Graduate Courses

 A review course in the fundamentals of physics, especially
in mechanics and electromagnetism; dynamics of a particle; systems of
particles and their conservation laws; motion of a rigid body; electrostatics,
magnetic fields and currents; electromagnetic induction.
       Typical text: Hallidy, Resnick and Walker, Fundamentals of
Physics.

The course will cover the most common atomic and nuclear effects, yet covers it in direct relation to a sophisticated quantum mechanical treatment. It thereby connects the theoretical models with the experimental results, showcasing agreement as well as disagreement to outline the validity range of each model. Topics covered include Brownian motion; charge and mass of electrons and ions; Zeeman effect; photoelectric effect; emission, absorption, reflection, refraction, diffraction, absorption, and scattering of X-rays; Compton effect; diffraction of electrons; uncertainty principle; electron optics; atomic spectra and electron distribution; radioactivity; disintegration of nuclei; nuclear processes; nuclear energy; and fission.    

Description of simple physical models which account for electrical conductivity and thermal properties of solids. Basic crystal lattice structures, X-ray diffraction and dispersion curves for phonons and electrons in reciprocal space. Energy bands, Fermi surfaces, metals, insulators, semiconductors, superconductivity and ferromagnetism. Fall semester. Typical text: Kittel, Introduction to Solid State Physics.

Theories of the universe, general relativity, Big Bang cosmology, and the inflationary universe; and elementary particle theory and nucleosynthesis in the early universe. Observational cosmology; galaxy formation and galactic structure; and stellar evolution and formation of the elements. White dwarfs, neutron stars and black holes, planetary systems, and the existence of life in the universe.

An overview of Microelectronics and Photonics Science and Technology.  It provides the student who wishes to specialize in the application, physics or fabrication with the necessary knowledge of how the different aspects are interrelated.  It is taught in three modules: design and applications, taught by EE faculty; operation of electronic and photonic devices, taught by Physics faculty; fabrication and reliability, taught by the
Materials faculty.

The general study of field phenomena; scalar and vector fields and waves; dispersion phase and group velocity; interference, diffraction and polarization; coherence and correlation; geometric and physical optics. Typical text: Hecht and Zajac, Optics. Spring semester.

The course is designed to familiarize students with a range of optical instruments and their applications. Included will be the measurement of aberrations in optical systems, thin-film properties, Fourier transform imaging systems, nonlinear optics, and laser beam dynamics. Fall term.  This course may sometimes be offered in the spring term if space

Historical introduction; radioactivity; laws of statistics of radioactive decay; alpha decay; square well model; gamma decay; beta decay; beta energy spectrum; neutrinos; nuclear reactions; relativistic treatment; semiempirical mass formula; nuclear models; uranium and the transuranic elements; fission; and nuclear reactors.

This course will cover topics encompassing the fundamental subject matter for the design of optical systems. Topics will include optical system analysis, optical instrument analysis, applications of thin-film coatings and opto-mechanical system design in the first term. The second term will cover the subjects of photometry and radiometry, spectrographic and spectrophotometric systems, infrared radiation measurement and instrumentation, lasers in optical systems and photon-electron conversion. Typical texts: Military Handbook 141 (U.S. Govt. Printing Office); S.P.I.E Reprint Series (Selected Issues); W.J. Smith, Modern Optical Engineering .

This course will cover topics encompassing the fundamental subject matter for the design of optical systems. Topics will include optical system analysis, optical instrument analysis, applications of thin-film coatings and opto-mechanical system design in the first term. The second term will cover the subjects of photometry and radiometry, spectrographic and spectrophotometric systems, infrared radiation measurement and instrumentation, lasers in optical systems and photon-electron conversion. Typical texts: Military Handbook 141 (U.S. Govt. Printing Office); S.P.I.E Reprint Series (Selected Issues); W.J. Smith, Modern Optical Engineering .

Numerical techniques. Numerical methods for integrating Newton’s laws, the diffusion equation, Poisson’s equation, and the wave equation are discussed. Topics also covered: discrete Fourier transform, stability theory,curve fitting , the diagonalization of matrices, and Monte Carlo methods. Spring semester. Typical text: Garcia, Computational Physics.

A phenomenological and theoretical introduction to the field of surface science, including experimental techniques and engineering applications. Topics will include: thermodynamics and structure of surfaces, surface diffusion, electronic properties and space-charge effects, physisorption, and chemisorption. Spring semester. Alternate years.

Lectures, demonstrations and laboratory experiments, selected from among the following topics, depending on student interest: vacuum technology; thin-film preparation; scanning electron microscopy; infrared spectroscopy, ellipsometry: electron spectroscopies-Auger, photoelectron, LEED; ion spectroscopies SIMS, IBS, field emission; surface properties-area, roughness,   and surface tension.   Alternate years.

