Browsing by Author "Hakioğlu, T."
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Item Open Access Canonical transformations in three-dimensional phase space(World Scientific Publishing Company, 2009) Dereli, T.; Teğmen, A.; Hakioğlu, T.Abstract Canonical transformation in a three-dimensional phase space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed as based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them is listed. Infinitesimal canonical transformations are also discussed. Finally, we show that decomposition of canonical transformations is also possible in three-dimensional phase space as in the usual two-dimensional one.Item Open Access The discrete harmonic oscillator, Harper's equation, and the discrete fractional Fourier transform(Institute of Physics Publishing, 2000) Barker, L.; Candan, C.; Hakioğlu, T.; Kutay, M. A.; Özaktaş, Haldun M.Certain solutions to Harper's equation are discrete analogues of (and approximations to) the Hermite-Gaussian functions. They are the energy eigenfunctions of a discrete algebraic analogue of the harmonic oscillator, and they lead to a definition of a discrete fractional Fourier transform (FT). The discrete fractional FT is essentially the time-evolution operator of the discrete harmonic oscillator.Item Open Access Operational approach to quantum limits on polarization measurement(Elsevier, 1994) Hakioğlu, T.; Shumovsky, A. S.; Aytür, O.We discuss the polarization measurement of a fully polarized coherent field in the weak intensity quantum limit within the framework of operational approach which was recently discussed by Noh, Fougéres and Mandel. We mainly focus on the fluctuations in the measurement of the parameters of polarization and on the uncertainty relations between them. A dependence of these parameters and their quantum fluctuations on the parameters of the initial coherent field is found. © 1994.Item Open Access Phonon squeezing via correlations in the superconducting electron-phonon interaction(American Physical Society, 1995) Hakioğlu, T.; Ivanov, V. A.; Shumovsky, A. S.; Tanatar, BilalSuperconductivity in the conventional BCS model with correlated squeezed phonons is discussed. It is shown that the energy gap and the critical temperature are maximally enhanced in an optimum and finite range of squeezed coupling. For finite-squeezed coupling the ratio 2Δ/Tc becomes coupling-constant dependent and increases beyond the BCS value of 3.53. Ion-mass dependence of the squeezed coupling constant can yield variations of the isotope exponent from its conventional BCS value of 0.5. © 1995 The American Physical Society.Item Open Access Quantum canonical transformations in Weyl-Wigner-Groenewold-Moyal formalism(2009) Dereli, T.; Hakioğlu, T.; Teğmen, A.A conjecture in quantum mechanics states that any quantum canonical transformation can decompose into a sequence of three basic canonical transformations; gauge, point and interchange of coordinates and momenta. It is shown that if one attempts to construct the three basic transformations in star-product form, while gauge and point transformations are immediate in star-exponential form, interchange has no correspondent, but it is possible in an ordinary exponential form. As an alternative approach, it is shown that all three basic transformations can be constructed in the ordinary exponential form and that in some cases this approach provides more useful tools than the star-exponential form in finding the generating function for given canonical transformation or vice versa. It is also shown that transforms of c-number phase space functions under linearnonlinear canonical transformations and intertwining method can be treated within this argument. © 2009 World Scientific Publishing Company.Item Open Access Quantum computational gates with radiation free couplings(Springer, 2002) Kulik, I. O.; Hakioğlu, T.; Barone, A.Abstract.We examine a generic three level mechanism of quantum computation in which all fundamentalsingle and double qubit quantum logic gates are operating under the effect of adiabatically controllablestatic (radiation free) bias couplings between the states. Under the time evolution imposed by these biascouplings the quantum state cycles between the two degenerate levels in the ground state and the quantumgates are realized by changing Hamiltonian at certain time intervals when the system collapses to a twostate subspace. We propose a physical implementation of the mechanism using Aharonov-Bohm persistent-current loops in crossed electric and magnetic fields, with the output of the loop read out by using aquantum Hall effect aided mechanism.Item Open Access Scattering of spin-1/2 particles from a PT-symmetric complex potential(IOP, 2020) Özgün, Ege; Hakioğlu, T.; Özbay, EkmelIn this letter, we study the scattering of spin- 1 2 particles from a spin-independent parity time (PT )-symmetric complex potential, and for the first time, theoretically demonstrate the coexistence of PT -symmetric and PT -broken phases for broadband energy spectra in this system. We also show the existence of anisotropic transmission resonances, accessible through the tuning of energy. Our results are promising for applications in spintronics, semiconductor-based devices, and a better understanding of the topological surface states.Item Open Access Unconventional Pairings and Radial Line Nodes in Inversion Symmetry Broken Superconductors(Elsevier B.V., 2016) Hakioğlu, T.; Günay, M.Noncentrosymmetric superconductors (NCSs) with broken inversion symmetry can have spin-dependent order parameters (OPs) with mixed parity which can also have nodes in the pair potential as well as the energy spectra. These nodes are distinct features that are not present in conventional superconductors. They appear as points or lines in the momentum space where the latter can have angular or radial geometries dictated by the dimensionality, the lattice structure and the pairing interaction. In this work we study the nodes in time reversal symmetry (TRS) preserving NCSs at the OP, the pair potential, and the energy spectrum levels. Nodes are examined by using spin independent pairing interactions respecting the rotational C∞v symmetry in the presence of spin-orbit coupling (SOC). The pairing symmetries and the nodal topology are affected by the relative strength of the pairing channels which is studied for the mixed singlet-triplet, pure singlet, and pure triplet. Complementary to the angular line nodes widely present in the literature, the C∞v symmetry here allows radial line nodes (RLNs) due to the nonlinear momentum dependence in the OPs. The topology of the RLNs in the mixed case shows a distinctly different characterization than the half-spin quantum vortex at the Dirac point. We apply this NCS physics to the inversion symmetry broken exciton condensates (ECs) in double quantum wells where the point and the RLNs can be found. On the other hand, for a pure triplet condensate, two fully gapped and topologically distinct regimes exist, separated by a QSHI-like zero energy superconducting state with even number of Majorana modes. We also remark on how the point and the RLNs can be manipulated, enabling an external control on the topology.Item Open Access Where are the edge-states near the quantum point contacts? A self-consistent approach(Elsevier B.V., 2007) Siddiki, A.; Cicek, E.; Eksi, D.; Mese, A. I.; Aktas, S.; Hakioğlu, T.Abstract In this work, we calculate the current distribution, in the close vicinity of the quantum point contacts (QPCs), taking into account the Coulomb interaction. In the first step, we calculate the bare confinement potential of a generic QPC and, in the presence of a perpendicular magnetic field, obtain the positions of the incompressible edge states (IES) taking into account electron–electron interaction within the Thomas–Fermi theory of screening. Using a local version of Ohm’s law, together with a relevant conductivity model, we also calculate the current distribution. We observe that, the imposed external current is confined locally into the incompressible strips. Our calculations demonstrate that, the inclusion of the electron–electron interaction, strongly changes the general picture of the transport through the QPCs.