Differential manifolds, tangent space, vector fields, local diffeomorphisms, cotangent space, differential forms, exterior derivative.  Differential geometric aspects of Lie groups, Lie algebras, orbit, homogeneous spaces, non-linear – model.  Fiber bundles, principal bundles, connections.  Yang-Mills gauge theories, applications of differential geometry in gauge.

Lie groups, Lie algebras, cartan sub-algebra, roots, Dynkin diagrams, classification of simple Lie algebras. Toda equations and their integrability.  Higgs fields, self-dual monopoles. Classification of unitary representations of simple Lie groups.  Weyl’s character formula.

Standard cosmology, Robertson-Walker metric, thermal history of the universe, relativistic thermodynamics, phase transitions. Nucleosynthesis, dark matter, density fluctuations, galaxy formation.  Inflation. Cosmic strings.  Recent work on cosmological models; super-strings.  Recent work on cosmological models; super-strings, super-gravity, Kaluza-Klein.

 Crystal optics (tensors, symmetry, anisotropy, resonance, momentum-space). Optical modulation (electrooptics, acoustoptics, magnetooptics). Second order nonlinearity (frequency doubling, parametric interactions, cascaded nonlinearity), Third order nonlinearity (optical Kerr effect, stimulated Brill scattering, stimulated Raman scat., bistability, phase conjugation, self focusing, solitons).. Nonlinearities in semiconductors. Ultrafast nonlinear optics. Nonlinear interaction of radiation with matter.

Nano, pico, femto second pulse generation. Q-switching, mode-locking, DFB, relaxation oscillation. Measurement: auto and cross correlation function, two photon, SH generation for detection, optical time delay, femto second, chirping, cooling pulses-generating compression. Applications in molecular relaxation, biology, semiconductor dynamics…etc.

Laser beam characteristics- Beam focusing effects - Semi classical theory of absorption and emission – Reflectivity & transmission of matter – Photon transport theory - Laser beam heating, melting, vaporization – Plasma formation- Rate of heating and cooling – Operational regimes in material processing -Depth of penetration – Key hole effect – Surface treatment (modification, cladding, alloying and hardening) – High power laser int. with solids (welding , cutting) – Optical properties of tissue - Laser tissue interaction (thermal, photochemical, photo mechanical, photo ablation, plasma induced ablation and photo description).

Propagation of EM waves in Dielectric wave guide – Fiber optics (boundary conditions, phase and group velocity, attenuation and dispersion, cut off frequency, single and multimode fibers) – Emitters (LED &laser diodes DH, QW, BDR, DFB, VCSEL’s) -  Fabrication techniques – Materials for photonics – Laser modulation (AM, FM and PM) and Demodulation – Receivers ( Detectors PIN, PMT, APD), homodyne and heterodyne detection – Sensors – Switching devices and wave guide switching.   

Laser safety, Lasers in Optical Communication and Data Storage,  Medical Applications: Optical properties of tissue – Models of laser-tissue propagation – Montecarlo simulation of laser tissue interaction – Laser effects on tissue (thermal, photochemical, photmechanical, ionizing..) – Medical applications (Opthalmology,  dermatology, dentistry, surgery, NET, gynecology, urology, neursurgery…..) - Low level laser therapy(LLLT)  – Laser safety and precautions- Diagnostic by laser – Laser types in medicine.  Industrial Applications, Metrological Applications, Holography.  Detectors, Laser system for remote sensing (CO2, Excimer, dye, semiconductor lasers. Optics. Telescopes). Basic equation for sensors. LIDAR, Differential Absorption, LIF, Raman, Atmospheric & Hydrospheric Monitoring., Industrial Pollution, Atmospheric / Underwater transmission, Practical Considerations, Deep Sea Coral Reefs, Industrial Pollution, Oil Spills.

Mixtures and the density operator (level damping, density matrix, vector model of density matrix)- CW field interactions(polarization of two-level medium, inhomogeneous broadened media, polarization of semiconductor gain media) – Laser theory(laser self-consistency equations, single-mode semiconductor laser theory, transverse variations and Gaussian beam....) -  Coherent transient – Field quantization (single and multimode field quantization, coherence of quantum fields..)- Interaction between atoms and quantized field- Squeezed states of light( squeezing the coherent state, two-side mode master equation, two-mode squeezing, squeezed vacuum).