Fourier series, Bessel functions, and Legendre polynomials as involved in the  solution of vibrating systems; tensors and vectors in the theory of  elasticity; applications of vector analysis to electrodynamics; vector  operations in curvilinear coordinates; numerical methods of interpolation and  of integration of functions and differential equations.

Vector and Tensor Fields: transformation properties, algebraic and  differential operators and identities, geometric interpretation of tensors,  integral theorems.  Dirac delta-function and Green's function technique for  solving linear inhomogeneous equations.  N-dimensional complex space:  rotations, unitary and hermitian operators, matrix-dyadic-Dirac notation,  similarity transformations and diagonalization, Schmidt orthogonalization.  Introduction to functions of a complex variable: analyticity, Cauchy's  theorem, Taylor and Laurent expansions, analytic continuation, multiple-  valued functions, residue theorem, contour integration, asymptotics.  As  techniques are developed, they are applied to examples in mechanics,  electromagnetism and/or transport theory.         Fall semester.

This course introduces students to the fundamental principles of physical science and develops in them a deeper understanding of the key issues in global energy production and consumption and global scale change and the engineering of solutions to the problems arising from these phenomena.  The concepts of energy and energy transformations will be at the core of this course.  These will be introduced using simple mechanical systems such as the pendulum and then will be generalized to discuss phenomena from the atomic scale to the global scale.

Introduction to Earth as a dynamic system through the study of the Earth, ocean and atmosphere as a complex interacting system involving large scale flows of energy and matter.  Topics include historic and physical geology, oceanography, atmospheric science and natural energy focused on content knowledge and research-based learning.

An integral course in the five-course cluster developed for the Stevens Math-Science Partnership Program, this course explores the science and technology behind energy production, distribution and consumption.  Fundamental principles about energy at the microscopic scale are shown to underlie the operation of multiple energy production systems in use today.  The course seeks to especially connect the concepts of societal energy usage with the underlying principles of chemical structure, thermodynamics, and chemical reactions to provide models for understanding critical energy issues.  Patterns of energy consumption that define the modern world and the global impact that energy use has on human society are explored and provide the context.                                                                      

Exploration of the physical basis of global climate change and the impact on the Earth’s large scale climate systems of human activity will be studied.  Topics include the analysis of the flow of energy and the energy transformations in the Earth system, the role of the carbon cycle and the greenhouse effect and the scientific data that has been used to establish the current viewpoint and predict future climates.  We will also discuss socio-political and technological strategies for mitigating climate change.   

Particle motion in one dimension. Simple harmonic oscillators. Motion in two and three dimensions, kinematics, work and energy, conservative forces, central forces, and scattering. Systems of particles, linear and angular momentum theorems, collisions, linear spring systems, and normal modes. Lagrange’s equations and applications to simple systems. Introduction to moment of inertia tensor and to Hamilton’s equations.

Charged particle motions in electric and magnetic fields; electron and ion optics; charged particle velocity and mass spectrometry; electron and ion beam confinement; thermionic emission; the Pierce gun; field emission; secondary emission; photoelectric effect; sputtering; surface ionization; volume ionization; and Townsend discharge.  Typical text: Beck and Ahmed, An Introduction to Physical Electronics.

Charged particle motion in electric and magnetic fields; electron and ion emission; ion-surface interaction; electrical breakdown in gases; dark discharges and DC glow discharges; confined discharge; AC, RF, and microwave discharges; arc discharges, sparks, and corona discharges; non-thermal gas discharges at atmospheric pressure; and discharge and low-temperature plasma generation. Typical texts: J.R. Roth, Industrial Plasma Engineering: Principles, Vol. 1, and Y.P. Raizer, Gas Discharge Physics.

Electrostatics; Coulomb-Gauss law; Poisson-Laplace equations; boundary value problems; image techniques;dielectric media; magnetostatics; multipole expansion; electromagnetic energy; electromagnetic induction; Maxwell’s equations; electromagnetic waves, radiation, waves in bounded regions, wave equations and retarded solutions; simple dipole antenna radiation theory; transformation law of electromagnetic fields. Spring semester. Typical text: Reitz, Milford and Christy, Foundation of Electromagnetic Theory.

Plasmas in nature and application of plasma physics; single particle motion; plasma fluid theory; waves in plasmas; diffusion and resistivity; equilibrium and stability; nonlinear effects and thermonuclear reactions; the Lawson condition; magnetic confinement fusion; and laser fusion. Fall semester. Typical text: F.Chen, Plasma Physics.

Basic plasma physics; some atomic processes; and plasma diagnostics. Plasma production; DC glow discharges and RF glow discharges; magnetron discharges. Plasma-surface interaction; sputter deposition of thin films; reactive ion etching, ion milling, and texturing; electron beam-assisted chemical vapor deposition; and ion implantation. Sputtering systems; ion sources; electron sources; and ion beam handling. Typical texts: Chapman, Glow Discharge Processes; Brodie, Muray, The Physics of Micro-fabrication. Fall semester.

