Marchenko method with incomplete data and singular nucleon scattering

We apply the Marchenko method of quantum inverse scattering to study nucleon scattering problems. Assuming a $\beta/r^2$ type repulsive core and comparing our results to the Reid93 phenomenological potential we estimate the constant $\beta$, determining the singularity strength, in various spin/isospin channels. Instead of using Bargmann type S-matrices which allows only integer singularity strength, here we consider an analytical approach based on the incomplete data method, which is suitable for fractional singularity strengths as well.Comment: 20 pages, 8 figures, published versio

Neutron-proton scattering and singular potentials

We consider a Bargmann-type rational parametrization of the nucleon scattering phase shifts. Applying Marchenko's method of quantum inverse scattering we show that the scattering data suggest a singular repulsive core of the potential of the form $2/r^2$ and $6/r^2$ in natural units, for the ${}^3S_1$ and ${}^1S_0$ channels respectively. The simplest solution in the ${}^3S_1$ channel contains three parameters only but reproduces all features of the potential and bound state wave function within one percent error. We also consider the ${}^3S_1$-${}^3D_1$ coupled channel problem with the coupled channel Marchenko inversion method.Comment: 39 pages. Extended version. Title changed, presentation improved and a new appendix on the coupled channel problem adde

Quantum Mechanıcal Systems Wıth Noncommutatıve Phase Space Varıables

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2008Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2008Bu çalışmada Moyal parantezinin yarıklasik limiti alınarak spin dinamiği incelenmiştir. Ele alınan sistemi tanımlayan lagrange fonksiyoneli tekil olduğundan sistemin bağları ve seçilen ayar alanları ile koordinatlar bir deformasyon parametresi yardımıyla uyuşumsuz hale gelmiş ve sistemin dinamiğini belirleyen yarıklasik parantezler ile Hall etkisi ve iki farklı formulasyonuyla spin Hall etkisi tartışılmıştır. Yarıklasik limitte hesaplar yapıldığından hem klasik olayları hem de kuantum mekaniksel olayları incelemek mümkün olmuştur. Klasik sistemler göz önüne alındığında yarıklasik parantezler Poisson parantezlerine dönüşmüşlerdir. Spin, kuantum mekaniksel bir olgu olması sebebi ile yarıklasik limitte incelenebilmiş ve iki farklı formulasyonda da spin Hall iletkenliği bulunmuştur. Hall etkisi incelenirken deformasyon parametresinin uygun seçimi ile kuantum Hall iletkenliği bulunmuş böylelikle etkileşimsiz bir teoriden etkileşimli bir teoriye geçiş sağlanmıştır. Spin Hall etkisi incelenirken deformasyon parametresinin uygun seçimi ile literatürdeki farklı spin Hall iletkenlik sonuçlarına ulaşılmıştır. Hesaplanan sonuçlar literatürdekilerle uyum içerisinde olmakla beraber yeni öngörüler de sunabilmektedir.In this study extending Moyal bracket in the semiclassical limit spin dynamics are discussed. Because the lagrangian describing the physical system is singular together with constraints and gauge fields the coordinates become noncommuting via a deformation parameter and with the help of semiclassical paranthesis obtained from Moyal brackets Hall effect and two different formulations of spin Hall effect are argued. It is possible to explain both classical and quantum dynamics in the semiclassical limit. When classical systems are considered semiclassical paranthesis those describes the dynamics of the physical systems turn to be classical Poisson brackets. Because spin is a quantum mechanical concept it can be discussed in the semiclassical limit and with two different formulations spin Hall conductivity is obtained. When Hall effect is discussed with an appropriate choice of deformation parameter quantum Hall conductivity is obtained so a passage from noninteracting theory to an interacting theory is found. Moreover when spin Hall effect is considered with an appropriate choice of deformation parameter different manifestations of the theory are obtained. All results found in the study are in a good agreement with the ones in the literature.Yüksek LisansM.Sc

Various disguises of the Pais-Uhlenbeck oscillator

Beginning with a simple set of planar equations, we discuss novel realizations of the Pais-Uhlenbeck oscillator in various contexts. First, due to the bi-Hamiltonian character of this model, we develop a Hamiltonian approach for the Eisenhart-Duval lift of the related dynamics. We apply this approach to the previously worked example of a circularly polarized periodic gravitational wave. Then, we present our further results. Firstly, we show that the transverse dynamics of the Lukash plane wave and a complete gravitational wave pulse can also lead to the Pais-Uhlenbeck oscillator. We express the related Carroll Killing vectors in terms of the Pais-Uhlenbeck frequencies and derive extra integrals of motion from the conformal Newton-Hooke symmetry. In addition, we find that the 3+1 dimensional Penning trap can be canonically mapped to the 6th order Pais-Uhlenbeck oscillator. We also carry the problem to the non-commutative plane. Lastly, we discuss other examples like the motion of a charged particle under electromagnetic field created with double copy.Comment: published version, 27 pages, no figure

Effective field theory of topological insulator and the Foldy-Wouthuysen transformation

Employing the Foldy-Wouthuysen transformation it is demonstrated straightforwardly that the first and second Chern numbers are equal to the coefficients of the 2+1 and 4+1 dimensional Chern-Simons actions which are generated by the massive Dirac fermions coupled to the Abelian gauge fields. A topological insulator model in 2+1 dimensions is discussed and by means of a dimensional reduction approach the 1+1 dimensional descendant of the 2+1 dimensional Chern-Simons theory is presented. Field strength of the Berry gauge field corresponding to the 4+1 dimensional Dirac theory is explicitly derived through the Foldy-Wouthuysen transformation. Acquainted with it the second Chern numbers are calculated for specific choices of the integration domain. A method is proposed to obtain 3+1 and 2+1 dimensional descendants of the effective field theory of the 4+1 dimensional time reversal invariant topological insulator theory. Inspired by the spin Hall effect in graphene, a hypothetical model of the time reversal invariant spin Hall insulator in 3+1 dimensions is proposed.Comment: 20 pages. Few corrections and Refs. adde

Spin Hall Effect in Noncommutative Coordinates

A semiclassical constrained Hamiltonian system which was established to study dynamical systems of matrix valued non-Abelian gauge fields is employed to formulate spin Hall effect in noncommuting coordinates at the first order in the constant noncommutativity parameter theta . The method is first illustrated by studying the Hall effect on the noncommutative plane in a gauge independent fashion. Then, the Drude model type and the Hall effect type formulations of spin Hall effect are considered in noncommuting coordinates and \theta deformed spin Hall conductivities which they provide are acquired. It is shown that by adjusting \theta different formulations of spin Hall conductivity are accomplished. Hence, the noncommutative theory can be envisaged as an effective theory which unifies different approaches to similar physical phenomena.Comment: 15 pages. Ref. added. Published versio