Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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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.Conference Object Phenomenological Aspects of U(1)' Models(American Institute of Physics, 2009) Demir, Durmuş AliThis talk summarizes certain phenomenological aspects of the supersymmetric models with an extra U(1) invariance broken at the TeV scale. The discussions involve the Higgs sector, CP violation, Neutrino masses and the LHC signatures.Article Citation - WoS: 12Citation - Scopus: 12Phenomenological Issues in Supersymmetry With Nonholomorphic Soft Breaking(American Physical Society, 2005) Çakır, Muammer Altan; Mutlu, Sevdiye; Solmaz, LeventWe present a through discussion of motivations for and phenomenological issues in supersymmetric models with minimal matter content and nonholomorphic soft-breaking terms. Using the unification of the gauge couplings and assuming SUSY is broken with nonstandard soft terms, we provide semianalytic solutions of the RGEs for low and high choices of tan β which can be used to study the phenomenology in detail. We also present a generic form of RGIs in mSUGRA framework which can be used to derive new relations in addition to those existing in the literature. Our results are mostly presented with respect to the conventional minimal supersymmetric model for ease of comparison.