## Graduate

Master Degree

02-700 M. S. Thesis (0 0 0) NC

02-501 Analytical Mechanics **(Must Course)**

02-502 Electromagnetic Theory I **(Must Course)**

02-503 Statistical Mechanics I

02-504 Quantum Mechanics I **(Must Course)**

02-505 Methods of Mathematical Physics I

02-540 Relativistic Quantum Mechanics I

02-541 Quantum Field Theory I

02-544 Particle Physics I

02-547 Nuclear Physics I

02-553 Gravitation and Cosmology I

02-554 Group Representations

02-560 Solid State Theory I

02-563 Optical Properties of Semiconductors

02-564 High Temperature Superconductors

02-567 High Vacuum Techniques

02-570 Nonlinear Optics

02-571 Laser Physics

02-572 Theoretical Atomic Physics

02-573 Molecular Physics I

02-574 Optoelectronics

02-581 Quantum Information Science

02-582 Scientific computing

02-583 Computational Physics

02-590 Nuclear Reactor Theory

02-591 Signal Processing and Instrumentation in Physics I

02-592 Signal Processing and Instrumentation in Physics II

02-593 Neutron Transport Theory

02-594 Physics of Solar Energy

02-595 Ionospheric Physics

02-705 Seminar in Physics

02-599 Directed Studies in Physics

PhD

52-800 Ph.D. Thesis (0 0 0) NC

52-602 Electromagnetic Theory II **(Must Course)**

52-603 Statistical Mechanics II **(Must Course)**

52-604 Quantum Mechanics II **(Must Course)**

52-605 Methods of Mathematical Physics II

52-640 Relativistic Quantum Mechanics II

52-641 Quantum Field Theory II

52-644 Partical Physics II

52-647 Nuclear Physics II

52-649 Experimental methods for nuclear and particle physics

52-651 Supersymmetry and Supergravity

52-652 Geometry of Gauge Fields

52-653 Gravitation and Cosmology II

52-655 Theory of Spinors

52-660 Solid State Theory II

52-661 Theory of Many-Particle Systems I

52-662 Theory of Many-Particle Systems II

52-663 Magnetism in Solids

52-664 Theoretical Survey and Irreversible Properties of Superconductors

52-665 Many-Body Theory for Condensed Matter Systems

52-666 Strongly Correlated Systems in Condensed Matter Physics

52-667 Correlations and Critical Behavior in Condensed Matter

52-668 Dielectric Materials

52-669 Type-II Superconductivity and its applications

52-673 Molecular Physics II

52-680 Introduction to Neural Networks

52-690 Plasma Physics

52-691 Solar and Planetary Plasma Physics

52-692 Fundamentals of Fusion Plasma Systems

52-696 Advanced Seminar in Physics

52-699 Advanced Directed Studies in Physics

02-7XX Special Studies

52-8XX Special Studies

52-697 Advanced Studies

**02-700 M. S. Thesis** (0 0 0) NC

Program of research leading to M.S. degree arranged between thestudent and a faculty member. Students register to this course inall semesters starting from the beginning of their second semester.

**02-501 Analytical Mechanics**

Lagrange's equation, central force problem, Rigid body problem, small oscillations, Hamilton's equations, canonical transformations, Hamilton-Jacobi theory, introduction to continuous systems and fields.

**02-502 Electromagnetic Theory I**

Electrostatics and magnetostatics; associated boundary-value problems and their solutions: introduction to Maxwell's equations and their simple consequences.

**02-503 Statistical Mechanics I**

The first law of thermodynamics, Entropy and second law of thermodynamics, Probability and statistics. The ideas of statistical mechanics, The canonical ensemble, identical particles, Plank's distribution, System with variable numbers of particles, Fermi and Bose particles.

**02-504 Quantum Mechanics I**

Fundamental concepts; quantum dynamics; theory of angular momentum and central potential problems; Wigner-Eckart theorem and addition of angular momenta; symmetry in quantum mechanics; approximation methods for time-independent and time-dependent perturbations.

**02-505 Methods of Mathematical Physics I**

Functions of a complex variable, special functions of mathematicalphysics, partial differential equations.

