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Deformed Calogero-Sutherland model and fractional Quantum Hall effect
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.ORCID iD: 0000-0003-1839-8128
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The deformed Calogero-Sutherland (CS) model is a quantum integrable systemwith arbitrary numbers of two types of particles and reducing to the standard CSmodel in special cases. We show that a known collective field description of theCS model, which is based on conformal field theory (CFT), is actually a collectivefield description of the deformed CS model. This provides a natural application ofthe deformed CS model in Wen’s effective field theory of the fractional quantumHall effect (FQHE), with the two kinds of particles corresponding to electrons andquasi-hole excitations. In particular, we use known mathematical results aboutsuper Jack polynomials to obtain simple explicit formulas for the orthonormal CFTbasis proposed by van Elburg and Schoutens in the context of the FQHE.

National Category
Condensed Matter Physics
URN: urn:nbn:se:kth:diva-193356OAI: diva2:1010345

QC 20161004

Available from: 2016-10-03 Created: 2016-10-03 Last updated: 2016-10-04Bibliographically 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.
TRITA-FYS, ISSN 0280-316X ; 2016:58
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
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)

QC 20161003

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

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Atai, FarrokhLangmann, Edwin
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