Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Author: search.filters.author.Gürkan, Zeynep Nilhan

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Now showing 1 - 5 of 5
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Energy Localization in Maximally Entangled Two- and Three-Qubit Phase Space
    (IOP Publishing Ltd., 2012) Pashaev, Oktay; Gürkan, Zeynep Nilhan
    Motivated 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.
  • Article
    Citation - WoS: 11
    Citation - Scopus: 10
    Entanglement in Two Qubit Magnetic Models With Dm Antisymmetric Anisotropic Exchange Interaction
    (World Scientific Publishing Co. Pte Ltd, 2010) Gürkan, Zeynep Nilhan; Pashaev, Oktay
    In 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
    Citation - WoS: 13
    Citation - Scopus: 12
    Berry'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
    Integrable Vortex Dynamics in Anisotropic Planar Spin Liquid Model
    (Elsevier Ltd., 2008) Gürkan, Zeynep Nilhan; Pashaev, Oktay
    The 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: 8
    Citation - Scopus: 6
    Abelian Chern-Simons Vortices and Holomorphic Burgers Hierarchy
    (Pleiades Publishing, 2007) Pashaev, Oktay; Gürkan, Zeynep Nilhan
    We 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.