Description of principle flow phenomena: pipe and channel flows, laminar flow, transition, and turbulence; flow past an object-boundary layer, wake, separation, vortices, and drag; convection in horizontal layers-conduction, convection, and transition from periodic to chaotic behavior. Equations of motion; dynamical scaling; simple viscous flows; inviscid flow; boundary layers, drag, and lift; thermal flows; flow in rotating fluids; hydro-dynamic stability; and transitions to turbulence. Typical text: Tritton, Physical Fluid Dynamics.

An experimental presentation of the evidence for atomic
and nuclear theories; typical experiments are: excitation potentials; electronic charge; specific charge of the electron; Balmer series; Zeeman splitting; spectroscopic isotope shifts; photovoltaic effect; Hall effect; gamma ray spectrometry; beta ray spectrometry; neutron activation of nuclides; statisticsof counting processes; optical and X-ray diffraction; Langmuir probe; nuclear magnetic resonance.
  Fall semester, repeated spring semester by arrangement.
  Typical texts: Young, Statistical Treatment of Experimental Data; Melissinos,  Experiments in Modern Physics.

Geometrical foundations of space-time theories, geometrical objects, affine geometry, and metric geometry; structure of space-time theories, symmetry, and conservation laws; Newtonian mechanics; special relativity; foundations of general relativity, Mach’s principle, principle of equivalence, principle of general covariance, and Einstein’s equations; solution of Einstein’s equations; experimental tests of general relativity; conservation laws in general relativity, gravitational radiation, and motion of singularities; and cosmology.

 This course is meant to serve as an introduction to formal quantum mechanics  as well as to apply the basic formalism to several generic and important  applications.

Basic concepts of quantum mechanics, states, operators; time development of  Schrödinger and Heisenberg pictures; representation theory; symmetries;  perturbation theory; systems of identical particles, L-S and j-j coupling;  fine and hyperfine structure; scattering theory; molecular structure.        Spring semester.    Typical texts: Gottfried, Quantum Mechanics, Schiff, Quantum Mechanics.

Kinetic theory: ideal gases, distribution functions, Maxwell-Boltzmann distribution, Boltzmann equation, H-theorem and entropy, and simple transport theory. Thermodynamics: review of first and second laws, thermodynamic potentials, Legendre transformation, and phase transitions. Elementary statistical mechanics: introduction to microcanonical, canonical, and grand canonical distributions, partition functions, simple applications, including ideal Maxwell-Boltzmann, Einstein-Bose, and Fermi-Dirac gases, paramagnetic systems, and blackbody radiation. Typical text: Reif, Statistical and Thermal Physics.Fall semester.

Interference phenomena in electromagnetism and quantum mechanics; interaction of light and matter, principles of coherent control; adaptive and optimal algorithms; Rabi flopping in two-level systems; control of three-level systems including STRIRAP and electromagnetically induced transparency; tools for quantum control; various current and proposed applications.

The course will focus on fundamentals of quantum computation. The topics to be covered include: quantum foundation, quantum channel, quantum qubits, noise and decoherence, master equation and Kraus operations, quantum entanglement, quantum circuits, universal quantum gates, quantum algorithms, quantum error correction codes. The course will not only cover the theoretical aspects of quantum computing and quantum information but also cover physical realizations of quantum computers in various physical contexts including quantum optical systems, solid state qubits etc.

This course introduces fundamentals of semiconductors and basic building blocks of semiconductor devices that are necessary for understanding semiconductor device operations. It is for first-year graduate students and upper-class undergraduate students in electrical engineering, applied physics, engineering physics, optical engineering and materials engineering, who have no previous exposure to solid state physics and semiconductor devices. Topics covered will include description of crystal structures and bonding; introduction to statistical description of electron gas; free-electron theory of metals; motion of electrons in periodic lattice-energy bands; Fermi levels; semiconductors and insulators; electrons and holes in semiconductors; impurity effects; generation and recombination; mobility and other electrical properties of semiconductors; thermal and optical properties; p-n junctions; metal-semiconductor contacts.

This course introduces operating principles and develops models of modern semiconductor devices that are useful in the analysis and design of integrated circuits. Topics covered include: charge carrier transport in semiconductors; diffusion and drift, injection, and lifetime of carriers; p-n junction devices; bipolar junction transistors; metal-oxide-semiconductor field effect transistors; metal-semiconductor field effect transistors and high electron mobility transistors, microwave devices; light emitting diodes, semiconductor lasers, and photodetectors; and integrated devices.

Review of electromagnetic theory; derivation of Fresnels’ equations; guided-wave propagation by metallic and dielectric waveguides, including step-index optical fibers and graded-index fibers; optical transmission systems; and nonlinear effects in optical fibers, solitons, and fiber-optic gyroscope.

