Gürkan, Zeynep Nilhan
Loading...
Profile URL
Name Variants
Gurkan, Zeynep N.
Gürkan, Zeynep N.
Gurkan, Zeynep Nilhan
Gurkan, Z. N.
Gürkan, Z. N.
Nilhan Gürkan, Zeynep
Nilhan Gurkan, Zeynep
Gürkan, Zeynep N.
Gurkan, Zeynep Nilhan
Gurkan, Z. N.
Gürkan, Z. N.
Nilhan Gürkan, Zeynep
Nilhan Gurkan, Zeynep
Job Title
Email Address
Main Affiliation
04.02. Department of Mathematics
Status
Former Staff
Website
ORCID ID
Scopus Author ID
Turkish CoHE Profile ID
Google Scholar ID
WoS Researcher ID
Sustainable Development Goals
SDG data is not available
Documents
17
Citations
106
h-index
6
This researcher does not have a WoS ID.
Scholarly Output
7
Articles
4
Views / Downloads
6909/3389
Supervised MSc Theses
1
Supervised PhD Theses
1
WoS Citation Count
36
Scopus Citation Count
32
Patents
0
Projects
0
WoS Citations per Publication
5.14
Scopus Citations per Publication
4.57
Open Access Source
7
Supervised Theses
2
| Journal | Count |
|---|---|
| Chaos, Solitons and Fractals | 1 |
| International Journal of Modern Physics B | 1 |
| New Journal of Physics | 1 |
| Physical Review A - Atomic, Molecular, and Optical Physics | 1 |
| Theoretical and Mathematical Physics | 1 |
Current Page: 1 / 1
Scopus Quartile Distribution
Competency Cloud
7 results
Scholarly Output Search Results
Now showing 1 - 7 of 7
Article Citation - WoS: 13Citation - Scopus: 12Berry's Phase Under the Dzyaloshinskii-Moriya Interaction(American Physical Society, 2008) Kwan, M. K.; Gürkan, Zeynep Nilhan; Kwek, L. C.In this paper, we study the Dzyaloshinskii-Moriya (DM) anisotropic XX spin-chain model in the presence of an external homogeneous magnetic field. We found that the Berry phase of the system varies interestingly with small and large amounts of DM interaction and the magnetic field. In addition, we also considered the concurrence (i.e., the amount of entanglement) of the system, and the relationship between the concurrence and the Berry phase. Finally, we calculate the Berry phase of thermal states and verify that the results are consistent with that of the pure states.Article Citation - WoS: 11Citation - Scopus: 10Entanglement in Two Qubit Magnetic Models With Dm Antisymmetric Anisotropic Exchange Interaction(World Scientific Publishing Co. Pte Ltd, 2010) Gürkan, Zeynep Nilhan; Pashaev, OktayIn the present paper, an influence of the anisotropic antisymmetric exchange interaction, the DzialoshinskiiMoriya (DM) interaction, on entanglement of two qubits in various magnetic spin models, including the pure DM model and the most general XYZ model, are studied. We find that the time evolution generated by DM interaction can implement the SWAP gate and discuss realistic quasi-one-dimensional magnets where it can be realized. It is shown that inclusion of the DM interaction to any Heisenberg model creates, when it does not exist, or strengthens, when it exists, the entanglement. We give physical explanation of these results by studying the ground state of the systems at T = 0. Nonanalytic dependence of the concurrence on the DM interaction and its relation with quantum phase transition is indicated. Our results show that spin models with the DM coupling have some potential applications in quantum computations and the DM interaction could be an efficient control parameter of entanglement. © 2010 World Scientific Publishing Company.Article Integrable Vortex Dynamics in Anisotropic Planar Spin Liquid Model(Elsevier Ltd., 2008) Gürkan, Zeynep Nilhan; Pashaev, OktayThe problem of magnetic vortex dynamics in an anisotropic spin liquid model is considered. For incompressible flow the model admits reduction to saturating Bogomolny inequality analytic projections of spin variables, subject the linear holomorphic Schrödinger equation. It allows us to construct N vortex configurations in terms of the complex Hermite polynomials. Using complex Galilean boost transformations, the interaction of the vortices and the vortex chain lattices (vortex crystals) is studied. By the complexified Cole-Hopf transformation, integrable N vortex dynamics is described by the holomorphic Burgers equation. Mapping of the point vortex problem to N-particle problem, the complexified Calogero-Moser system, showing its integrability and the Hamiltonian structure, is given. © 2006 Elsevier Ltd. All rights reserved.Conference Object Citation - WoS: 8Citation - Scopus: 6Abelian Chern-Simons Vortices and Holomorphic Burgers Hierarchy(Pleiades Publishing, 2007) Pashaev, Oktay; Gürkan, Zeynep NilhanWe consider the Abelian Chern-Simons gauge field theory in 2+1 dimensions and its relation to the holomorphic Burgers hierarchy. We show that the relation between the complex potential and the complex gauge field as in incompressible and irrotational hydrodynamics has the meaning of the analytic Cole-Hopf transformation, linearizing the Burgers hierarchy and transforming it into the holomorphic Schrödinger hierarchy. The motion of planar vortices in Chern-Simons theory, which appear as pole singularities of the gauge field, then corresponds to the motion of zeros of the hierarchy. We use boost transformations of the complex Galilei group of the hierarchy to construct a rich set of exact solutions describing the integrable dynamics of planar vortices and vortex lattices in terms of