Ph.D. Theses

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Analytic solutions of scalar field cosmology with minimal and nonminimal coupling and deformed discrete and finite quantum systems
(Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022., 2022) İldeş, Medine.; Turgut, Osman Teoman.; Arık, Metin.
In this thesis first, we study analytic solutions of cosmology. We investigate the most general cosmological model with real scalar field which is minimally coupled to gravity and Brans- Dicke cosmology. Field equations consist of three differential equations. We switch independent variable from time to scale factor by change of variable ˙a/a = H(a). Thus a new set of differential equations are analytically solvable with known methods. a(t) can be explicitly found as long as methods of integration techniques are available. We investigate the dynamics of the universe at early times as well as at late times in light of these formulas. We find mathematical machinery which turns on and turns off early accelerated expansion. On the other hand late time accelerated expansion is explained by cosmic domain walls. φ 4 potential is studied in Brans-Dicke Cosmology. In this thesis we also study discrete and finite quantum systems. We define a deformed kinetic energy operator for a discrete position space with a finite number of points. The structure may be either periodic or nonperiodic with well-defined end points. It is shown that for the nonperiodic case the translation operator becomes nonunitary due to the end points. This uniquely defines an algebra which has the desired unique representation. Energy eigenvalues and energy wave functions for both cases are found. In addition, we uncover the mathematical structure of the Schwinger algebra and introduce almost unitary Schwinger operators which are derived by considering translation operators on a finite lattice.
Black holes in an expanding universe
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2016., 2016.) Şenikoğlu, Yorgo.; Turgut, Teoman.; Arık, Metin.
By performing transformations on the isotropic forms of di erent metrics, new cosmological black hole solutions were obtained by generalizing the static solution, the Schwarzchild solution, the McVittie and the Kerr solutions. We present cosmological black holes solutions that satisfy the known behaviours of the scale factor through the history of our Universe, the Radiation, Matter and Dark Energy dominated eras. In the static case we presented solutions satisfying all of the energy conditions, then a time generalization and analysis of the previous isotropic solution gave us the behaviour in time of the Schwarzschild black hole solution. By a choice of parameter, we obtained a non-singular equation of state parameter even though the energy density and pressure tend to in nity at the horizon. In that case the solution suggests that in the expanding universe, the equation of state parameter is negative and may eventually be satis ed by a dark energy dominated representation of the Universe. For the classical McVittie and Kerr solutions, an inductive reasoning led us to obtain all the solutions, Radiation, Matter and Dark energy dominated eras, by introducing two conformal factors and generalizing the metrics. Finally, the Weyl curvature and the volume expansion are calculated for the cosmological black holes and the e ects, increases or decreases, of the volume expansions for all the cases are discussed. It is shown at the end that a multitude of black holes can impact the Universe as a whole by increasing or decreasing its volume.
Black holes, cosmology and Brans-Dicke theories in 4+1 dimensional universe
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2007., 2007.) Çiftci, Dilek.; Arık, Metin.
We consider the embedding of 3+1 dimensional cosmology in 4+1 dimensional Jordan-Brans-Dicke theory. We show that exponentially growing and power law scale factors are implied. We solve the Brans-Dicke equations and we realize that only a linear warp factor satisfies these equations. In both exponentially expanding and power law expanding cases we find out that the scalar field is a function of the warp factor and the scale factor. Whereas the 4 + 1 dimensional scalar field is approximately constant for each case, the effective 3 + 1 dimensional scalar field is constant for exponentially growing scale factor and time dependent for power law scale factor. We calculate the effective gravitational constant and realize that same results are valid. We construct a static solution for 4 + 1 dimensional bulk such that the 3 + 1 dimensional world has a linear warp factor and describes the Schwarzschild-dS4 black hole. The 4 + 1 dimensional space-time is taken to be flat. For zero mass this four dimensional universe and Friedmann-Robertson-Walker universe are related with an explicit coordinate transformation. Also we realize that if there is a contribution from the mass term, both energy momentum and cosmological constant vanish in the bulk. We explain the four dimensional cosmological constant originates from the hidden brane and its effects cause the localized mass densities in our visible brane. Using hierarchy between the Planck mass and electroweak energy scale, we obtain the size of the extra dimension as close to Hubble length but smaller than it. We emphasize that for linear warp factors the effect of bulk on the brane world shows up as the dS4 background which is favored by the Big Bang cosmology.
