M.S. Theses

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Geometrical approaches to soliton equations
(Thesis (M.S.)- Bogazici University. Institute for Graduate Studies in Science and Engineerig, 1981., 1981.) Muğan, Uğurhan.; Güven, Rahmi.
Weinberg-Salam model and e+ e- -> m+ m- process
(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 1981., 1981.) Kalaycı, Jan.; Hortaçsu, Mahmut.
Grand unified models and neutrino oscillations
(Thesis (M.S.)- Bogazici University. Institute for Graduate Studies in Science and Engineering, 1982., 1982.) Neyzi, Fahrünisa.; Arık, Metin.
Path integrals in quantum theory and some applications to homogeneous spaces
(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 1985., 1985.) Yenice, Kamil Mehmet.; Arık, Metin.
In this work we consider the path integrals in quantum theory and some of their applications to homogeneous spaces from the semiclassical point of view. We begin with the basic principles underlying the Feynman path integral formulation of quantum mechanics and show the do;nain where the method is useful and powerful. We present a method for calculating the path integrals for quadratic Lagrangians and apply it to the example of harmonic oscillator. Semiclassical propagator given by the Van Vleck-Pauli formula is also discussed. We next handle the Hamiltonian derivation of path integral. The starting-point for this derivation is the usual operator formalism of quantum mechanics. Later on we consider path integrals on homogeneous spaces concentrating on the motion on group manifolds. It turns out that for the free motion on the group manifold the semiclassical approximation the exact solution. We thus study the path integrals for U(l) and SU(2) groups. In these cases the Propagator is calculated directly by two methods : the sum over classical paths and the stationary state expansion, which are shown explicitly to be equivalent. We finally give some remarks for motion on the hyperspheres S2n +1 and S2n. Deriving a recursion relation for the propagator of S2n +1 we claim that there is the possibility of getting the exact solution from some kind of semiclassical propagator for S2n +1.
The design and construction of a tea molecular nitrogen laser system
(Thesis (M.S.)- Bogazici University. Institute for Graduate Studies in Science and Engineering, 1988., 1988.) Kurt, Adnan.; Wetherilt, James A.
In this study the design and construction of a molecular nitrogen laser intended as a pump source for a dye laser system is presented. This . laser radiation at a wavelength of 337.1 nanometers and uses Blumlein switching to achieve fast (N a few nanosecond width) and high peaK power (N a few hundred Kilowatts) pulses. It operates using atmospheric pressure nitrogen with a cavity length of ten centimeters. The incorporation of this laser into a wavelength tunable, pumped dye laser system is outlined. Methods for studying fast optical pulses are given. iv
Gauge theories based on quantum groups, representations of the braid group
(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 1993., 1993.) Yıldız, Ali.; Arık, Metin.
Possible formulations of gauge field models where the gauge group is a quantum group are discussed. The exponential map from the generators of the Lie algebra analog of the quantum group SUq(2) to the quantum group SUq(2) itself is presented. The q-deformed Yang-Mills theory is introduced via the definition of the q-trace and the q-deformed YangMills lagrangian which is invariant under the quantum group gauge transformations. The gauge field takes values in the quantum universal enveloping algebra of SUq(2). As a result of this construction a Weinberg type mixing angle which depends on the quantum group deformation parameter q is obtained. The representations of the n-braid group where generators are given essentially by 2 x 2 matrices whose elements belong to a noncommutative algebra are presented. The Burau representation arises as a special (commuting) case of this algebra. A closely related algebra to the braid algebra is introduced and it is shown that the generalized oscillator system given by this algebra generates a hydrogen-like spectrum.
Unitary group and quantum group invariant q-oscillators and fibonaccization
(Thesis (M.S.)- Bogazici University. Institute for Graduate Studies in Science and Engineering, 1994., 1994.) Ünel, N. Gökhan.; Arık, Metin.
After a review of different types of q-oscillators and the relationship between their creation/ annihilation operators, the derivation of the q generalized version of the LeviCivita tensor (E) is given. The properties of the quantum group SLq(n) are obtained through the invariance properties of the new q-epsilon tensor. The relations between the inner products of n-particle states of the various q-oscillators are also investigated. Finally, a two parameter generalization of the Coon-Baker-Yu q-oscillator (which we call Fibonaccization) is presented.
Determination of density of states of n-type hydrogenated amorphous silicon by phase shift analysis of modulated photocurrent method
(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 1995., 1995.) Kocabıyık, Ferhat.; Aktaş, Gülen, 1951- .
