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Deformed Calogero-Sutherland model and fractional Quantum Hall effect
KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.ORCID-id: 0000-0003-1839-8128
KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
(Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
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.

Nationell ämneskategori
Den kondenserade materiens fysik
Identifikatorer
URN: urn:nbn:se:kth:diva-193356OAI: oai:DiVA.org:kth-193356DiVA, id: diva2:1010345
Anmärkning

QC 20161004

Tillgänglig från: 2016-10-03 Skapad: 2016-10-03 Senast uppdaterad: 2016-10-04Bibliografiskt granskad
Ingår i avhandling
1. A kernel function approach to exact solutions of Calogero-Moser-Sutherland type models
Öppna denna publikation i ny flik eller fönster >>A kernel function approach to exact solutions of Calogero-Moser-Sutherland type models
2016 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Stockholm: Kungliga Tekniska högskolan, 2016. s. 57
Serie
TRITA-FYS, ISSN 0280-316X ; 2016:58
Nyckelord
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
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Annan fysik
Forskningsämne
Fysik
Identifikatorer
urn:nbn:se:kth:diva-193322 (URN)978-91-7729-132-9 (ISBN)
Disputation
2016-10-27, Oskar Kleins auditorium FR4, Roslagstullsbacken 21, Stockholm, 10:00 (Engelska)
Opponent
Handledare
Anmärkning

QC 20161003

Tillgänglig från: 2016-10-04 Skapad: 2016-09-30 Senast uppdaterad: 2016-10-04Bibliografiskt granskad

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Atai, FarrokhLangmann, Edwin
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