CERN LINAC4 beam dynamics studies and commissioning up to 12 MeV
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2015., 2015.) Yıldız, Veli.; Özcan, Veysi Erkcan.; Arık, Metin.
Linac4 is a normal conducting, 160 MeV H{u100000} ions accelerator that is being constructed within the scope of the LHC Injectors Upgrade project. Linac4 will be connected to the Proton Synchrotron Booster during the next long LHC shutdown and it will replace the current 50 MeV proton linac, Linac2. Linac4 is being commissioned progressively with the installation of the accelerating structures into the Linac4 tunnel. Movable diagnostic benches, with various instruments, are used at each step to allow the detailed characterization of operational parameters that will play a key role in the overall future performance. The rst three stages of the commissioning, up to 12 MeV beam energy, were completed by the end of 2014 with a temporary version of the ion source. Using the permanent diagnostic instruments and a movable diagnostic bench, the Low Energy Beam Transport (LEBT) at 45 keV, the Radio Frequency Quadrupole (RFQ) and Medium Energy Beam Transport (MEBT) at 3 MeV, as well as the rst tank of the Drift Tube Linac (DTL) at 12 MeV were fully characterized.
Cononical structure and integrability of new-dimensional field theories
(Thesis (Ph.D.)- Bogazici University. Institute for Graduate Studies in Science and Engineering, 1984., 1984.) Neyzi, Fahrünisa.; Arık, Metin.
Cosmology and spontaneous symmetry breaking
(Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 1998., 1998.) Saygılı, Kamuran.; Arık, Metin.
In the first problem we investigate a model which incorporates spontaneous symmetry breaking and gravitation in the context of scalar-tensor theory. Present day value of the gravitational constant is induced by the vacuum expectation value of the scalar field. Cosmology is dominated by the scalar field both in the early and the present universe and the scalar field supplies the critical density of the universe today. In the second problem we applied the long-wavelength approximation to low energy effective string action in the context of Hamilton-Jacobi theory. The Hamilton-Jacobi equation is explicitly invariant under scale factor duality. We present the leading order general solution near a singularity, which also contains the quasi-isotropic one. The duality transformation is written as a coordinate transformation in an abstract space of fields.
Cylindrically symmetric spacetimes with pure rediation
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2006., 2006.) Delice, Özgür.; Arık, Metin.
In this thesis we have investigated some solutions of Einstein's field equations having cylindrical symmetry. The corresponding energy momentum tensor of most of these solutions has pure radiation equation of state. First, the static Levi-Civita solution has been generalized to a Kasner type time dependent solution. Using this solution, we have presented a time dependent Vaidya type solution representing pure and gravitational radiation emitted from a nonstatic cylindrical source. As an application, we have analyzed a radiating nonstatic cosmic string like object. Next, we have presented cylindrically symmetric, static solutions of the Einstein field equations around a line singularity such that the energy momentum tensor corresponds to infinitely thin photonic shells composed of counter propagating pure radiation in certain directions. Positivity of the energy density of the thin shell and the line singularity is discussed. Among these solutions, a particular solution corresponding to a photonic shell whose interior and exterior is flat is interesting since the cylinder becomes a plane for an outside observer. We have also investigated the generalization of these solutions to multiple thin shells and found that line singularities including cosmic strings may be screened by photonic shells until they all appear as a planar wall. Lastly we have investigated solutions corresponding to circulating or counter circulating pure radiation around the axis. The first solution we have studied was an approximate thin shell solution corresponding to counter rotating photons with small contribution from an anisotropic fluid. Next, we study a cylindrical circulating beam of light. The gravitational field of a counter rotating pure radiation field is presented as a last solution for this thesis. These solutions can smoothly match to the corresponding vacuum solutions from either interior or exterior.