This course treats scattering, absorption and emission of electromagnetic radiation in planetary media. The radiative transfer equation is derived, approximate solutions are found. Important heuristic models (Lorentz atom, two-level atom, vibrating rotator) as well as fundamental concepts are discussed including reflectance, absorptance, emittance, radiative warming/cooling rates, actinic radiation, photolysis and biological dose rates. A unified treatment of radiative transfer within the atmosphere and ocean is provided, and extensive use of two-stream and approximate methods is emphasized. Applications to the climate problem focus on the role of greenhouse gases, aerosols and clouds in explaining the temperature structure of the atmosphere and the equilibrium temperature of the earth. The course is suitable for beginning graduate and upper-level undergraduate students.

 An introductory course to the theory of lasers; treatment of spontaneous and  stimulated emission, atomic rate equations, laser oscillation conditions,  power output and optimum output coupling; CW and pulsed operation, Q  switching, mode selection, and frequency stabilization; excitation of lasers,  inversion mechanisms, and typical efficiencies; detailed examination of  principal types of lasers, gaseous, solid state, and liquid; chemical lasers,  dye lasers, Raman lasers, high power lasers, TEA lasers, gas dynamic lasers.  Design considerations for GaAlAs, argon ion, helium neon, carbon dioxide,  neodymium YAG and pulsed ruby lasers.      Fall semester.         Typical text: Yariv, Optical Electronics.

Integrated optics, nonlinear optics, Pockels effect, Kerr effect, harmonic generation, parametric devices, phase conjugate mirrors, and phase matching. Coherent and incoherent detection, Fourier optics, image processing and holography, and Gaussian optics. Detection of light, signal to noise, PIN and APD diodes, and optical communication. Scattering of light, Rayleigh, Mie, Brillouin, Raman, and Doppler shift scattering. Spring semester.

This course is dedicated to give students a working knowledge of the fundamental concepts and modern applications of nonlinear optics in optical communications, lasers, optical metrology, and quantum computing. Through this course, students will gain in-depth understanding and master mathematical tools for modeling nonlinear optical susceptibilities, wave propagation and coupling in nonlinear media, harmonic, sum, and difference frequency generation, parametric amplification and oscillation, phase-conjugation via four-wave mixing, self-phase modulation, and solitons.

Electronic, magnetic, optical, and thermal properties of materials, the description of these properties based on solid state physics. Description and principles of operation of devices. Spring semester.

Physical design of wireless communication systems, emphasizing present and next-generation architectures; impact of non-linear components on performance; noise sources and effects; interference; optimization of receiver and transmitter architectures; individual components(LNAs, power amplifiers, mixers, filters, VCOs, phase-locked loops, frequency synthesizers, etc.); digital signal processing for adaptable architectures; analog-digital converters; new component technologies (SiGe, MEMS, etc.); specifications of component performance; reconfigurability and the role of digital signal processing in future generation architectures; direct conversion; RF packaging; and minimization of power dissipation in receivers.

Treatment of the electrical, chemical, environmental, and mechanical driving forces that compromise the integrity and lead to the failure of devices. Both chip and packaging level failures will be modeled and quantified statistically. On the packaging level, thermal stresses, solder creep, fatigue and fracture, contact relaxation, corrosion and environmental degradation will be treated.

Discussions of aspects of the technology of processing procedures involved in the fabrication of microelectronic devices and microelectromechanical systems (MEMS). Topics with respect to IC fabrication include crystal growth, epitaxy, silicon oxide growth, impurity doping, ion implantation, photo and electron beam lithography, etching, sputtering, thin film metallization, passivation and packaging. Students will also learn that MEMS are sensors and actuators that are designed using different areas of engineering disciplines and they are constructed using a microlithographically-based manufacturing process in conjunction with both semiconductor and micromachining microfabrication technologies.

The course is the first part of the graduate certificate program "Wireless  Secure Network Design" which includes also three other courses - PEP 602, 603  and 604.  Program focuses on heterogeneous wireless systems used by  first-responders - police, fire fighters, National Guard and other emergency  forces - to protect the public during large scale crises, such as natural  disasters and acts of terrorism.  The program also includes analysis of  homeland defense, financial and military operations using secure wireless  systems.  At the end of the program students will learn how protect existing  wireless systems and how design highly secure systems for a future use.      The course presents a comprehensive analysis of different parts of the   electromagnetic spectrum, transmission and modulation technologies, hardware   new artificially engineered materials, and MEMS with accent on security and    robustness of communications.Fall Semester

The course presents an overview of areas of first responders and military  activities and using of different heterogeneous wireless systems during large  scale crises, such as natural disasters, acts of terrorism, and also during  homeland defense, financial and military operations.  The course includes an  analysis of different wireless network architectures from security point of  view.  The course is the second part of the graduate certificate program  "Wireless Secure Network Design" which includes also three other courses - PEP  601, 603 and 604. Fall semester.

