ömer dayı - Academia.edu (original) (raw)

Papers by ömer dayı

Journal of High Energy Physics

Fluid of spin-1/2 fermions is represented by a complex scalar field and a four-vector field coupl... more Fluid of spin-1/2 fermions is represented by a complex scalar field and a four-vector field coupled both to the scalar and the Dirac fields. We present the underlying action and show that the resulting equations of motion are identical to the (hydrodynamic) Euler equations in the presence of Coriolis force. As a consequence of the gauge invariances of this action we established the quantum kinetic equation which takes account of noninertial properties of the fluid in the presence of electromagnetic fields. The equations of the field components of Wigner function in Clifford algebra basis are employed to construct new semiclassical covariant kinetic equations of the vector and axial-vector field components for massless as well as massive fermions. Nonrelativistic limit of the chiral kinetic equation is studied and shown that it generates a novel three-dimensional transport theory which does not depend on spatial variables explicitly and possesses a Coriolis force term. We demonstrate...

Employing the Foldy-Wouthuysen transformation it is demonstrated straightforwardly that the first... more 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.

A generalized algebra of quantum phase space variables of non–commutative coordinates and momenta... more A generalized algebra of quantum phase space variables of non–commutative coordinates and momenta embracing non–Abelian gauge fields, is proposed. Through a two–dimensional realization of this algebra for a gauge field leading to a transverse magnetic field and two spin–orbit–like couplings, a Dirac–like Hamiltonian is introduced. We established the corresponding energy spectrum and from that we derived the relation between the energy level quantum number and the magnetic field at the maxima of Shubnikov–de Haas oscillations. By tuning the non–commutativity parameter in terms of the values of magnetic field at the maxima we accomplished the experimentally observed Landau plot of the peaks for graphene. Accepting that the experimentally observed behavior is due to the confinement of carriers, we conclude that our approach constitutes a new formulation of the confined massless Dirac fermions in graphene.

Annals of Physics, 2018

The semiclassical Boltzmann transport equation of charged, massive fermions in a rotating frame o... more The semiclassical Boltzmann transport equation of charged, massive fermions in a rotating frame of reference, in the presence of external electromagnetic fields is solved in the relaxation time approach to establish the distribution function up to linear order in the electric field in rotating coordinates, centrifugal force and the derivatives. The spin and spin current densities are calculated by means of this distribution function at zero temperature up to the first order. It is shown that the nonequilibrium part of the distribution function yields the spin Hall effect for fermions constrained to move in a plane perpendicular to the angular velocity and magnetic field. Moreover it yields an analogue of Ohm's law for spin currents whose resistivity depends on the external magnetic field and the angular velocity of the rotating frame. Spin current densities in three-dimensional systems are also established.