Effects of different types of fields to cosmology and of extra dimension to FCNC hadronic processes of the SM
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2013., 2013.) Katırcı, Ayşe Nihan.; Arık, Metin.; Azizi, Kazem.
The Effects of Different Types of Fields to Cosmology. Alternative cosmological models are proposed as a harbinger of new physics to overcome the perceived short- comings of the standard theory of cosmology (ACDM). We consider a non-minimally coupled massive complex scalar field to the curvature in the Jordan-Brans-Dicke (JBD) framework. We obtain an extra term to the Friedmann equation and it fits to super- nova observations with a slightly lesser chi-squared value compared to the ACDM. We assign the vector field as the photon field in JBD theory, a small photon mass leads to the late time infation. The background electric potential of the photon permeates the universe and explains the weakness of the gravitational interaction by coupling to the curvature, hence the smallness of the Hubble parameter is linked with the smallness of the photon mass. Another feature of our model is that the Planck mass is interpreted as the electric potential of the photon field that fills the universe. The Effects of an Extra Dimension to Some Hadronic Processes of the SM. Although the SM of particle physics is in perfect consistency with all confirmed collider data and the precision tests so far, it has some deficiencies such as scale hierarchy problem, etc. The compactified extra dimensions have been proposed to reduce the difference between the Planck mass scale and the strength of the electro-weak force. We analyze the effects of a single universal extra dimension (UED) on some flavor changing neutral current (FCNC) decays of hadrons such as baryonic ... and the mesonic B - K2 (1430)... transitions. We calculate some physical quantities such as branching ratio, lepton forward-backward asymmetry, double lepton polarization asymmetries and hadron polarizations in terms of the compactification scale of the extra dimension. Using the experimental data provided by the CDF Collaboration on the branching ratio of decay channel and comparing with our theoretical prediction, we put a constraint on the lower limit of the compactification scale of extra dimension to be 250 GeV . The results of UED show overall considerable deviations from those of the SM which can be considered as indications for the existence of extra dimensions which we should look for them at hadron colliders.
General unitary quantum groups and generalized Fermion algebras
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2009., 2009.) Altıntaş, Azmi Ali.; Arık, Metin.
Since the middle of the twentieth century, physicists have concentrated on finding quantum counterparts of classical systems. When a classical system is quantized its invariance group may still be a classical group. In the nineteen-eighties it was shown that when some classical systems are quantized, their classical group becomes a quantum group so that the system is invariant under a quantum group. So quantum groups play an important role in carrying physical properties to the quantum world. In this thesis, after presenting structure of Hopf algebra as a quantum group, structure of matrix quantum groups are investigated using inhomogeneous quantum groups, fermionic inhomogeneous orthogonal quantum invariance groups FIO, and bosonic inhomogeneous symplectic quantum invariance groups BISp. Then using invariance quantum groups of orthofermion algebra a general structure for unitary quantum groups are constructed in chapter three. Commuting fermion algebra is defined using the Heisenberg spin algebra and its inhomogeneous quantum group is defined in chapter four. Chapter three and chapter four of the thesis is based on original research.
Modified theories of gravity via alternative couplings and their cosmological analyses
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2015., 2015.) Kavuk, Mehmet.; Rador, Tonguç.; Arık, Metin.