**02-540 Relativistic Quantum Mechanics I**

Relativistic Wave Equation for Spin-0 Particles: The Klein-Gordon Equation and Its Applications. a Wave Equation for Spin -1/2 Particles: The Dirac Equations, Lorentz Covariance of the Dirac Equation, Spinors Under Spatial Reflection, Bilinear Covariants of

the Dirac Spinors, Another Way of Constructing Solutions of the Free Dirac Equation: Construction by Lorentz Transformations, Projection Operators For Energy and Spin.

**02-541 Quantum Field Theory I**

Classical field theory. Canonical quantization of Klein-Gordon, Dirac and Maxwell fields. Interacting fields, perturbation theory and Feynman diagrams. Elementary processes of quantum electrodynamics. Radiative corrections. Divergences, regularization and renormalization.

**02-544 Particle Physics I**

Electromagnetism as a gauge theory; Klein-Gordon and Dirac wave equations; introduction to quantum field theory of bosons and fermions. Quantum electrodynamics: interactions of spin 0 particles and spin 1/2 particles, deep inelastic electron-nucleon scattering and the quark parton model.

**02-547 Nuclear Physics I**

General properties of the nucleus and the nuclear many-body problem, nuclear forces, static properties, nuclear matter, Hartre-Fock theory, nuclear shell model. Collective models of the nucleus, deformed nuclei, nuclear rotations. Particle hole st ates and pairing in nuclei.

**02-553 Gravitation and Cosmology I**

Spacetime manifold. Causal structure. Lorentzian metric. Tensors on manifolds. Orthonormal frame bundles. Connection and curvature. Einstein equations. Variational methods. Noether's theorem. Conservation laws. Schwarzchild geometry. Kruskal extension. Interior solutions. Formation of black holes. Black hole temperature and entropy. Charged rotating black holes. Gravitational waves.

**02-554 Group Representations**

Lie groups. Lie algebras. Symmetry groups of differential equations. Invariant forms on Lie groups. Ideals, solvability and nilpotency. Cartan subalgebras and root spaces. Coxeter-Dynkin diagrams. Classical Lie algebras. Representation theory. Tens or products. Enveloping algebras and Casimir operators. Physical applications.

**02-560 Solid State Theory I**

Crystal symmetry; electron states; dynamics of electrons; transport properties; optical properties.

**02-563 Optical Properties of Semiconductors**

Optical constant of solids, band structure of semiconductors, absorption processes in semiconductors, radiative recombination and photoconductivity in semiconductors.

**02-564 High Temperature Superconductors**

Review of conventioanl superconductors: two-fluid model, London equation, nonlocal fields. Normal state properties: charges and molecular orbitals, resistivity behavior, Hall effect, structural phase transitions. Fermi liquid, band theory, two-dimensioanl bands, one-electron bads. Photoemission spectroscopy. Superconductivity: Tc values, Cooper pairs, paired electrons, energy gap, tunneling spectroscopy, specific heat, infrared results, Raman results and NMR results. Isotope effect. Magnetic properties: type II materials, penetration depth and coherence length. Vortex behavior: flux lattice, flux glass, flux creep and flux pinning. Irreversibility line, levitation and large- and small-scale applications.

**02-567 High Vacuum Techniques**

The production of vacua: water-jet pump, oil-sealed mechanical pumps, turbo molecular pumps, back-streaming: baffles and traps, getter pumps and getter-ion pumps, sorption pumps; measurement of vacua, partial pressure measurements, gas analyzers, vacuum systems, components and leak detection, viscous and molecular flow of gases, ultra-high vacuum systems.

**02-570 Nonlinear Optics**

Electro optic modulators, harmonic generation, and frequency conversion devices. Nonlinear effects in optical fibers including self phase modulation, nonlinear wave propagation, and solitons. Interaction of light with matter, density matrix techniques, and nonlinear laser spectroscopies including femtosecond optics.

**02-571 Laser Physics**

Light-matter interaction. Lorentz model and quantum mechanics. Semiclassical radiation theory. Laser electronics: resonators, gain, threshold, coherence, power, frequency, pumping, mode-locking, Q-switching, applications. Coherent transients. Nonlinear optics.

**02-572 Theoretical Atomic Physics**

Review of Atomic Physics; Review of quantum Mechanics; Interaction of electrons with EM field; Spectra of Atoms, Collisions.