 The course presents an overview of different methods of
authentication and authorization in secure wireless networks.  The course
focused on different methods of physical data and link protection, probability of detection and interception, anti-jam and covert capabilities, active and passive protection methods and equipment.  The course is the third part of the graduate certificate program "Wireless Secure Network Design" which includes also three other courses - PEP 601, 602 and 604.  Spring Semester

The course presents an overview of different methods used in secure  heterogeneous wireless systems design.  Large scale infrastructure and ad hoc  networks test and simulation are one of the major parts of the course.  The  course also includes practical exercises and lab experiments.  The course is  the last part of the graduate certificate program "Wireless Secure Network  Design" which includes also three other courses - PEP 601, 602 and 603.  Students successfully finished all four courses will receive a graduate  certificate in wireless secure network design.                 Spring Semester.

Motion of charged particles in electromagnetic field; Boltzmann equation for plasma; properties of magnetoplasmas; and fundamentals of magnetohydrodynamics. Applications to include: mirror geometry, high frequency confinement, plasma confinement, and heating by means of magnetic fields; motion of plasmas along and across magnetic field lines; magnetohydrodynamic stability theory; plasma oscillations; microinstabilities waves in magnetoplasma; dispersion relations; Fokker-Planck equation for plasmas; plasma conductivity; runaway electrons; relaxation times; radiation phenomena in magnetoplasmas; stability theories; finite Larmor radius stabilization; minimum-B stability; and universal instabilities. Typical text: Schmidt, Physics of High Temperature Plasmas. Fall semester.

Motion of charged particles in electromagnetic field; Boltzmann equation for plasma; properties of magnetoplasmas; and fundamentals of magnetohydrodynamics. Applications to include: mirror geometry, high frequency confinement, plasma confinement, and heating by means of magnetic fields; motion of plasmas along and across magnetic field lines; magnetohydrodynamic stability theory; plasma oscillations; microinstabilities waves in magnetoplasma; dispersion relations; Fokker-Planck equation for plasmas; plasma conductivity; runaway electrons; relaxation times; radiation phenomena in magnetoplasmas; stability theories; finite Larmor radius stabilization; minimum-B stability; and universal instabilities. Typical text: Schmidt, Physics of High Temperature Plasmas. Spring semester.

A continuation of PEP 510 for those students desiring a more thorough knowledge of optical systems. Included would be the use of an OTDR, ellipsometry, vacuum deposition of thin films, and other instrumentation. Students are encouraged to pursue their individual interests using the available equipment.Spring or fall term by arrangement.

Operating principle, modeling, and fabrication of solid state devices for modern optical and electronic system implementation; recent developments in solid state devices and integrated circuits; devices covered include bipolar and MOS diodes and transistors, MESFET, MOSFET transistors, tunnel, IMPATT and BARITT diodes, transferred electron devices, light emitting diodes, semiconductor injection and quantum-well lasers, PIN, and avalanche photodetectors.

Theorems and postulates of quantum mechanics; operator relationships; solutions of the Schrödinger equation for model systems; variational and perturbation methods; pure spin states; Hartree-Fock self-consistent field theory; and applications to many-electron atoms and molecules. CH 520 is an alternative prerequisite.

Topics covered include components for and design of optical communication systems; propagation of optical signals in single mode and multimode optical fibers; optical sources and photodetectors; optical modulators and multiplexers; optical communication systems: coherent modulators, optical fiber amplifiers and repeaters, transcontinental and transoceanic optical telecommunication system design; optical fiber local area networks.

Definition of dynamical systems; phase space and equilibrium states and their classification; nonlinear oscillator with and without dissipation; Van der Pol generator; Poincare map; slow and fast motion; forced nonlinear oscillator: linear and nonlinear resonances; forced generators: synchronization; Poincaré indices and bifurcations; solitons; shock waves; weak turbulence; regular patterns in dissipative media; and chaos: fractal dimension, and Lyapunov exponents. Typical textbooks: H.D.I. Abarbanel, M.I. Rabinovich, and M.M. Sushchik, Introduction to Nonlinear Dynamics for Physicists; R.H. Abraham and C.D. Shaw, Dynamics: The Geometry of Behavior.

Lagrangian and Hamiltonian formulations of mechanics, rigid body motion, elasticity, mechanics of continuous media, small vibration theory, special relativity, canonical transformations, and perturbation theory. Typical text: Goldstein, Classical Mechanics.

Electrostatics, boundary value problems, Green’s function techniques, methods of image, inversion, and conformal mapping; multipole expansion. Magnetostatics, vector potential. Maxwell’s equations and conservation laws. Electromagnetic wave propagation in media. Crystal optics. Fall semester. Typical texts: Jackson, Classical Electrodynamics; Landau and Lifshitz, Electrodynamics in Continuous Media.

Interaction of electromagnetic waves with matter, dispersion, waveguides and resonant cavities, radiating systems, scattering and diffraction, covariant electromagnetic theory, motion of relativistic particles in electromagnetic fields, relativistic radiation theory, radiation damping, and self-fields. Spring semester. Typical texts: Jackson, Classical Electrodynamics and Landau and Lifshitz, The Classical Theory of Fields, Electrodynamics in Continuous Media.