Exp. Data Analysis, Detector Theory and Performance Parameters, Thermal Detectors (pneumatic, pyroelectric, thermpelectric,  bolometers, ) , Photon Detectors (photemissive, vacuum photodiode, photomultiplier, photncounting, image intensifier), Junction detectors (PIN, APD, Schottky PD, phototransistor), Vidicon , Plumbicon , Diode arrays, CCD Camera. Noise in photon devices.

Gas Laser Design: Gas discharge phenomena – Vacuum techniques- Cooling systems – Power supplies for low and high power cw lasers – High power pulsed lasers(CO2, TEA…) - Blumbin  circuits (TEA, Excimer, N2 dynamic and chemical lasers design). Liquid Lasers Design: Preparation of dye solvents – pump geometry –jet flow transverse pumping – high energy dye laser (flash and laser pumped) – fs lasers. Insulator Solid Lasers: Flash and arc lamp – Diode pumped YAG lasers – Ti:sapphire laser design – Ring and Traveling wave laser design. Injection Lasers: Fabrication and characterization- Diode array lasers for pumping. Laser Mirrors: Dielectric coating – thin films – dichroic mirrors. Detection circuits problems.

Vacuum principles and vacuum system design basics, Overview of thin film technology, crystal structures of thin films, Defects sin Thin films, Nano crystalline, polycrystalline, and epitaxial thin films, thin film nucleation and growth models, (2D, 3D, and 2D- Epitaxial growth of thin films, super lattice structures and quantum wells, diffusions: inter-diffusion, grain boundary diffusions, reaction and phase transformation, Thin film growth techniques (CBD, Spray, Reactive evaporation,  PVD, Sputtering, MBE, Laser MBE PLD, CVD, PECVD, MOCVD, Sol-Gel, PAD.), Thin film processing, Thin film characterization techniques.

Renewable energy assessment, Solar radiation models, Solar-Thermal, Photovoltaic systems, Wind energy systems, Fuel cells applications, Biomass: Gas and liquid conversion, Hydrogen energy applications, Other renewable energies, Renewable energy economics and feasibility studies, Environmental factors and renewable energy, Typical examples at national and international levels. Waste and recycled energy, Ecological effects and thermal pollution and Energy policy for future.

Structure in Materials, Techniques and advanced systems in materials, Destructive and non-destructive testing, Mechanical properties, Metals, Polymers,, Ceramics and carbon materials, Composites, Electronics and Optical properties, Nano Materials, Biomaterials and Biological Materials, Gas Sensing Materials, Photo & IR Detectors.

Energy States in Semiconductors, Perturbation of Semiconductors by external parameters, Absorption, Relationships between Optical constants, Absorption spectroscopy, Radiative and nonradiative transitions, processes in p-n junctions, stimulated emission, Excitation of luminescence and lasing in semiconductors, Photoelectric emission, Photovoltaic and photochemical  effects, Effect of traps on luminescence, Optical characteristics related to mobile electrons, Absorption of light by electronic transitions, Interaction of radiation with oriented quantum wells, Photoconductivity.

Electrical conductivity, mobility, and Hall effect in semiconductors, Temperature dependence of mobility , Geometric magneto resistance, Four point probe and sheet resistivity, Spreading resistance techniques, Capacitance - voltage techniques, Depth profiling and electrical assessment, Deep Level transient Spectroscopy, Determining the structures of semiconductors using X-rays, Rocking curves and crystal perfections, EXAFS and SEXAFS, Raman spectroscopy, The experimental measurement of optical constants, Photoluminescence, photoconductivity and photo thermal effects, Secondary ion beam spectroscopy, Auger electron spectroscopy, Electron microscopy, Atomic Force Microscopy (AFM), FTIR (Fourier Transform Infra Red Spectroscopy), TED, LEED, RHEED.

Symmetry in quantum mechanics: Symmetries, conservation laws, and degeneracies.  Discreet symmetries, parity.  Lattice translation, Time –Reversal.

Identical particles:  Permutation symmetry, Symmetrization postulate, two-electron system. The Helium atom. Permutation symmetry and Young Tableaux.

Scattering theory:  The Lippmann-Schwinger equation, The Born approximation, Optical theorem. Methods of partial waves, Low energy scattering and bound states, Resonance scattering.  Identical particles and scattering, Coulomb scattering. 

Quantization of a free scalar field.  Classical e.m. field, gauge transformations. Quantization of the e.m. field, Lorentz gauge, extended Fock space, Green’s functions.   Dirac equation. Interaction picture, Perturbation theory, Feynman rules, phase space.  The processes e , e  and e+e-.  Divergences, regularization and renormalization., General gauges.