We propose alternative gravitational couplings, fields and design some models to explain some cosmological problems. We investigate a cosmological model in which the Stueckelberg fields describing a massive photon are non-minimally coupled to the scalar curvature in a gauge invariant manner. We present not only a solution that can be considered in the context of the late time acceleration of the universe but also a solution compatible with the inflationary cosmology. The mass mechanism that gains to the vector field in a gauge invariant manner, designed by Stueckelberg, and via coupling to gravitation is used as a first in cosmology and we investigate cosmological effects. While Stueckelberg mechanism is generally used in particle physics , distinct behaviors of the scalar and vector fields together with the real valued mass gained by the Stueckelberg mechanism lead the universe to go through the two different accelerated expansion phases with a decelerated expansion phase between them. On the other hand, in the solutions we present, if the photon mass is null then the universe is either static or exhibits a simple power law expansion due to the vector field potential. In other work in this thesis, we propose a new model of gravity where the Ricci scalar (R) in Einstein-Hilbert action is replaced by an arbitrary function of R and of the norm of energy-momentum tensor i.e., f(R, TμνTμν) in metric formalism. We find that the equation of motion of massive test particles is non-geodesic and these test particles are acted upon by a extra force which is orthogonal to the four-velocity of the particles. We also find the Newtonian limit of the model to calculate the extra acceleration which can affect the perihelion of Mercury. There is a deviation from the general relativistic(GR) result unless the energy density of the fluid is constant. Arranging α parameter gives an opportunity to cure the inconsistency between the observational values for the abundance of light elements and the standard Big Bang Nucleosynthesis results. Even the dust dominated universe undergoes an accelerated expansion without using a cosmological constant in Model II. With this specific choice of f(R, TμνTμν) we get the so-called Cardassian-like expansion in which standard Friedmann equation is modified as H2 = Aρ + Bρn in an ad hoc way in the literature.
Multiparameter generalization of deformed particle algebras
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2004., 2004.) Arıkan, Ali Serdar.; Arık, Metin.
In this study, we generalize deformed boson and fermion algebras by considering as many deformation parameters as possible. The restriction on the number of deformation parameters emerges from the relations leaving the algebra consistent. In the bosonic part, we consider the Newton oscillator which is a one parameter generalization of the harmonic oscillator as a starting point. Then, we achieve the multiparameter generalization with d(d+1) parameters for d dimensional oscillator system. We also present the Fock representation of this oscillator. In the fermionic part, we first study the quantum group covariant two-parameter deformed fermion algebra. Then we show that if the quantum group symmetry is not preserved, then the number of deformation parameters in d dimension can be increased to 2(d-1). We study the limiting case where all deformation parameters go to zero such that the deformed fermionic oscillator reduces to the orthofermion algebra. Finally, we investigate the symmetry properties of this limiting case.
Primordial and late-time inflation in Brans-Dicke cosmology
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2006., 2006.) Çalık, Mehmet.; Arık, Metin.
The basic motivation of this work is to attempt to explain the rapid primordial inflation and the observed slow late-time inflation by using the Brans-Dicke theory of gravity. We show that the ratio of primordial and late-time inflation parameters is proportional to the square root of the Brans-Dicke parameter w(). We also calculate the Hubble parameter H and the time variation of the time dependent Newtonian gravitational constant G for both regimes. The variation of the Hubble parameter predicted by Brans-Dicke cosmology is shown to be consistent with recent measurements: The value of H in the late-time future is predicted as 0.86 times the present value of H0. By using a linearized non-vacuum late time solution in Brans-Dicke cosmology we account for the seventy five percent dark energy contribution but not for approximately twenty-three percent dark matter contribution to the present day energy density of the universe. In the context of Brans-Dicke scalar tensor theory of gravitation, the cosmological Friedmann Equation which relates the expansion rate H of the universe to the various fractions of energy density is analyzed rigorously. And it is shown that Brans-Dicke scalar tensor theory of gravitation brings a negligible correction to the power of the scale size term in the matter density component of Friedmann equation. In addition to 歔 and M in standard Einstein cosmology, another density parameter, ¢, is expected by the theory. This implies that if ¢ is found to be nonzero, data will favor this model instead of the standard Einstein cosmological model with cosmological constant and will enable more accurate predictions for the rate of change of Newtonian gravitational constant in the future.
Quantum group structures associated with invariances of some physical algebras
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2005., 2005.) Kayserilioğlu, Ufuk.; Arık, Metin.