Advanced laboratory work in modern physics arranged to suit your requirement.             Fall and spring semesters.Typical text: see PEP551.

This course is a continuation of PEP 554. Topics include: principles of quantum dynamics, time-dependent perturbation theory, scattering theory, the density matrix, quantization of the electromagnetic field, interaction of photons with atoms and non-relativistic particles, identical particles, and second quantization for many-body systems. Typical text: Quantum Mechanics by E. Merzbacher.

Dirac notation; Transformation theory; Second quantization; Particle creation and annihilation operators; Schrodinger, Heisenberg and
Interaction Pictures; Linear response; S-matrix; Density matrix; Superoperators and non-Markovian kinetic equations; Schwinger Action Principle and variational calculus; Quantum Hamilton equations; Field equations with particle sources, potential and phonon sources; Retarded Green's functions; Localized state in continuumand chemisorption; Dyson equation; T-matrix; Impurity scattering; Self-consistent Born approximation;Density-of-states;Greens function matching; Ensemble averages and statistical thermodynamics, Bose and Fermi distributions, Bose condensation; Thermodynamic Green's functions; Lehmann spectral representation; periodicity/antipeiodicity in imaginary time and Matsubara Fourier series/frequencies; Anallytic continuation to real time; Multiparticle Green's functions; Electromagnetic current-current correlation  response; Exact variational relations for multiparticle Green's functions; Cumulants; Linked cluster theorem; Random phase approximation; Perturbation  theory for green's functions, self-energy and vertex functions by variational differential formulation; Shielded potential perturbation theory;Imaginary time contour ordering Langreth algebra and the GKB Ansatz.      Typical texts: Kadanoff and Baym, Quantum Statistical
Mechanics, and Inkson, Many-Body Theory of Solids.

The course features the application of modern field theory methods and especially Feynman diagrams to fermion and boson system and critical phenomena.  The initial text will be Quantum field theory and statistical physic by Abrikosov, Gorkov and Dzyalizhinski.  Also discussed will be an introduction to scaling and the renormalization group (Wilson papers, texts of Pfeuty and Toulose, Ma and Reichl).  Other topics will include broken symmetry non-phonon mechanisms in fermion superconductivity, field theory generalizations of the independent particle or Hartree-Fock model for non-homogeneous Fermion systems, Feynman path integrals and Wiener measure in statistical physics, exact properties of the Ising model,Feynman path integrals and Wiener measure in statistical physics, onset of ferromagnetism and spin-fluctuations.

The course features the application of modern field theory methods and         especially Feynman diagrams to fermion and boson system and critical           phenomena.  The initial text will be Quantum field theory and statistical     
physic by Abrikosov, Gorkov and Dzyalizhinski.  Also discussed will be an      
introduction to scaling and the renormalization group (Wilson papers, texts of Pfeuty and Toulose, Ma and Reichl).  Other topics will include broken symmetry non-phonon mechanisms in fermion superconductivity, field theory generalizations of the independent particle or Hartree-Fock model for non-homogeneous Fermion systems, Feynman path integrals and Wiener measure in statistical physics, exact properties of the Ising model,Feynman path integrals and Wiener measure in statistical physics, onset of ferromagnetism and spin-fluctuations.

Crystal symmetry. Space-group-theory analysis of normal modes of lattice vibration, phonon dispersion relations, and Raman and infrared activity. Crystal field splitting of ion energy level and transition selection rules. Bloch theorem and calculation of electronic energy bands through tight binding and pseudopotential methods for metals and semiconductors and Fermi surfaces. Transport theory, electrical conduction, thermal properties, cyclotron resonance, de Haas van Alfen, and Hall effects. Dia-, para-, and ferro-magnetism and magnon spinwaves. Fall semester. Typical texts: Callaway, Quantum Theory of Solid State; Ashcroft and Mermin, Solid State Physics; and Kittel, Quantum Theory of Solids.

Crystal symmetry. Space-group-theory analysis of normal modes of lattice vibration, phonon dispersion relations, and Raman and infrared activity. Crystal field splitting of ion energy level and transition selection rules. Bloch theorem and calculation of electronic energy bands through tight binding and pseudopotential methods for metals and semiconductors and Fermi surfaces. Transport theory, electrical conduction, thermal properties, cyclotron resonance, de Haas van Alfen, and Hall effects. Dia-, para-, and ferro-magnetism and magnon spinwaves. Spring semester. Typical texts: Callaway, Quantum Theory of Solid State; Ashcroft and Mermin, Solid State Physics; and Kittel, Quantum Theory of Solids. 

Advanced transport theory, classical statistical mechanics, fluctuation theory, quantum statistical mechanics, ideal Bose and Fermi gases, imperfect gases, phase transitions, superfluids, Ising model critical phenomena, and renormalization group. Typical text: Huang, Statistical Mechanics.