Renormalization of quantum field theories, normalization conditions, counter-terms, Zero-mass limit, asymptotic behavior. Functional method in Q.F.T., path integrals, generating functional, effective action, effective potential.  The -model, Renormalization, symmetry breaking, anomalies, Gauge fields, Quantization of gauge fields.

Gauge theories, symmetry breaking.  Standard electroweak model, particle representations, generations, neutral currents, relation to four-fermion theory, particle masses, GIM mechanism, universality.  The electroweak interactions.  Kobayashi-Maskawa matrix, experimental determination of the parameters.  The running coupling constants, implications of the renormalization group equations, grand unification.

Quark model of hadrons, solutions, bag models. Gluon exchange, mass formulae, quark masses, heavy quarks.  Quark-parton model, deep inelastic electron-nucleon scattering, scaling, corrections to scaling behaviour, jets.  Chiral symmetry, chiral symmetry breaking, quark masses.

The colour group, asymptotic freedom, scaling violatius in deep in elastic scattering.  Renormalization group – functions.  Operator-produce expansions, anomalous dimensions.  Non-perturbative QCD, dispersion sum rules. The QCD vacuum, U(1)-problem, confinement; strong CP violation.

Review of Lie groups and their representations.  The groups SU(5), SO(10) and E6.  Unification I the standard model.  Georgi-Glashow SU(5) model.  Proton decay.  Other unification models: SO(10), E6, SU(4) x SU(4).  Problems of grand unified models.  Future outlook.

Two-dimensional superspace, superfield, scalar and vector multiplets; N=1/2, N=1, N=2. Four-dimensional superspace, supersymmetry groups, super-integration, expansion, projection operators. Classical N=1, superfield propagators, super      . Explicit and spontaneous supersymmetry breaking, super-Higgs.

Path integrals, Faddeev-Popov quantization.  Free bosonic strings.  Quantization; light-cone, BRST. Trees, vertex operators, closed strings.  Superstrings, NSR-model, ghosts, extended supersymmetry.  String group, tangent space, connections, covariant derivative.  Anomalies, Atiyah-Singer theorem.

Classical N=1 supergravity, covariant approach to supergravity, constraints, actions, Quantum  superields,  regularization, anomalies, Quantum N=1 supergravity, background splitting, ghosts, Feynman’s rules, dimensional regularization.  Supergravity and symmetry breaking.

Selected topics are chosen by the supervisor related to the PhD dissertation.

electron-electron interactions, electron-phonon interactions, Magnetism in solids, Magnetic Properties, Magnetic Resonance, Dielectric and Optical Properties, Diamagnetism and Paramagnetism, Superconductivity and Ginzburg-Landau equations.

Classical models for the electronic properties of metals: Drude and Sommerfeld models.  Quantum mechanics of particles in periodic potentials (Bloch's theorem).  Band structure models: Nearly Free and Tight Binding electronic models. Semiconductors and insulators:  Energy gap, Number of carriers, Density of states.  Associated physical phenomena: electrical, optical, thermal and magnetic properties. Characterization and device applications.  Wavevector (K) and effective mass of electrons in solids.   Band-structure engineering: multilayers and quantum wells.  Magnetoresistance and the quantum Hall effect.

Magnetic field in free space and matter, magnetic quantities and units, types of magnetism. Spin and atomic magnetism.   Quantum mechanics of magnetic properties.  Interaction of spins.  Exchange interactions. Itinerant electrons and localized interactions.  Magnetization curves.  Magnetic resonance ESR and NMR. Magnetic properties of superconductors. Magnetoresistance. Superparamagnetism.  Nanoscale magnetism, spintronics. Spin entanglement. 

Introduction to Fortran 90,Numerical integration (basic integration schemes, stochastic methods for multidimensional integrals), Numerical solutions of differential equations (classical equations of motion, studies of systems with chaotic dynamics, eigenstates of the Schrodinger equation, time evolution of wave-packets in quantum mechanics), Molecular dynamics simulations (basic schemes for classical many-particle dynamics, simulations at fixed energy and temperature), Monte Carlo simulations (the Metropolis algorithm for equilibrium statistical mechanics, studies of the phase transition in the Ising model of magnetism, liquids and gases), Optimization using simulated annealing, Exact diagonalization of quantum systems (ground state and finite-temperature properties of quantum magnets).

Introduction, the complex refractive index, Lorentz oscillators, dispersion, birefringence, Interband absorption, excitons, Luminescence, Quantum wells, Metals, doped semiconductors, Phonon absorption and reflectivity, Nonlinear optics.