Determination of density of states of hydrogenated amorphous siliconby phase shift analysis of modulated photocurrent.Determination of the energetic distribution of localized statesdue to random network and structural defects within the mobility gap of amorphous semi conductorsis of great importance for understanding the transport properties of these materials. Since there is no structural order,the band states can be only determined experimentally.In this thesis, the density of states (DOS) distribution in the energy gapof Hydrogenated n-type amorphous silicon is determined. For this purpose a The Phase shift analysis of modulated photocurrent (PSAMP) method is studied. The validity of the PSAMP theorem for the doped a-H:Si is discussed. The theorem is verified for this type of semiconductors and the distribution of the states is determined for a range of 400 meV.
Muon track reconstruction from cathode strip readout of streamer tube planes in chorus muon spectrometer
(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 1996., 1996.) Perdahçı, Nazım Ziya.; Arık, Engin.
We have studied several methods to achieve the best spatial resolution and the highest track reconstruction efficiency using the limited streamer tube planes with external pickup strips orthogonal to signal wires and the analog readout of the CHORUS Muon Spectrometer. The analysis has been performed with real data of 100 GeV beam muons at CERN Labarotary in Geneva. Using a combined algorithm of common bias level subtraction and an empirical function to determine the center of the induced charge distribution on the 18 mm wide strips, we have obtained a spatial resolution of about 3 mm
Stereographic coordinates for unitary quantum groups
(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 1998., 1998.) Arıkan, Ali Serdar.; Arık, Metin.
In this thesis, unitary matrix representation of quantum group SUq(2) is studied in terms of stereographic coordinates z, z* and its central unitary phase u. It is observed that this parametrization of SUq(2) can be regarded as q-1-oscillator representation of SUq(2) where q-1>1. The fractional linear transformation of z and z* which gives the action of SUq(2) on the quantum sphere SUq(2)/U(1) is studied. Then we extend this action to SUq(2) and derive the transformation law of u. In the final part of this work, transformation laws for dz and are also studied.
Determination of optical constants of thin films
(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 1998., 1998.) Yıldız, Ali.; İnci, Naci.
In this thesis, a new approach is explored to determine the optical constants of thin dielectric layers. This study is based on the measurement of the reflection at various angles to determine the optical constants of a thin film. For this reason, this method allows using absorbing or non-transparent substrates. Study consists of not only theoretical derivations but also experimental measurements. A 650 nm laser diode was used as a light source and the reflected light from the surface of the film was measured by the BPX65 silicon photodiode. These reflection values were taken at various angles and numerical calculations were carried out. Results were consistent with previous studies. In addition, this method provided more information about the thin film, such as extinction coefficient, which was neglected in previous studies.
AE AQR :|a DQ her type cataclysmic variable binary system
(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 1998., 1998.) Erkut, M. Hakan.; Ercan, E. Nihal.
AE Aquarii, a DQ Her type Cataclysmic Variable X-ray binary system, is observed with rosat, PSPC in the energy range 0.1-2.4 keV with a total of 5.74 hr period. As a result of spectral and timing analyses of the ROSAT X-ray data of AE Aquarii, it is found that both a very low mass accretion rate of 8.59 x 10-13M yr-1 estimated from the X-ray luminosity and a QPO like structure obderved in the X-ray average power spectrum support the magnetic propeller scenario in which the gas blobs of the inhomogeneous accretion stream from the secondary star to the white dwarf are radiated thermally near the white dwarf surface because of the shock heating of the gas blobs at supersonic speeds in the high accretion state of AE Aquarii. On the other hand, the accreted gas particles are radiated magnetically in ~ 10 Gauss of magnetospere far away from the white dwarf surface during the low accretion states.
Integrability of non-linear differential equations; lax formulation and bi-Hamiltonian structures
(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Sciences and Engineering, 1998., 1998.) Güntürk, Kamil Serkan.; Oğuz, Ömer.
The integrability of non-linear differential equations are studied on the basis of Lax and bi-Hamiltonian formulations. The relations between the Lax formalism and bi-Hamiltonian structures are analysed and illustrated with well known examples such as the KdV system. Various methods resulting from this analysis are then applied to multicomponent KdV equations.
Archaelogical provenancing of marble by pore size analysis, using phase transition porosimetry
(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 1999., 1999.) Öztürk, M. Kaan.; Aktaş, Gülen, 1951- .; Özbal, Hadi.