generalized Kampe de Feriet and Hermite polynomials. We apply the results to the holomorphic reduction of the Ishimori model and the corresponding hierarchy, describing the dynamics of magnetic vortices and the corresponding lattices in terms of complexified Calogero-Moser models. We find corrections (in terms of Airy functions) to the two-vortex dynamics from the Moyal space-time noncommutativity.Article Citation - WoS: 4Citation - Scopus: 4Energy Localization in Maximally Entangled Two- and Three-Qubit Phase Space(IOP Publishing Ltd., 2012) Pashaev, Oktay; Gürkan, Zeynep NilhanMotivated by theMobius transformation for symmetric points under the generalized circle in the complex plane, the system of symmetric spin coherent states corresponding to antipodal qubit states is introduced. In terms of these states, we construct the maximally entangled complete set of two-qubit coherent states, which in the limiting cases reduces to the Bell basis. A specific property of our symmetric coherent states is that they never become unentangled for any value of from the complex plane. Entanglement quantifications of our states are given by the reduced density matrix and the concurrence determinant, and it is shown that our basis is maximally entangled. Universal one- and twoqubit gates in these new coherent state basis are calculated. As an application, we find the Q symbol of the XY Z model Hamiltonian operator H as an average energy function in maximally entangled two- and three-qubit phase space. It shows regular finite-energy localized structure with specific local extremum points. The concurrence and fidelity of quantum evolution with dimerization of double periodic patterns are given.Master Thesis Integrable Vortex Dynamics and Complex Burgers' Equation(Izmir Institute of Technology, 2005) Gürkan, Zeynep Nilhan; Pashaev, OktayIntegrable dynamical models of the point magnetic vortex interactions in the plane are studied. Reformulating the Euler equations for vorticity in the Helmholtz form, the Hamiltonian and Lax representations are found. Reduction of these equations for the point vortices to the Kirchho equations, and non-integrability of the system of N 4 hydrodynamical vortices are discussed.As an integrable model of planar motion with given vorticity for the stationary and its solutions are given. For non-stationary planar vortex diffusion and exactly solvable Initial Value Problem for the one dimensional Burgers equation are solved.By the complexied Cole-Hopf transformation, the complex Burgers equation with integrable N vortex dynamics is introduced and linearization of this equation in terms of the complex Schr odinger equation is found.This allows us to construct N vortex congurations in terms of the complex Hermite polynomials, the vortex chain lattices and study their mutual dynamics. Mapping of our vortex problem to N-particle problem, the complexied Calogero-Moser system, showing its integrability and Hamiltonian structure is given. As an applicaton of the general results, we consider the problem of magnetic vortices in a magnetic fluid model. The holomorphic reduction of topological magnetic system to the linear complex Schrodinger equation, allows us to apply all results on integrable vortex dynamics in the complex Burgers equation to the magnetic vortex evolution, including magnetic vortex lattices and the bound states of vortices.Doctoral Thesis Entanglemend and Topological Soliton Structures in Heisenberg Spin Models(Izmir Institute of Technology, 2010) Gürkan, Zeynep Nilhan; Pashaev, OktayQuantum entanglement and topological soliton characteristics of spin models are studied. By identifying spin states with qubits as a unit of quantum information, quantum information characteristic as entanglement is considered in terms of concurrence. Eigenvalues, eigenstates, density matrix and concurrence of two qubit Hamiltonian of XY Z, pure DM, Ising, XY , XX, XXX and XXZ models with Dzialoshinskii- Moriya DM interaction are constructed. For time evolution of two qubit states, periodic and quasiperiodic evolution of entanglement are found. Entangled two qubit states with exchange interaction depending on distance J(R) between spins and influence of this distance on entanglement of the system are considered. Different exchange interactions in the form of Calogero- Moser type I, II, III and Herring-Flicker potential which applicable to interaction of Hydrogen molecule are used. For geometric quantum computations, the geometric (Berry) phase in a two qubit XX model under the DM interaction in an applied magnetic field is calculated. Classical topological spin model in continuum media under holomorphic reduction is studied and static N soliton and soliton lattice configurations are constructed. The holomorphic time dependent Schrödinger equation for description of evolution in Ishimori model is derived. The influence of harmonic potential and bound state of solitons are studied. Relation of integrable soliton dynamics with multi particle problem of Calogero-Moser type is established and N soliton and N soliton lattice motion are found. Special reduction of Abelian Chern-Simons theory to complex Burgers. hierarchy, the Galilean group, dynamical symmetry and Negative Burgers. hierarchy are found.