Nuclear Collective Motion: Review of collective vibration, collective rotation of nuclei.

Variable moment of Inertia: Backbending phenomenon , physical interpretation through broken pairs, band crossing, band mixing.

 Many-Body States: Deformed Potentials for deformed nuclei, deformed harmonic oscillator potential, deformed single particle states, and deformed many particle states.

Algebraic Models: The interacting boson model, Deformed Lie algebra models.

Superdeformed Nuclei: High spin states of nuclei, dynamic and kinematic moment of inertia, properties of superdeformed nuclei, population of superdeformed nuclei, superdeformed rotational bands. Nilsson –Strutinsky approach

Sources of environmental radioactivity; Analysis of environmental radionuclides; Radioactivity in the terrestrial environment; Radioactive aerosols; Marine radioactivity; U-Th series radionuclides in the environment.

Neutron sources , Introduction to elastic neutron scattering theory, Diffraction,  Spectroscopy , Small Angle Neutron Scattering, Polarised neutrons, Experimental Technique, Data treatment .

Introduction to Nuclear track Detectors, Interaction of charged particles with matter, The nature of charged- particle tracks and some possible Track formation Mechanisms in Insulating Solids.

Track etching: Methodology and Geometry, Thermal Fading of Latent Damage Trail, The use of Dielectric Track Recorders in Particle Identification, Some applications of Track detectors.

Basic principles, Nuclear activation analysis, Nuclear magnetic resonance, Particle induced x-ray emission

X-ray crystallography - Nuclear Magnetic Resonance - Fluorescence,  Fluorescence Microscopy - Ultraviolet-Visible, and Infra Red and  Fourier  Spectroscopy - AC & DC Dielectric relaxation -  Chromatography.

The aims of this course are: 1) to provide students with an understanding of the fundamental principles of a range of advanced biophysical techniques. 2) to give students an understanding of how to use these techniques to get an information about the structure of macromolecules, electronic structure, size, shape, and modes of interaction of biological molecules along with studying the dynamics of cellular processes.

Radiobiology: Effects of ionizing radiations on living cells and organisms, including physical, chemical, and physiological bases of radiation cytotoxicity, mutagenicity, and carcinogenesis.

Radiological Physics and Dosimetry: Interactions and energy deposition by ionizing radiation in matter; concepts, quantities and units in radiological physics; principles and methods of radiation dosimetry.

Radiotherapy Physics: Ionizing radiation use in radiation therapy to cause controlled biological effects in cancer patients; physics of interaction of the various radiation modalities with body-equivalent materials; physical aspects of clinical applications.

- Introduction to medical imaging, Image formation and quality, Processing and reconstruction of medical images, Imaging modalities.

- X-ray imaging: X-ray imaging methods, Computed tomography (CT), clinical applications of x-ray imaging,

- Nuclear medicine imaging: Radiopharmaceuticals materials, Single photon emission computed tomography (SPECT), Positron emission tomography (PET), and their clinical applications.

- Ultrasound imaging: Physics of ultrasound, applications of ultrasound imaging in medicine.

Electronic and nuclear spin.  Electronic and nuclear magnetism. Magnetic atoms and ions.  Microwave and radio frequency absorption.  Magnetic resonance.  Nuclear Magnetic Resonance (NMR) and Electron Spin Resonance (ESR).  Magnetic interactions, saturation and relaxation.  Computerized detection of magnetic resonance.  Magnetic Resonance Imaging (MRI).  Image detection and enhancement.  Magnetic Resonance applications in physics, chemistry and medicine.

Biomagnetic fields.  The Josephson effect. SQUID Magnetometers: layout, noise cancellation, rf, dc, and high Tc SQUIDs. Magnetoencephalography (MEG). Magnetocardiography (MCG).  Magnetoneumography (MPG).

General molecular bonding and structures -  Definition of free radicals - Free radicals in chemical and biochemical interactions – Chemical properties of free radicals – Magnetic properties of free radicals – Biradicals – Generation of free radicals by  spin resonance of free radicals – Hyperfine interactions of free radicals – Free radical labeling – Beneficial and damaging roles of free radicals in biological systems – Antioxidants and free radical scavengers.

Radiation and environmental radioactivity. Sources of environmental radioactivity.  Radioecological pollution. radiation interaction with matter. radiation effects on living system. stochastic and non-stochastic effects. delayed effects and physical-chemical properties of radiation effect in cells. environmental pathways analysis and dose assessment; radioactivity risk assessment