In this study, the anticommuting spin algebra is introduced and it is shownto be invariant under the action of the quantum group SOq=-1(3). Furthermore, itsrepresentations and Hopf algebra structure are studied and found to be closely resemble the similar results for the angular momentum algebra. The invariance propertiesof the bosonic and fermionic oscillator algebras under inhomogeneous transformationsare also studied. The bosonic inhomogeneous symplectic group, BISp(2d,R) , andthe fermionic inhomogeneous orthogonal group, FIO(2d,R) , are defined as the inhomogeneous invariance quantum groups of these algebras. The sub(quantum)groupsand contractions of these quantum groups are studied as a source for new quantumgroups. Finally, the fermionic inhomogeneous orthogonal quantum group is defined forodd number of dimensions and its sub(quantum)groups and contractions are studied.
Quantum phenomena and shape dynamics
(Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2018., 2018.) Dündar, Furkan Semih.; Akant, Levent.; Arık, Metin.
In this thesis, we considered quantum phenomena (Unruh eﬀect) in Shape Dy namics, version of Bohmian Mechanics that is compatible with Mach’s Principle, and a solution (gravitational collapse of a spherically symmetric thin shell of dust) of Shape Dynamics. First, it is interesting that we proved the existence of Unruh radiation in Shape Dynamics where there is no Lorentz symmetry and no unbounded ﬂat space. In order to detect the existence of Unruh eﬀect we used an Unruh-DeWitt detector. Second, a toy model for Shape Dynamics that is suitable for particle interactions is considered. It brings three constraints for solutions: Energy constraint, angular mo mentum constraint and dilational momentum constraint. We applied these constraints to particle variables of Bohmian Mechanics and obtained a constrained Bohmian Me chanics that is Machian. Third, we considered a spherically symmetric thins shell of dust in Shape Dynamics in a space manifold which is [0,1]×S2. We calculated the symplectic form and its inverse. The phase space variables turned out to be the coordinate radius and total momentum of the shell, the expectation value of the trace of the metric momentum, and the volume of the space. We laid the foundations for future research.
Search for axions with micromegas detectors in the cern cast experiment
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2013., 2013.) Yıldız, Süleyman Cenk.; Arık, Metin.
The CAST experiment is searching for the axion, which is a light, weakly interacting pseudoscalar particle, that is proposed to solve the so called Strong Charge-Parity Problem. The axions CAST is looking for are produced from photons in the solar core and CAST aims to convert them back into photons in a superconducting LHC dipole magnet and detect the photons in the x-ray detectors attached to ends of each magnet bore. CAST uses three micromegas and a CCD detector and can track the Sun during sunset and sunrise. The two of the micromegas take tracking data during the sunset solar tracking, and were used for the rst time in 2008. The analysis of the data taken in 2008 with these two detectors show no signal of axions, and new upper limits on the axion mass-coupling constant parameter space are established due to sensitivity of detectors for the axion mass range of 0:38eV to 0:65eV.
Thermodynamical properties of bosons and fermions for lattice motivated dispersion relationships
(Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2023., 2023) Güner, Metin Mehmet.; Akant, Levent.; Arık, Metin.
In this thesis, we have studied the coupled simple harmonic oscillator physics of one-dimensional strings, for acoustical phonons, and n-dimensional physics for the optical case (for arbitrary n). For the acoustical modes, we have calculated only the Bosonic Simple Harmonic Oscillator (BSHO), for the optical mode, we have included both BSHO and Fermionic Simple Harmonic Oscillator (FSHO). For the optical modes, for both BSHO’s and FSHO’s, we have found that the problem is reduced to the physics of a single oscillator with a partial vibration frequency. For the FSHO’s in the optical cases, we have encountered the presence of negative temperatures for all n. In both cases, we have discovered the presence of correct asymptotical behavior as T → 0 and T → ∞. In the acoustical case, we have used Mellin Transform and a summation formula due to Euler to calculate the partition function and the thermodynamical properties thereof. Again we have obtained the correct asymptotical behavior as T → 0 and T →∞. We note that whenever possible, we have included more than one method of calculation and obtained similar results.

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