Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Citation - WoS: 4Citation - Scopus: 4Energy Localization in Maximally Entangled Two- and Three-Qubit Phase Space(IOP Publishing Ltd., 2012) Pashaev, Oktay; Pashaev, Oktay; Gürkan, Zeynep Nilhan; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyMotivated 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: 6Citation - Scopus: 7Existence of Hamiltonians for Some Singular Interactions on Manifolds(American Institute of Physics, 2012) Doğan, Çağlar; Erman, Fatih; Turgut, Osman Teoman; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyThe existence of the Hamiltonians of the renormalized point interactions in two and three dimensional Riemannian manifolds and that of a relativistic extension of this model in two dimensions are proven. Although it is much more difficult, the proof of existence of the Hamiltonian for the renormalized resolvent for the non-relativistic Lee model can still be given. To accomplish these results directly from the resolvent formula, we employ some basic tools from the semigroup theory.Conference Object Citation - WoS: 1Citation - Scopus: 2Applications of Graph Coloring(Springer Verlag, 2005) Ufuktepe, Ünal; Bacak, Gökşen; Ufuktepe, Ünal; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyA graph G is a mathematical structure consisting of two sets V(G) (vertices of G) and E(G) (edges of G). Proper coloring of a graph is an assignment of colors either to the vertices of the graphs, or to the edges, in such a way that adjacent vertices / edges are colored differently. This paper discusses coloring and operations on graphs with Mathematica and webMathematica. We consider many classes of graphs to color with applications. We draw any graph and also try to show whether it has an Eulerian and Hamiltonian cycles by using our package ColorG