Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Whitham–Broer–Kaup Systems in Multi-Dimensions: Quantum and Resonant NLS Connections(World Scientific Publ Co Pte Ltd, 2025) Pashaev, Oktay K.; Rogers, ColinAn overview is presented of quantum and resonant nonlinear Schro<spacing diaeresis>dinger equation links to Whitham-Broer-Kaup type systems. A novel n + 1 dimensional extension of the Whitham-Broer-Kaup hydrodynamic system is constructed with connection to an equivalent multi-dimensional resonant NLS equation. Hybrid Ermakov-Painleve II and associated Painleve XXXIV integrable similarity reductions are derived.Conference Object Citation - Scopus: 1Binet–Fibonacci Calculus and N = 2 Supersymmetric Golden Quantum Oscillator(Springer International Publishing AG, 2025) Pashaev, Oktay K.The Binet-Fibonacci calculus, as phi phi'-two base quantum calculus, relates Fibonacci derivative with Binet formula of Fibonacci number operator, acting in Fock space of quantum states. It provides a tool to study the Golden oscillator with energy spectrum in form of Fibonacci numbers. Here we generalize this model to supersymmetric number operator and corresponding Binet formula for supersymmetric Fibonacci operator F-N. It determines the Hamiltonian of supersymmetric Golden oscillator, acting in. H-f circle times H-b-fermion-boson Hilbert space and belonging to N = 2 supersymmetric algebra. Trace on fermions of this model reduces the Hamiltonian to the Golden oscillator. The eigenstates of the super Fibonacci number operator are double degenerate and can be characterized by a point of the super-Bloch sphere. By the supersymmetric Fibonacci annihilation operator, we construct the coherent states as eigenstates of this operator. Entanglement of fermions with bosons in these states is calculated by the concurrence, represented by the Gram determinant and Fibonacci exponential functions. These functions have been appeared as descriptive for inner product of the Golden coherent states in Fock-Bargmann representation. The reference state, coming from the limit alpha -> 0 and corresponding von Neumann entropy, measuring fermion-boson entanglement, are characterized by the Golden ratio.Conference Object Geometry and Entanglement of Super-Qubit Quantum States(Springer International Publishing AG, 2025) Pashaev, Oktay K.; Kocak, AygulWe introduce the super-qubit quantum state, determined by superposition of the zero and the one super-particle states, which can be represented by points on the super-Bloch sphere. In contrast to the one qubit case, the one super-particle state is characterized by points in extended complex plane, equivalent to another super-Bloch sphere. Then, geometrically, the super-qubit quantum state is represented by two unit spheres, or the direct product of two Bloch spheres. By using the displacement operator, acting on the super-qubit state as the reference state, we construct the super-coherent states, becoming eigenstates of the super-annihilation operator, and characterized by three complex numbers. The states are fermion-boson entangled, and the concurrence of states is the product of two concurrences, corresponding to two Bloch spheres. We show geometrical meaning of concurrence as distance from point-state on the sphere to vertical axes. Then, probabilities of collapse to the north pole state and to the south pole state are equal to half-distances from vertical coordinate of the state to corresponding points at the poles. For complimentary fermion number operator, we get the flipped super-qubit state and corresponding super-coherent state, as eigenstate of transposed super-annihilation operator. The infinite set of Fibonacci oscillating circles in complex plane, describing quantum states with uncertainty relations as the ratio of two Fibonacci numbers, and in the limit at infinity becoming the Golden Ration uncertainty, is derived.Article Citation - WoS: 4Citation - Scopus: 4The Bell-Based Super-Coherent States: Uncertainty Relations, Golden Ratio and Fermion-Boson Entanglement(World Scientific Publ Co Pte Ltd, 2024) Pashaev, Oktay K.; Kocak, AygulThe set of maximally fermion-boson entangled Bell super-coherent states is introduced. A superposition of these states with separable bosonic coherent states, represented by points on the super-Bloch sphere, we call the Bell-based super-coherent states. Entanglement of bosonic and fermionic degrees of freedom in these states is studied by using displacement bosonic operator. It acts on the super-qubit reference state, representing superposition of the zero and the one super-number states, forming computational basis super-states. We show that the states are completely characterized by displaced Fock states, as a superposition with non-classical, the photon added coherent states, and the entanglement is independent of coherent state parameter alpha alpha and of the time evolution. In contrast to never orthogonal Glauber coherent states, our entangled super-coherent states can be orthogonal. The uncertainty relation in the states is monotonically growing function of the concurrence and for entangled states we get non-classical quadrature squeezing and representation of uncertainty by ratio of two Fibonacci numbers. The sequence of concurrences, and corresponding uncertainties hF(n)/Fn+1, in the limit n ->infinity n ->infinity, convergent to the Golden ratio uncertainty h/phi, where phi=1+root 5/2 is found.