Mathematics / Matematik

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  • Conference Object
    Citation - Scopus: 2
    Maximally Entangled Two-Qutrit Quantum Information States and De Gua’s Theorem for Tetrahedron
    (Springer, 2023) Pashaev, Oktay
    Geometric 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, Oktay
    A 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.