Itudergisi C, May 26, 2011

Bu makale, birinci yazar tarafından İTÜ Fen Bilimleri Enstitütsü, Fizik Mühendisliği Programı'nda... more Bu makale, birinci yazar tarafından İTÜ Fen Bilimleri Enstitütsü, Fizik Mühendisliği Programı'nda tamamlanmış olan "Duality in noncommutative gauge theories: A parent action approach" adlı doktora tezinden hazırlanmıştır. Makale metni 10.04.2006 tarihinde dergiye ulaşmış, 09.06.2006 tarihinde basım kararı alınmıştır. Makale ile ilgili tartışmalar 30.06.2007 tarihine kadar dergiye gönderilmelidir. Özet Komütatif olmayan (noncommutative) uzaylar farklı çerçevelerde karşımıza çıksa da bu tip kuramların gittikçe artan bir şekilde çalışılması, bunların sicim kuramı ile olan yakın ilişkilerinin kurulması ile olmuştur. Komütatif olmayan uzaylar üzerinde tanımlanan alan kuramları sicim kuramının ayrışma (decoupling) limitinde ortaya çıkmaktadırlar ve bu tip kuramlar komütatif benzerlerinden farklı özellikler göstermeleri nedeniyle ilgi çekmektedirler. Bu şekilde komütatif olmayan ayar kuramlarından elde edilecek sonuçların sicim kurumlarının çeşitli özelliklerinin anlaşılmasında önemli olması beklenmektedir. Dual kuramlar bir fiziksel modelin iki farklı, fakat eşdeğer formülasyonunu tanımlarlar. S dualite olarak adlandırılan kuvvetli ve zayıf etkileşimli modeller arasındaki ilişki, birinden diğerine gidilerek bir fiziksel modelin farklı etkileşme bölgelerindeki özelliklerinin çalışılmasına imkân verir. Bu çalışmada biz komütatif olmayan U(1) ayar kuramında S dualiteyi inceleyeceğiz. Öncelikle komütatif olmayan U(1) kuramının duali için hamilton fonksiyonunun nasıl kurulabileceğini inceleyeceğiz. Dual kuramda uzay ve zaman koordinatları arasıda komütatiflik özelliğinin bulunmaması nedeniyle bilinen kuantizasyon yöntemleri ile bunun nasıl yapılacağı açık değildir. Ana (parent) eylem bu iş için uygun bir araç olmaktadır. Ana eylemde uygun değişkenlere göre hareket denklemleri çözülür ve bu çözümler ana eylemde yerine konulursa orijinal kuram veya onun duali elde edilebilmektedir. Ana eylemin bu tanımlaması dual Lagrange fonksiyonu kullanılmaksızın hamilton fonksiyonunun elde edilebilmesine imkân verir. Yöntem öncelikle normal (komütatif) durum için geliştirilecek daha sonra elde edilen sonuçlar komütatif olmayan duruma genelleştirilecektir. İkinci olarak komütatif olmayan U(1) ayar kuramı ve onun duali için hem Lagrange hem de Hamilton yoğunluklarında elektrik-manyetik dualite dönüşümlerinin nasıl tanımlanacağını göstereceğiz.

In terms of the matrix valued Berry gauge field strength for the Weyl Hamiltonian in any even spa... more In terms of the matrix valued Berry gauge field strength for the Weyl Hamiltonian in any even spacetime dimensions a symplectic form whose elements are matrices in spin indices is introduced. Definition of the volume form is modified appropriately. A simple method of finding the path integral measure and the chiral current in the presence of external electromagnetic fields is presented. It is shown that within this new approach the chiral magnetic effect as well as the chiral anomaly in even d + 1 dimensions are accomplished straightforwardly.

International Journal of Geometric Methods in Modern Physics, 2016

A semiclassical formulation of the spin Hall effect for physical systems satisfying Dirac-like eq... more A semiclassical formulation of the spin Hall effect for physical systems satisfying Dirac-like equation is introduced. We demonstrate that the main contribution to the spin Hall conductivity is given by the spin Chern number whether the spin is conserved or not at the quantum level. We illustrated the formulation within the Kane–Mele model of graphene in the absence and in the presence of the Rashba spin-orbit coupling term.

Physics Letters B, 2015

Kinetic theory of Dirac fermions is studied within the matrix valued differential forms method. I... more Kinetic theory of Dirac fermions is studied within the matrix valued differential forms method. It is based on the symplectic form derived by employing the semiclassical wave packet build of the positive energy solutions of the Dirac equation. A satisfactory definition of the distribution matrix elements imposes to work in the basis where the helicity is diagonal which is also needed to attain the massless limit. We show that the kinematic Thomas precession correction can be studied straightforwardly within this approach. It contributes on an equal footing with the Berry gauge fields. In fact in equations of motion it eliminates the terms arising from the Berry gauge fields.

Physics Letters A, 2009

A semiclassical constrained Hamiltonian system which was established to study dynamical systems o... more 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 θ. 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 θ deformed spin Hall conductivities which they provide are acquired. It is shown that by adjusting θ 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.

Journal of High Energy Physics, 2002

Journal of High Energy Physics, 2003

Journal of High Energy Physics, 2005

A parent action is introduced to formulate (S-) dual of non-anticommutative N = 1 2 supersymmetri... more A parent action is introduced to formulate (S-) dual of non-anticommutative N = 1 2 supersymmetric U (1) gauge theory. Partition function for parent action in phase space is utilized to establish the equivalence of partition functions of the theories which this parent action produces. Thus, duality invariance of non-anticommutative N = 1 2 supersymmetric U (1) gauge theory follows. The results which we obtained are valid at tree level or equivalently at the first order in the nonanticommutativity parameter C µν .

