-10-04Bibliographically approved

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