**02-573 Molecular Physics I**

Introduction to molecular structure: Electronic, vibrational and rotational energies of molecules. Dipole transitions; electronic structure analysis of diatomic molecules, hybridization; general methods of molecular calculations; spectroscopic methods and spectroscopic analysis of small molecules.

**02-574 Optoelectronics**

Principles of quantum optics; optoelectronic materials; rare-earth-doped silica fiber lasers; cw performance of fiber optics; Q-switching of optical fiber lasers; digital optics; atmospheric and intersattelite optical communications; thermal imaging; ring laser gyro.

**02-581 Quantum Information Science**

Subject examines quantum computation and quantum information. Topics include quantum circuits, quantum Fourier transform and search algorithms, physical implementations, the quantum operations formalism, quantum error correction, stabilizer and Calderbank-Shor-Steans codes, fault tolerant quantum computation, quantum data compression, entanglement, and proof of the security of quantum cryptography.

**02-582 Scientific computing**

Computational techniques for scientific problems with emphasis on practical applications and effective programming. Review of computers, programming, floating-point numbers, and numerical stability. Survey of basic numerical algorithms and numerical subroutine libraries and their application to scientific problems.

**02-583 Computational Physics**

Basic mathematical tools; differential equations and boundary value problems; special functions; matrix operations; algebraic methods; Monte Carlo methods.

**02-590 Nuclear Reactor Theory**

Fundamentals of neutron behaviour in nuclear reactors; the fission process; diffusion of neutrons; slowing down of neutrons and thermal reactors; reactor control, perturbation theory.

**02-591 Signal Processing and Instrumentation in Physics I**

An experimental course on signal analysis; analysis of periodic signals; transient signals; correlation; spectral analysis; operational amplifiers; computing networks; generalization; transfer functions; analog circuit examples.

**02-592 Signal Processing and Instrumentation in Physics II**

General description of operational devices, departures from ideal and previsions, measurements, linear circuits, non-linear circuits, constant current and voltage sources, signal generation, filters, signal conditioners, memory, measurement circuits

**02-593 Neutron Transport Theory**

Linear Boltzmann equation and its mathematical and physical properties; approximate and exact solutions of the linear Boltzmann equation; variational methods.

**02-594 Physics of Solar Energy**

Solar thermal properties, solar materials, alternative energy sources.

**02-595 Ionospheric Physics**

Formation of the ionosphere; photochemical or transport processes in the ionosphere; the D, E, F1 and F2 layers; the day-time and night-time ionosphere; example of irregular behavior and anomalies; geomagnetism and the ionosphere; the solar wind an d its interaction with the Earth's magnetic field.

**02-705 Seminar in Physics**

Students prepare and present a progress report or literature review on their thesis topic. The course is normally taken by students in their third semester.

**02-599 Directed Studies in Physics**

M.S. Students prepare an advanced topic in the form of project or seminar in contemporary physics other than their research fields.

**52-800 Ph.D. Thesis (0 0 0) NC**

Program of research leading to Ph.D. degree arranged between the student and a faculty member. Students register to this course in all semesters starting from the beginning of their third semester.

**52-602 Electromagnetic Theory II **

Diffraction radiation; introduction to special relativity and the covariant formulation; radiation from moving charges; multiple expansions; radiation reaction.

**52-603 Statistical Mechanics II**

Klasik ve kuantum istaistiğinin öğeleri, üleşim fonksiyonu, ideal Fermi gazı, ideal Bose gazı, İsing modeli ve süperakışkanlar.

**52-604 Quantum Mechanics II**

Systems of identical particles and second quantization; semiclassical and quantum theory of radiation; scattering theory; relativistic single-particle equations; Dirac equation and central potential problems.

**52-605 Methods of Mathematical Physics II**

Integral equations, Series, calculus of variations, Green's function, group theory and applications.

**52-640 Relativistic Quantum Mechanics II**

Wave Packets of Plane Dirac Waves, Dirac Particles in External Fields: Examples and Problems, The Two-Centre Dirac Equation,The Flody-Wouthuysen Representation for Free particles, The Hole Theory, Klein's Paradox, The weyl Equation-The Neutrino, Wave Equations for particles with Arbitrary Spins.