Journal of High Energy Physics, 2004

Physics Letters B, 2000

Constrained hamiltonian structure of noncommutative gauge theory for the gauge group U (1) is dis... more Constrained hamiltonian structure of noncommutative gauge theory for the gauge group U (1) is discussed. Constraints are shown to be first class, although, they do not give an Abelian algebra in terms of Poisson brackets. The related BFV-BRST charge gives a vanishing generalized Poisson bracket by itself due to the associativity of *-product. Equivalence of noncommutative and ordinary gauge theories is formulated in generalized phase space by using BFV-BRST charge and a solution is obtained. Gauge fixing is discussed.

Physics Letters A, 2011

Two different gauge potential methods are engaged to calculate explicitly the spin Hall conductiv... more Two different gauge potential methods are engaged to calculate explicitly the spin Hall conductivity in graphene. The graphene Hamiltonian with spin-orbit interaction is expressed in terms of kinematic momenta by introducing a gauge potential. A formulation of the spin Hall conductivity is established by requiring that the time evolution of this kinematic momentum vector vanishes. We then calculated the conductivity employing the Berry gauge fields. We show that both of the gauge fields can be deduced from the pure gauge field arising from the Foldy-Wouthuysen transformations.

Physics Letters A, 2001

We consider the behavior of electrons in an external uniform magnetic field B where the space coo... more We consider the behavior of electrons in an external uniform magnetic field B where the space coordinates perpendicular to B are taken as noncommuting. This results in a generalization of standard thermodynamics. Calculating the susceptibility, we find that the usual Landau diamagnetism is modified. We also compute the susceptibility according to the nonextensive statistics of Tsallis for (1 − q) ≪ 1, in terms of the factorization approach. Two methods agree under certain conditions.

Modern Physics Letters A, 2002

An electron moving on plane in a uniform magnetic field orthogonal to the plane is known as the L... more An electron moving on plane in a uniform magnetic field orthogonal to the plane is known as the Landau problem. Wigner functions for the Landau problem when the plane is noncommutative are found employing solutions of the Schrödinger equation as well as solving the ordinary ⋆-genvalue equation in terms of an effective Hamiltonian. Then, we let momenta and coordinates of the phase space be noncommutative and introduce a generalized ⋆-genvalue equation. We solve this equation to find the related Wigner functions and show that under an appropriate choice of noncommutativity relations they are independent of noncommutativity parameter.

Journal of Physics A: Mathematical and Theoretical, 2013

2+1 dimensional topological insulator described by the Kane-Mele model in the presence of Rashba ... more 2+1 dimensional topological insulator described by the Kane-Mele model in the presence of Rashba spin-orbit interaction is considered. The effective action of the external fields coupled to electromagnetic and spin degrees of freedom is accomplished within this model. The Hamiltonian methods are adopted to provide the coefficients appearing in the action. It is demonstrated straightforwardly that the coefficients of the Chern-Simons terms are given by the first Chern number attained through the related non-Abelian Berry gauge field. The effective theory which we obtain is in accord with the existence of the spin Hall phase where the value of the spin Hall conductivity is very close to the quantized one.

Journal of Physics A: Mathematical and General, 1998

Quantum Hall effect wave functions corresponding to the filling factors 1/2p+1, 2/2p+1, • • • , 2... more Quantum Hall effect wave functions corresponding to the filling factors 1/2p+1, 2/2p+1, • • • , 2p/2p+1, 1, are shown to form a basis of irreducible cyclic representation of the quantum algebra U q (sl(2)) at q 2p+1 = 1. Thus, the wave functions Ψ P/Q possessing filling factors P/Q < 1 where Q is odd and P, Q are relatively prime integers are classified in terms of U q (sl(2)).

Journal of Physics A: Mathematical and General, 1999

The quantum group SL q (2, R) at roots of unity is introduced by means of duality pairings with t... more The quantum group SL q (2, R) at roots of unity is introduced by means of duality pairings with the quantum algebra U q (sl(2, R)). Its irreducible representations are constructed through the universal T-matrix. An invariant integral on this quantum group is given. Endowed with that some properties like unitarity and orthogonality of the irreducible representations are discussed.