Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Conference Object Citation - Scopus: 2Maximally Entangled Two-Qutrit Quantum Information States and De Gua’s Theorem for Tetrahedron(Springer, 2023) Pashaev, OktayGeometric relations between separable and entangled two-qubit and two-qutrit quantum information states are studied. For two qubit states a relation between reduced density matrix and the concurrence allows us to characterize entanglement by double area of a parallelogram, expressed by determinant of the complex Hermitian inner product metric. We find similar relation in the case of generic two-qutrit state, where the concurrence is expressed by sum of all 2 × 2 minors of 3 × 3 complex matrix. We show that for maximally entangled two-retrit state this relation is just De Gua’s theorem or a three-dimensional analog of the Pythagorean theorem for triorthogonal tetrahedron areas. Generalizations of our results for arbitrary two-qudit states are discussed © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.Conference Object Hirota Bilinear Method and Relativistic Dissipative Soliton Solutions in Nonlinear Spinor Equations(Springer, 2023) Pashaev, OktayA new relativistic integrable nonlinear model for real, Majorana type spinor fields in 1+1 dimensions, gauge equivalent to Papanicolau spin model, defined on the one sheet hyperboloid is introduced. By using the double numbers, the model is represented as hyperbolic complex valued relativistic massive Thirring type model. By Hirota’s bilinear method, an exact one and two dissipative soliton solutions of this model are constructed. Calculation of first three integrals of motion for one dissipation solution shows that the last one represents a particle-like nonlinear excitation, with relativistic dispersion and highly nonlinear mass. A nontrivial solution of the system of algebraic equations, showing fusion and fission of relativistic dissipations is found. Asymptotic analysis of exact two dissipaton solution confirms resonant character of our dissipaton interactions. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.Conference Object Citation - Scopus: 1Pq-Calculus of Fibonacci Divisors and Method of Images in Planar Hydrodynamics(Springer, 2022) Pashaev, OktayBy introducing the hierarchy of Fibonacci divisors and corresponding quantum derivatives, we develop the golden calculus, hierarchy of golden binomials and related exponential functions, translation operator and infinite hierarchy of Golden analytic functions. The hierarchy of Golden periodic functions, appearing in this calculus we relate with the method of images in planar hydrodynamics for incompressible and irrotational flow in bounded domain. We show that the even hierarchy of these functions determines the flow in the annular domain, bounded by concentric circles with the ratio of radiuses in powers of the Golden ratio. As an example, complex potential and velocity field for the set of point vortices with Golden proportion of images are calculated explicitly.Article Citation - WoS: 3Citation - Scopus: 3A Direct Method for the Low Energy Scattering Solution of Delta Shell Potentials(Springer, 2022) Erman, Fatih; Seymen, SemaA direct method for the bound states and the low energy scattering from a circular and a spherical delta shell potentials is proposed, and the results are compared with the one using the standard partial wave analysis developed for potentials with rotational symmetry. The formulation is presented in momentum space, and the scattering solutions are obtained by considering the elementary use of distributions. In this approach, the outgoing boundary conditions are imposed explicitly in contrast to the iϵ prescription often used in quantum mechanics.Article Citation - WoS: 21Citation - Scopus: 28Angular Analysis of the Decay B+-> K*(892)(+)mu(+)mu(-) in Proton-Proton Collisions at Root S=8 Tev(Springer, 2021) CMS Collaboration; Karapınar, GülerAngular distributions of the decay B+-> K*(892)(+)mu(+)mu(-) are studied using events collected with the CMS detector in root s = 8 TeV proton-proton collisions at the LHC, corresponding to an integrated luminosity of 20.0 fb(-1). The forward-backward asymmetry of the muons and the longitudinal polarization of the K*(892)(+) meson are determined as a function of the square of the dimuon invariant mass. These are the first results from this exclusive decay mode and are in agreement with a standard model prediction.Article Citation - WoS: 27Citation - Scopus: 31Development and Validation of Herwig 7 Tunes From Cms Underlying-Event Measurements(Springer, 2021) Karapınar, GülerThis paper presents new sets of parameters (tunes) for the underlying-event model of the herwig 7 event generator. These parameters control the description of multiple-parton interactions (MPI) and colour reconnection in herwig 7, and are obtained from a fit to minimum-bias data collected by the CMS experiment at v s = 0.9, 7, and 13 TeV. The tunes are based on the NNPDF3.1 next-to-nextto-leading-order parton distribution function (PDF) set for the parton shower, and either a leading-order or next-to-nextto-leading-order PDF set for the simulation of MPI and the beam remnants. Predictions utilizing the tunes are produced for event shape observables in electron-positron collisions, and forminimum-bias, inclusive jet, top quark pair, and Zand Wboson