Matrix quantum mechanics an dintegrable systems

Pehlivan, Yamaç
In this thesis we improve and extend an algebraic technique pioneered by M. Gaudin. The technique is based on an infinite dimensional Lie algebra and a related family of mutually commuting Hamiltonians. In order to find energy eigenvalues of such Hamiltonians one has to solve the equations of Bethe ansatz. However, in most cases analytical solutions are not available. In this study we examine a special case for which analytical solutions of Bethe ansatz equations are not needed. Instead, some special properties of these equations are utilized to evaluate the energy eigenvalues. We use this method to find exact expressions for the energy eigenvalues of a class of interacting boson models. In addition to that, we also introduce a q-deformation of the algebra of Gaudin. This deformation leads us to another family of mutually commuting Hamiltonians which we diagonalize using algebraic Bethe ansatz technique. The motivation for this deformation comes from a relationship between Gaudin algebra and a spin extension of the integrable model of F. Calogero. Observing this relation, we then consider a well known periodic version of Calogero's model which is due to B. Sutherland. The search for a Gaudin-like algebraic structure which is in a similar relationship with the spin extension of Sutherland's model naturally leads to the above mentioned q-deformation of Gaudin algebra. The deformation parameter q and the periodicity d of the Sutherland model are related by the formula q=i{


Inverse Sturm-Liouville problems with pseudospectral methods
Altundag, H.; Boeckmann, C.; Taşeli, Hasan (2015-07-03)
In this paper a technique to obtain a first approximation for singular inverse Sturm-Liouville problems with a symmetrical potential is introduced. The singularity, as a result of unbounded domain (-infinity, infinity), is treated by considering numerically the asymptotic limit of the associated problem on a finite interval (-L, L). In spite of this treatment, the problem has still an ill-conditioned structure unlike the classical regular ones and needs regularization techniques. Direct computation of eigen...
Oscillation of integro-dynamic equations on time scales
Grace, Said R.; Graef, John R.; Zafer, Ağacık (2013-04-01)
In this paper, the authors initiate the study of oscillation theory for integro-dynamic equations on time-scales. They present some new sufficient conditions guaranteeing that the oscillatory character of the forcing term is inherited by the solutions.
Geometrical phases and magnetic monopoles
Değer, Sinan; Tekin, Bayram; Department of Physics (2011)
In this thesis, we study the subject of geometrical phases in detail by considering its various forms. We focus primarily on the relation between quantum geometrical phases and magnetic monopoles, and study how one can make use of the concepts of geometrical phases to define magnetic monopoles.
Circular plates on elastic foundations modelled with annular plates
Utku, M; Citipitioglu, E; Inceleme, I (2000-11-01)
In this paper, a new formulation is presented for the analysis of circular plates supported on elastic foundations. The formulation is based on the flexibility and stiffness methods of structural analysis. Classical thin plate theory for small deformations is applied to obtain the flexibility and stiffness coefficients. The circular plate is represented as a series of simply supported annular plates resting on support springs along their common edges. The computer implementation of the method is given, and ...
Density functional theory investigation of TiO2 anatase nanosheets
Sayın, Ceren Sibel; Toffoli, Hande; Department of Physics (2009)
In this thesis, the electronic properties of nanosheets derived from TiO2 anatase structure which acts as a photocatalyst, are investigated using the density functional theory. We examine bulk constrained properties of the nanosheets derived from the (001) surface and obtain their optimized geometries. We investigate properties of lepidocrocite-type TiO2 nanosheets and nanotubes of different sizes formed by rolling the lepidocrocite nanosheets. We show that the stability and the band gaps of the considered ...
Citation Formats
Y. Pehlivan, “Matrix quantum mechanics an dintegrable systems,” Ph.D. - Doctoral Program, Middle East Technical University, 2004.