This course explains the physics behind modern optical communication systems at high data rates. The first half of this course covers information theory and light propagation over fiber optic waveguide channels; semiconductor laser sources and detectors; high speed digital optic links; and dense wavelength division multiplexing methods and devices. The second half of this course covers quantum optical information theory; coherent systems and quantum correlations; optical solition-based communication; squeezed light and noise limitations; de-phasing and de-coherence; teleportation and secure communication system protocols; and cryptography and chaotic optics.

Abbe diffraction theory of image formation, spatial filtering, coherence lengths, and areas. Holograms; speckle photography; impulse response function; CTF, OTF, and MTF of lens system; and coherent and incoherent optical signal processing. Spring semester. Typical text: Goodman, Introduction to Fourier Optics.

This course explores the quantum mechanical aspects of the theory of electromagnetic radiation and its interaction with matter. Topics covered include Einstein’s theory of emission and absorption, Planck’s law, quantum theory of light-matter interaction, classical fluctuation theory, quantized radiation field, photon quantum statistics, squeezing, and nonlinear interactions. Offered in alternate years. Typical text: Loudon, Quantum Theory of Light.

Physical design of wireless communication systems, emphasizing present and  next generation architectures.  Impact of non-linear components on  performance; noise sources and effects; interference; optimization of receiver  and transmitter architectures; individual components (LNAs, power amplifiers,  mixers, filters, VCOs, phase-locked loops, frequency synthesizers, etc.);  digital signal processing for adaptable architectures; analog-digital  converters; new component technologies (SiGe, MEMS, etc.); specifications of  component performance; reconfigurability and the role of digital signal  processing in future generation architectures; direct conversion; RF  packaging; minimization of power dissipation in receivers.

Introduction to the principles and design techniques of very large scale integrated circuits (VLSI). Topics include: MOS transistor characteristics, DC analysis, resistance, capacitance models, transient analysis, propagation delay, power dissipation, CMOS logic design, transistor sizing, layout methodologies, clocking schemes, case studies. Students will use VLSI CAD tools for layout, and simulation.

This course is intended to introduce the concept of electronic energy band engineering for device applications. Topics to be covered are electronic energy bands, optical properties, electrical transport properties of multiple quantum wells, superlattices, quantum wires, and quantum dots; mesoscopic systems, applications of such structures in various solid state devices, such as high electron mobility, resonant tunneling diodes, and other negative differential conductance devices, double-heterojunction injection lasers, superlattice-based infrared detectors, electron-wave devices (wave guides, couplers, switching devices), and other novel concepts and ideas made possible by nano-fabrication technology. Fall semester. Typical text: M. Jaros, Physics and Applications of Semiconductor Microstructures; G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures.

This seminar is focused on nanostructure-scale electron systems that are so small that their dynamic and statistical properties can only be properly described by quantum mechanics. This includes many submicron semiconductor devices based on heterostructures, quantum wells, superlattices, etc., and it interfaces solid state physics with surface physics and optics. Outstanding visiting scientists make presentations, as well as some faculty members and doctoral research students discussing their thesis work and related journal articles. Participation in these seminars is regarded as an important part of the research education of a physicist working in condensed matter physics and/or surface physics and optics.

This seminar is focused on current topics in physics and their applications in various areas. The format of the seminar is similar to PEP 700, but the scope of the seminar covers a broader range of topics, including interdisciplinary areas and applications such as low-temperature plasma science and technology, atmospheric and environmental science and technology, and other topics. One credit per semester. PEP 700 and PEP 701 may be taken for up to three credits.

Group theory for physicists with applications to solid state and molecular physics. Relation between group theory and quantum (or classical) mechanics, between classes and observables, and between representations and states. Point groups: full rotation group, crystallographic point groups, and spin-associated double groups. Crystal field theory with and without spin, selection rules and character tables, and use of product representation. Form of macroscopic crystal tensors molecular vibrational states and spectra. Translational properties of crystals. Energy band structure. Formal classification of space groups with examples. Time reversal and Onsager relations with examples. Lattice vibrations and phonons. Localized valence orbitals in chemistry. Hartree-Fock many-electron wave-functions. Phase transitions. Representative texts: M. Lax Symmetry, Principles in Solid State and Molecular Physics; Heine Group, Theory in Quantum Mechanics.

Theoretical foundations of spectroscopic methods and their application to the study of atomic and molecular structure and properties; theory of absorption and emission of radiation; line spectra of complex atoms; group theory; rotational, vibrational, and electronic spectroscopy of diatomic and polyatomic molecules; infrared, Raman, and uv-vis spectroscopy; laser spectroscopy and applications; photoelectron spectroscopy; and multi-photon processes.

Progress in the technology of nanostructure growth; space and time scales; quantum confined systems; quantum wells, coupled wells, and superlattices; quantum wires and quantum dots; electronic states; magnetic field effects; electron-phonon interaction; and quantum transport in nanostructures: Kubo formalism and Butikker-Landau formalism; spectroscopy of quantum dots; Coulomb blockade, coupled dots, and artificial molecules; weal localization; universal conductance fluctuations; phase-breaking time; theory of open quantum systems: fluctuation-dissipation theorem; and applications to quantum transport in nanostructures.

