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Series solutions of the non-stationary Heun equation
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]

We consider the non-stationary Heun equation, also known as quantum PainlevéVI, which has appeared in dierent works on quantum integrable models and conformaleld theory. We use a generalized kernel function identity to transform the problemto solve this equation into a dierential-dierence equation which, as we show, canbe solved by ecient recursive algorithms. We thus obtain series representations ofsolutions which provide elliptic generalizations of the Jacobi polynomials. These seriesreproduces, in a limiting case, a perturbative solution of the Heun equation due toTakemura, but our method is dierent in that we expand in non-conventional basisfunctions that allow us to obtain explicit formulas to all orders;

Nyckelord [en]
Heun equation, Lamé equation, Kernel functions, quantum Painlevé VI, perturbation theory
Nationell ämneskategori
Annan fysik
Identifikatorer
URN: urn:nbn:se:kth:diva-193357OAI: oai:DiVA.org:kth-193357DiVA, id: diva2:1010347
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
Nationell ämneskategori
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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