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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/6
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Publication Open Access Erratum: Geometric phase, bundle classification, and group representation(American Institute of Physics (AIP) Publishing, 1999) Department of Mathematics; Department of Physics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; Department of Physics; College of Sciences; 4231Publication Open Access New perspectives on the relevance of gravitation for the covariant description of electromagnetically polarizable media(Institute of Physics (IOP) Publishing, 2007) Gratus, J; Tucker, R.W.; Department of Physics; Dereli, Tekin; Faculty Member; Department of Physics; College of Sciences; 201358By recognizing that stress-energy-momentum tensors are fundamentally related to gravitation in spacetime it is argued that the classical electromagnetic properties of a simple polarizable medium may be parameterized in terms of a constitutive tensor whose properties can in principle be determined by experiments in non-inertial ( accelerating) frames and in the presence of weak but variable gravitational fields. After establishing some geometric notation, discussion is given to basic concepts of stress, energy and momentum in the vacuum where the useful notion of a drive form is introduced in order to associate the conservation of currents involving the flux of energy, momentum and angular momentum with spacetime isometries. The definition of the stress energy-momentum tensor is discussed with particular reference to its symmetry based on its role as a source of relativistic gravitation. General constitutive properties of material continua are formulated in terms of spacetime tensors including those that describe magneto-electric phenomena in moving media. This leads to a formulation of a self-adjoint constitutive tensor describing, in general, inhomogeneous, anisotropic, magneto-electric bulk matter in arbitrary motion. The question of an invariant characterization of intrinsically magneto-electric media is explored. An action principle is established to generate the phenomenological Maxwell system and the use of variational derivatives to calculate stress-energy-momentum tensors is discussed in some detail. The relation of this result to tensors proposed by Abraham and others is discussed in the concluding section where the relevance of the whole approach to experiments on matter in non-inertial environments with variable gravitational and electromagnetic fields is stressed.Publication Open Access Explicit construction of the eigenvectors and eigenvalues of the graph Laplacian on the Cayley tree(Elsevier, 2020) Erzan, Ayşe; Department of Physics; Tuncer, Aslı; Researcher; Department of Physics; Graduate School of Sciences and EngineeringA generalized Fourier analysis on arbitrary graphs calls for a detailed knowledge of the eigenvectors of the graph Laplacian. Using the symmetries of the Cayley tree, we recursively construct the family of eigenvectors with exponentially growing eigenspaces, associated with eigenvalues in the lower part of the spectrum. The spectral gap decays exponentially with the tree size, for large trees. The eigenvalues and eigenvectors obey recursion relations which arise from the nested geometry of the tree.Publication Open Access Route to supersolidity for the extended Bose-Hubbard model(American Physical Society (APS), 2011) Department of Physics; Işkın, Menderes; Faculty Member; Department of Physics; College of Sciences; 29659We use the Gutzwiller ansatz and analyze the phase diagram of the extended Bose-Hubbard Hamiltonian with on-site (U) and nearest-neighbor (V ) repulsions. For d-dimensional hypercubic lattices, when 2dV < U, it is well known that the ground state alternates between the charge-density-wave (CDW) and Mott insulators, and the supersolid (SS) phase occupies small regions around the CDW insulators. However, when 2dV > U, in this Rapid Communication, we show that the ground state has only CDW insulators, and more importantly, the SS phase occupies a much larger region in the phase diagram, existing up to very large hopping values which could be orders of magnitude higher than that of the well-known case. In particular, the SS-superfluid phase boundary increases linearly as a function of hopping when 2dV 1.5U, for which the prospects of observing the SS phase with dipolar Bose gases loaded into optical lattices is much higher.Publication Open Access Linear connections on light-like manifolds(Scientific and Technological Research Council of Turkey (TUBITAK), 2008) Koçak, Ş.; Limoncu, M.; Department of Physics; Dereli, Tekin; Faculty Member; Department of Physics; College of Sciences; 201358It is well-known that a torsion-free linear connection on a light-like manifold (M, g) compatible with the degenerate metric g exists if and only if Rad(TM) is a Killing distribution. In case of existence, there is an infinitude of connections with none distinguished. We propose a method to single out connections with the help of a special set of 1-forms by the condition that the 1-forms become parallel with respect to this connection. Such sets of 1-forms could be regarded as an additional structure imposed upon the light-like manifold. We consider also connections with torsion and with non-metricity on light-like manifolds.Publication Open Access Degenerate spin structures and the Lévy-Leblond equation(Scientific and Technological Research Council of Turkey (TUBITAK), 2006) Koçak, Ş.; Limoncu, M.; Department of Physics; Dereli, Tekin; Faculty Member; PhD Student; Department of Physics; College of Sciences; 201358Newton-Cartan manifolds and the Galilei group are defined by the use of co-rank one degenerate metric tensor. Newton-Cartan connection is lifted to the degenerate spinor bundle over a Newton Cartan 4-manifold by the aid of degenerate spin group. Levy-Leblond equation is constructed with the lifted connection.Publication Open Access Erratum: Pseudo-Hermiticity for a class of nondiagonalizable Hamiltonians(American Institute of Physics (AIP) Publishing, 2003) Department of Mathematics; Department of Physics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; Department of Physics; College of Sciences; 4231