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Publication Metadata only Comment on the possibility of a geometric constraint in the Schrodinger quantum mechanics(World Scientific Publ Co Pte Ltd, 2000) Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231It is shown that the geometric constraint advocated in [R. S. Kaushal, Mod. Phys. Lett.A15, 1391 (2000)] is trivially satisfied. Therefore, such a constraint does not exist. We also point out another flaw in Kaushal's paper.Publication Metadata only Entropy of the quantum fluctuations of fermionic instantons in the universe(World Scientific Publishing Co Pte Ltd, 2022) Akilli, Mahmut; Department of Physics; Yılmaz, Nazmi; Teaching Faculty; Department of Physics; College of Sciences; 178427The aim of this paper is to study the entropy of quantum fluctuations of fermionic instantons. For this purpose, we focus on the spinor-type instanton solution family of the massless pure fermionic Thirring model because it is a well-known quantized toy model in the quantum field theory since 1958. We calculate the Boltzmann-Gibbs-Shannon (BGS) entropy of the Thirring model by the normalized inner scalogram (NIS) and find that the entropy of quantum fluctuations of Thirring fermionic instantons increase slightly just after the big bang. This result leads us to discuss the relation between the increasing entropy in the Universe due to quantum fluctuations of the fermionic Thirring instantons during the creation of fermionic type particles.Publication Metadata only Exact solutions in five-dimensional axi-dilaton gravity with euler-poincare term(Iop Publishing Ltd, 2007) Aliev, A. N.; Cebeci, H.; Department of Physics; Dereli, Tekin; Faculty Member; Department of Physics; College of Sciences; 201358We examine the effective field equations that are obtained from the axi-dilaton gravity action with a second-order Euler-Poincare term and a cosmological constant in all higher dimensions. We solve these equations for five-dimensional-spacetimes possessing homogeneity and isotropy in their three-dimensional subspaces. For a number of interesting special cases, we show that the solutions fall into two main classes: the first class consists of time-dependent solutions with spherical or hyperboloidal symmetry which require certain fine-tuning relations between the coupling constants of the model and the cosmological constant. Solutions in the second class are locally static and prove the validity of Birkhoff's staticity theorem in the axi-dilaton gravity. We also give a class of static solutions, among them the well known charged black hole solutions with a cosmological constant in which the usual electric charge is superseded by an axion charge.Publication Metadata only Neutrino fields in a sandwich gravitational wave background(Institute of Physics (IOP) Publishing, 2022) Gürtuğ, Özay; Halilsoy, Mustafa; Şenikoğlu, Yorgo; Department of Physics; Dereli, Tekin; Faculty Member; Department of Physics; College of Sciences; 201358Sandwich gravitational waves are given globally in terms of step functions at the boundaries. Linearized Einstein-Weyl equations are solved exactly in this background in Rosen coordinates. Depending on the geometry and composition of the sandwich wave, the neutrino's energy-momentum redistributes itself. At the test field level, since the background will not change, the neutrino's energy density in particular will show variations between positive and negative extrema when crossing the sandwich wave. This may reveal facts about the weakly interacting neutrinos in cosmology.Publication Metadata only On the detection of scalar field induced space-time torsion(World Scientific Publishing Co Pte Ltd, 2002) Tucker, RW; Department of Physics; Dereli, Tekin; Faculty Member; Department of Physics; College of Sciences; 201358We argue that the geodesic hypothesis based on autoparallels of the Levi-Civita connection may need refinement in the scalar-tensor theories of gravity. Based on a reformulation of the Brans-Dicke theory in terms of a connection with torsion determined dynamically in terms of the gradient of the Brans-Dicke scalar field, we compute the perihelion shift in the orbit of Mercury on the alternative hypothesis that its worldline is an autoparallel of a connection with torsion. If the Brans-Dicke scalar field couples significantly to matter and test particles move on such worldlines, the current time keeping methods based on the conventional geodesic hypothesis may need refinement.Publication Metadata only On the pseudo-hermiticity of a class of PT-symmetric Hamiltonians in one dimension(World Scientific Publ Co Pte Ltd, 2002) Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231For a given standard Hamiltonian H = [p - A(x)]2/(2m) + V(x) with arbitrary complex scalar potential V and vector potential A, with x ∈ ℝ, we construct an invertible antilinear operator τ such that H is τ-anti-pseudo-hermitian, i.e. H† = τHτ-1. We use this result to give the explicit form of a linear hermitian invertible operator with respect to which any standard PT-symmetric Hamiltonian with a real degree of freedom is pseudo-hermitian. Our results do not make use of the assumption that H is diagonalizable or that its spectrum is discrete.Publication Metadata only Supersymmetry of PT-symmetric tridiagonal hamiltonians(World Scientific Publ Co Pte Ltd, 2021) N/A; Almasri, Mohammad Walid; PhD Student; Graduate School of Sciences and Engineering; N/AWe extend the study of supersymmetric tridiagonal Hamiltonians to the case of non-Hermitian Hamiltonians with real or complex conjugate eigenvalues. We find the relation between matrix elements of the non-Hermitian Hamiltonian H and its supersymmetric partner H+ in a given basis. Moreover, the orthogonal polynomials in the eigenstate expansion problem attached to H+ can be recovered from those polynomials arising from the same problem for H with the help of kernel polynomials. Besides its generality, the developed formalism in this work is a natural home for using the numerically powerful Gauss quadrature techniques in probing the nature of some physical quantities such as the energy spectrum of PT-symmetric complex potentials. Finally, we solve the shifted PT-symmetric Morse oscillator exactly in the tridiagonal representation.