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.Article Malleability and Ownership of Proxy Signatures: Towards a Stronger Definiton and Its Limitations(American Institute of Mathematical Sciences, 2020) Chatterjee, Sanjit; Ustaoğlu, BerkantProxy signature is a cryptographic primitive that allows an entity to delegate singing rights to another entity. Noticing the ad-hoc nature of security analysis prevalent in the existing literature, Boldyreva, Palacio and Warinschi proposed a formal security model for proxy signature. We revisit their proposed security definition in the context of the most natural construction of proxy signature - delegation-by-certificate. Our analysis indicates certain limitations of their definition that arise due to malleability of proxy signature as well as signature ownership in the context of standard signature. We propose a stronger definition of proxy signature to address these issues. However, we observe that the natural reductionist security argument of the delegation-by certificate proxy signature construction under this definition seems to require a rather unnatural security property for a standard signature.Article Multiparticle Correlations and Higher Order Harmonics in Ppb Collisions at Root S(nn)=8.16 Tev(Elsevier Ltd., 2019) Karapınar, Güler; CMS CollaborationThe elliptic and higher-order azimuthal anisotropy Fourier harmonics (v(n)) are obtained for pPb collisions at root s(NN) = 8.16 TeV over a wide range of event multiplicities based on multiparticle correlations. The data were collected by the CMS experiment during the 2016 LHC run. A sample of peripheral PbPb collisions at root s(NN) = 5.02 TeV covering a similar range of event multiplicities to the pPb results is also analyzed for comparison. The ratios of different harmonic moments are obtained for both v(2) and v(3) with high precision, which allows a direct comparison to theoretical predictions assuming a hydrodynamic evolution of the created medium with initial-state density fluctuations, particularly probing the non-Gaussian nature of initial-state fluctuations in small collision systems. The presented results provide crucial insights into the origin of collective long-range correlations observed in small collision systems.