events in proton-proton collisions, and are compared with data. Each of the new tunes describes the data at a reasonable level, and the tunes using a leading-order PDF for the simulation of MPI provide the best description of the data.Article Citation - WoS: 4Citation - Scopus: 4Quantum Invariants of Knotoids(Springer, 2021) Güğümcü, Neslihan; Kauffman, Louis H.In this paper, we construct quantum invariants for knotoid diagrams in R-2. The diagrams are arranged with respect to a given direction in the plane (Morse knotoids). A Morse knotoid diagram can be decomposed into basic elementary diagrams each of which is associated to a matrix that yields solutions of the quantum Yang-Baxter equation. We recover the bracket polynomial, and define the rotational bracket polynomial, the binary bracket polynomial, the Alexander polynomial, the generalized Alexander polynomial and an infinity of specializations of the Homflypt polynomial for Morse knotoids via quantum state sum models.Conference Object Citation - Scopus: 5Kaleidoscope of Classical Vortex Images and Quantum Coherent States(Springer, 2018) Pashaev, Oktay; Koçak, AygülThe Schrödinger cat states, constructed from Glauber coherent states and applied for description of qubits are generalized to the kaleidoscope of coherent states, related with regular n-polygon symmetry and the roots of unity. This quantum kaleidoscope is motivated by our method of classical hydrodynamics images in a wedge domain, described by q-calculus of analytic functions with q as a primitive root of unity. First we treat in detail the trinity states and the quartet states as descriptive for qutrit and ququat units of quantum information. Normalization formula for these states requires introduction of specific combinations of exponential functions with mod 3 and mod 4 symmetry, which are known also as generalized hyperbolic functions. We show that these states can be generated for an arbitrary n by the Quantum Fourier transform and can provide in general, qudit unit of quantum information. Relations of our states with quantum groups and quantum calculus are discussed. © Springer Nature Switzerland AG 2018.Article Citation - WoS: 137Citation - Scopus: 174Search for Narrow and Broad Dijet Resonances in Proton-Proton Collisions at ?s=13 Tev and Constraints on Dark Matter Mediators and Other New Particles(Springer, 2018) CMS Collaboration; Karapınar, GülerSearches for resonances decaying into pairs of jets are performed using proton-proton collision data collected at s=13 TeV corresponding to an integrated luminosity of up to 36 fb−1. A low-mass search, for resonances with masses between 0.6 and 1.6 TeV, is performed based on events with dijets reconstructed at the trigger level from calorimeter information. A high-mass search, for resonances with masses above 1.6 TeV, is performed using dijets reconstructed offline with a particle-flow algorithm. The dijet mass spectrum is well described by a smooth parameterization and no evidence for the production of new particles is observed. Upper limits at 95% confidence level are reported on the production cross section for narrow resonances with masses above 0.6 TeV. In the context of specific models, the limits exclude string resonances with masses below 7.7 TeV, scalar diquarks below 7.2 TeV, axigluons and colorons below 6.1 TeV, excited quarks below 6.0 TeV, color-octet scalars below 3.4 TeV, W′ bosons below 3.3 TeV, Z′ bosons below 2.7 TeV, Randall-Sundrum gravitons below 1.8 TeV and in the range 1.9 to 2.5 TeV, and dark matter mediators below 2.6 TeV. The limits on both vector and axial-vector mediators, in a simplified model of interactions between quarks and dark matter particles, are presented as functions of dark matter particle mass and coupling to quarks. Searches are also presented for broad resonances, including for the first time spin-1 resonances with intrinsic widths as large as 30% of the resonance mass. The broad resonance search improves and extends the exclusions of a dark matter mediator to larger values of its mass and coupling to quarks.Article Citation - WoS: 98Citation - Scopus: 89Measurement of the Cross Section for Top Quark Pair Production in Association With a W or Z Boson in Proton-Proton Collisions at ?s = 13 Tev(Springer, 2018) Karapınar, GülerA measurement is performed of the cross section of top quark pair production in association with a W or Z boson using proton-proton collisions at a center-of-mass energy of 13 TeV at the LHC. The data sample corresponds to an integrated luminosity of 35.9 fb−1, collected by the CMS experiment in 2016. The measurement is performed in the same-sign dilepton, three- and four-lepton final states. The production cross sections are measured to be σ(tt¯W)=0.77−0.11+0.12(stat)−0.12+0.13(syst)pb and σ(tt¯Z)=0.99−0.08+0.09(stat)−0.10+0.12(syst)pb. The expected (observed) signal significance for the t t ¯ W production in same-sign dilepton channel is found to be 4.5 (5.3) standard deviations, while for the t t ¯ Z production in three- and four-lepton channels both the expected and the observed significances are found to be in excess of 5 standard deviations. The results are in agreement with the standard model predictions and are used to constrain the Wilson coefficients for eight dimension-six operators describing new interactions that would modify t t ¯ W and t t ¯ Z production.