**52-641 Quantum Field Theory II**

Gauge field theories and functional integral formulation. Systematics of renormalization. Renormalization and symmetries. Renormalization group. Non-Abelian gauge theories and their quantization. Quantum chromodynamics. Anomalies. Gauge theories with spontaneous symmetry breaking.

**52-644 Partical Physics II**

Non-Abelian gauge theories; introduction to quantum chrodynamics, phenomenology of weak interactions; hadronic weak current and neutral currents; hidden gauge invariance; spontaneous symmetry breakdown; Hooft's gauges; Glashow-Salam-Weinberg gauge theory of electro-weak interactions; intermediate bosons; Higgs sector; grand unification; supersymmetry.

**52-647 Nuclear Physics II**

Electromagnetic and weak interactions with nuclei; electron scattering, beta decay, muon capture, neutrino reactions, weak neutral current effects. Hadronic interactions; pion-nucleus interaction, optical potential, nuclear reactions, heavy ion col lisions.

**52-649 Experimental methods for nuclear and particle physics**

This course is intended as an introduction to current experimental methods and techniques in nuclear and particle physics. The course will discuss radiation properties, passage of radiation through matter and the statistical treatment of experimental data. It will cover the general characteristics and the principles of operation of different detectors.

**52-651 Supersymmetry and Supergravity**

Lie superalgebras. Superspace and superfields. Dynamics of spinning point particles. Spinning string dynamics. Wess-Zumino model. Supersymmetric Yang-Mills theories. Simple supergravity theory. Extended supergravities.

**52-652 Geometry of Gauge Fields**

Principal fibber bundles and connections. Curvature and G-valued differential forms. Particle fields and gauge invariant Lagrangians. Principle of least action and Yang-Mills field equations. Free Dirac electron fields. Interactions. Orthonormal frame bundle. Linear connections and Riemannian curvature. Unification of gauge fields and gravitation.

.

**52-653 Gravitation and Cosmology II**

Homogeneity and isotropy of the universe. Maximally symmetric spaces. Bianchi types. Standard cosmological model. Observational cosmology: expansion of the universe. Dust filled and radiation filled universes. Inflationary models. Initial and final singularities (Big bang and big crunch). Chaotic mixmaster cosmology. Quantum cosmology. Wheeler-deWitt equation. Quantum field theory in curved spacetimes.

**52-655 Theory of Spinors**

Vector spaces and inner products. Algebra and their representations. Clifford calculus on manifolds. Spinor fields. Dirac equation. Covariances of the Dirac equation. Conserved currents.

**52-660 Solid State Theory II**

Phonons; electron-phonon interactions; interatomic forces and atomic properties; principles of many-body techniques; superconductivity.

**52-661 Theory of Many-Particle Systems I**

Nonrelativistic many-particle systems, ground-state formalism, Green's function, Fermi systems, Bose systems, linear response and collective modes.

**52-662 Theory of Many-Particle Systems II**

Field theory at finite temperature; physical systems at finite temperature, real-time Green's functions; canonical transformations, nuclear matter, superconductivity.

**52-663 Magnetism in Solids**

Electronic Conduction. Boltzmann Equation and Relaxation Time Approximation. Classical Theory of Magnetoconductivity. Hall Effect, Boltzmann Equation in Magnetic Field, Density of States in Magnetic Field, Magnetoresistance in Two Band Bodels, k-Space Analysis in Magnetic Field, Phenomenon of Magnetism, Magnetic susceptibility, Curie Point and Nell Temperature, Magnetic domains, Magnetic Interactions of a Many-Electron Systems, Magnetic Properties of Metals, Diamagnetism, Paramagnetism and Ferromagnetism.

**52-664 Theoretical Survey and Irreversible Properties of Superconductors**

Fundamental properties of superconductors, superconducting state, diamagnetism, field and current induced phase transitions, thermodynamics of phase transitions, magnetic properties of first and second kind superconductors, critical fields, vortex state, London theory, Ginzburg-Landau (GL) theory, solution of linearized GL equations, Pippard's nonlocal theory, electron-phonon interaction, BCS theory, vortex motion in type-II superconductors, flux creep theory, DC and AC Josephson effects, Josephson tunneling.