Determination of the source of a particular marble sample is an ongoing subject of study among archaeometrists. In this study, categorization according to pore size distribution is suggested. The employed method for pore size analysis is Phase Transition Porosimetry (PTP). The principles on which PTP works are described. PTP requires a computer system for data taking and data processing. The electronic data-acquisition system and the control software are discussed extensively. After construction of a dilatometric Phase Transition Porosimeter, marble samples collected from field have been studied with this method and the results are given. The precision of PTP in low-porosity materials are discussed using the results.
Accretion discs around compact objects
(Thesis (M.S.)- Bogazici University. Institute for Graduate Studies in Science and Engineering, 1999., 1999.) Ekşi, K.Yavuz.; Ercan, E. Nihal.
Accretion onto a compact object is the process that is thought to power unexpectedly intense radiation of some astrophysical objects like Active Galactic Nuclei and X-Ray Binaries. A similar process is known to exist in Cataclysmic Variables and Young Stellar Objects. When the accreting matter has enough angular momentum it forms a disc around the compact object (a black hole, neutron star or white dwarf) and this disc is called an accretion disc. In this thesis accretion discs around compact objects are studied both analytically and numerically. Simplifying hydrodynamic equations in their full generality by the assumptions of the standart accretion disc theory, both time-independent and time-dependent equations were solved analytically. Time-dependent solutions are supported by numerical results. In all solutions a viscosity prescription which is a little more generalized than the standart prescription is used. The solution of the time-dependent equations with the generalized viscosity belong to the same family with the earlier ones.
Approximate ground state energies of one dimensional potential wells by the s-matrix formalism
(Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2003., 2003.) Erkol, Hakan.; Beker, Haluk.
One dimensional potential wells are described as a collection of consecutive thin slices, each approximated by a Dirac delta well. Bound state energies of these Dirac delta well conglomerates are calculated, using a method based on Transfer and S-Matrix formalisms. It is observed that the method, a variant of the Born approximation, works best for the ground state energies of narrow and shallow wells. The approximate results compare favorably with the known exact results of several potential well problems.
D.C. photoconductivity in As2Se3 thin films
(Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2003., 2003.) Atak, Kaan.; Aktaş, Gülen, 1951- .
In this thesis, the D.C. photoconductivity in amorphous thin films of As2Se3 is investigated. The temperature dependence of dark, and photo currents are explored at the interval 240 - 360 K. Three regimes are observed in the photoconductivity at the given range of temperature. The results are criticized according to the and other data and found to be in accordance with them.
Noncommutative phase and the unitarization of the quantum group GL(2)
(Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2003., 2003.) Kaynak, Burak Tevfik.; Saçlıoğlu, Cihan,
In this thesis, a new *-operation (or unitarized form) is defined for the two-parameter quantum group GLp,q(2) in the case that pq is real, and the new group is denoted by Up,q(2). The most interesting aspect of our construction is the appearance of the noncommutative phase described by the unitary operator u. The operator u with a central hermitian operator s allow us to extend the algebra of the quantum group GLp,q(2) in order to obtain not only the *-operation but also the *-relations throughout the new algebra of Up,q(2). It is shown how certain *-representations of the quantum group SUq(2) can be extended in order to give *-representations of Up,q(2). This not only allows us to verify the algebraic relations in a representation, it also gives a hint of possible physical interpretations of the algebraic generators as operators.
Inhomogeneous quantum invariance group of commuting fermions
(Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2004., 2004.) 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 we will first review the fermionic and the bosonic algebras and their inhomogeneous invariance quantum groups. Then we will introduce the commuting fermion algebra and construct its inhomogeneous invariance quantum group.
Spectral and scattering properties of point interactions
(Thesis (M.S)-Bogazici University.Institute for Graduate Studies in Science and Engineering, 2005., 2005.) Altunkaynak, İsmet Barış.; Turgut, Osman Teoman.
Point interactions in all relevant dimensions are important to model short rangeinteractions in quantum mechanics. They are exactly solvable and play an important role in solid state, nuclear and atomic physics. In this thesis, we investigate point interactions on flat space and on a general compact manifold in two and three dimensions.The problem contains divergences and they can be renormalized using the couplingconstant renormalization method. We derive the properties of the bound states, provethat the resolvent operator that we have found defines a Hamiltonian, and calculatescattering cross sections. We repeat some of our calculations on a general compactRiemannian manifold and solve the same problem on a sphere and hyperbolic planesH2 and H3. At the end we give some numerical examples.

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