**52-665 Many-Body Theory for Condensed Matter Systems**

Interacting boson/fermion systems, Fermi liquid theory and bosonization, symmetry breaking and non-linear sigma-model, quantum gauge theory, quantum Hall theory, mean-field theory of spin liquids and quantum order, string-net condensation and emergence of light and fermions.

**52-666 Strongly Correlated Systems in Condensed Matter Physics**

Study of condensed matter systems where interactions between electrons play an important role. Topics vary depending on lecturer but may include low-dimension magnetic and electronic systems, disorder and quantum transport, magnetic impurities (the Kondo problem), quantum spin systems, the Hubbard model and high temperature superconductors.

**52-667 Correlations and Critical Behavior in Condensed Matter**

Views condensed-matter physics through space- and time-dependent correlation functions measured by scattering spectroscopy. Treats in detail experimental techniques of x-ray, light, electron, and neutron scattering. Theoretical development is strongly phenomenological to elucidate physical behavior with minimal mathematical complexity. Uses conservation laws, broken symmetry, and the fluctuation-dissipation theorem to illustrate the interconnection between apparently diverse systems, with special attention to behavior near phase transitions.

**52-668 Dielectric Materials **

Macroscopic and microscopic approaches. Types of polarization, complex dielectric constant and refractive index. Frequency response, polar and non-polar materials. The Debye equation, effective field and dielectric breakdown. Piezoelectricity and ferroelectricity. Optical fibres, Xeros process and liquid crystals.

**52-669 Type-II Superconductivity and its applications**

Irreversible and thermodynamic properties, field of an isolated vortex, lower and upper critical fields, surface barriers and surface superconduc tivity, interaction of vortices with pinning centers, resistive state in a Type- II superconductor, critical current of a Type-II superconductor, and calculation of current-voltage curves, solution of critical state, analytical calculation of magnetization curves (M-H curves), equlibrium magnetization reversible magnetization of a Type-II superconductor, high field magnet designe, power transmition cables, current limiters, bolometers, and SQUID`s.

**52-673 Molecular Physics II**

Intermolecular forces: long and short-range interactions; interactions of small atomic system; physical absorption; molecular collision theory: scattering by a central force; elastic and inelastic collisions; transition probabilities and collisional energy transfer. Scattering of atoms and molecules from solid surfaces.

**52-680 Introduction to Neural Networks**

Organization of synaptic connectivity as the basis of neural computation and learning. Single and multilayer perceptrons. Dynamical theories of recurrent networks: amplifiers, integrators, attractors, and hybrid computation. Backpropagation, Hebbian, and reinforcement learning. Models of perception, motor control, memory, and neural development.

**52-690 Plasma Physics**

The basic equations and conservation laws; first order orbit theory; adiabatic invariants; ideal MHD model; plasma equilibrium and stability; energy principle; plasma waves; waves-particle interaction; wave-wave interaction; weak turbulence theory.

**52-691 Solar and Planetary Plasma Physics**

Kinetic properties of coronal gas; hydrostatic properties of coronal atmosphere; extension of the solar wind into space; interplanetary magnetic fields; interplanetary irregularities; propagation of energetic solar particles; pulsars.

**52-692 Fundamentals of Fusion Plasma Systems**

Energy alternative thermonuclear fusion; inertial and magnetic confinement systems; Tokomak, stellorators and mirror machines; plasma focus and pinches; alternative magnetic confinement systems; Laser fusion systems; concept of fusion reactors; for mation and heating of a plasma.

**52-696 Advanced Seminar in Physics**

Ph.D. Students study and present a topic under the guidance of a faculty member.

**52-699 Advanced Directed Studies in Physics**

Ph.D. Students prepare an advanced topic in the form of project or seminar in contemporary physics other than their research fields.

**02-7XX Special Studies**

Courses not listed in the catalogue. Contents vary from year to year according to interest of students and instructor in charge.

**52-8XX Special Studies**

M.S. Students choose and study a topic under the guidance of a faculty member, normally his/her advisor.

**52-697 Advanced Studies**

Graduate students as a group or a Ph.D. student choose and study advanced topics under the guidance of a faculty member, normally his/her advisor.