This course is open to students who have taken PEP 754 or its equivalent. It concerns itself with modern field theory; such topics as Yang-Mills fields, the renormalization group, and functional integration. It will concern itself with applications to both elementary particles and condensed matter physics; i.e. the theory of critical exponents. Typical text: C. Quigg, Gauge Theories of Strong, Weak, and Electromagnetic Interactions.

This course is open to students who have taken PEP 754 or its equivalent. It is an introduction to the theory of elementary particles. It stresses symmetries of both the strong and weak interactions. It presents a detailed study of SU(3) and the quark model, as well as the Cabbibo theory of the weak interactions. Typical text: F. Close, An Introduction to Quarks and Partons.

This course is an introduction to relativistic quantum mechanics and quantum field theory. Relativistic wave equations, including the Klein-Gordon equation and the Dirac equation. Commutation relation and canonical quantization of free fields. Spin and statistics of Bose and Fermi fields. Interacting quantum fields: interaction representation and S-matrix perturbation theory, Feynman diagrams, and renormalization theory with applications to quantum electrodynamics. Typical texts: Advanced Quantum Mechanics by J. J. Sakurai and Quantum Field Theory by F. Mandl and G. Shaw.

Second quantization of Bose and Fermi fields; interaction and Heisenberg  pictures; S-matrix theory; quantum electrodynamics; diagrammatic techniques.         Fall semester, by reqeust. Typical texts: Mandl, Introduction to Quantum Field Theory; Sakurai, Advanced  Quantum Mechanics.

Since its emergence over 75 years ago, quantum mechanics brings each generation new challenging investigations and discoveries of quantum phenomena. In this course we introduce the results of research on quantum properties of light and matter that afford the possibility of unprecedented control over dynamics of atoms and molecules.
The course Methods of Quantum Control is developed for students interested in understanding of the light-matter interactions and learning about advanced methods of control of ultrafast dynamics in atomic and molecular systems using femtosecond laser pulses that allow one to achieve a desired quantum yield.
Topics include: Photoexcitation of a molecule with a pulse of light.  Photodissociation. Energy-resolved quantities. Weak-field coherent control. Photodissociation from a Superposition State. One- vs. Three-Photon Interference.  Pump-dump control, Tannor-Rice scheme. Wave packet motion on a potential energy surface. Pump-dump excitation with many levels. Silberberg's model using the phase step. Applications for selective excitation. Strong-field control. Femtosecond pulses. Time-dependent problems. Two-level systems. Rotating-wave approximation. State-interaction representation. Field-interaction representation. Dressed-state analysis.  Rabi Oscillations. Strong-field control by pulse area, pi-pulses. Stimulated Raman Spectroscopy. Maxwell-Bloch equations. Control by femtosecond pulse amplitude modulation.  Strong-field control using chirped pulses. Characteristics of chirped laser pulses. Adiabatic dressed states. Adiabatic passage. Dark states, Stimulated Raman adiabatic passage. Non-impulsive Raman scattering. Chirped pulse adiabatic passage control. Optimal Control theory. Adaptive learning technique. Applications: selective excitation of vibrational modes in molecular gas CO2 and liquid methanol. Coherent control in equilibrated condensed phases. Density matrix representation. Liouville von Neumann equations with relaxation terms in the field-interaction representation. Dressed states in the density matrix representation in the  presence of dephasing.

Topics include any one of the following: magnetohydrodynamics, quantum mechanics, general relativity, many-body problem, nuclear physics, quantum field theory, low temperature physics, diffraction theory,and particle physics. Limit of six credits for the master’s degree.

One to six credits. Limit of six credits for the degree of Doctor of Philosophy.

A participating seminar on topics of current interest and importance in Physics and Engineering Physics.

For the degree of Master of Science. Five to ten credits with departmental approval.

For the degree of Master of Engineering. Five to ten credits with departmental approval.

Original experimental or theoretical research undertaken under the guidance of the faculty of the department which may serve as the basis for the dissertation required for the degree of Doctor of Philosophy. Hours and credits to be arranged. This course is open to students who have passed the doctoral qualifying examination; a student who has already taken the required doctoral courses may register for this in the term in which s/he intends to take the qualifying examination.

Description of simple physical models which account for electrical conductivity and thermal properties of solids. Basic crystal lattice structures, X-ray diffraction and dispersion curves for phonons and electrons in reciprocal space. Energy bands, Fermi surfaces, metals, insulators, semiconductors, superconductivity and ferromagnetism. Fall semester. Typical text: Kittel, Introduction to Solid State Physics.

Lectures, demonstrations and laboratory experiments, selected from among the following topics, depending on student interest: vacuum technology; thin-film preparation; scanning electron microscopy; infrared spectroscopy, ellipsometry: electron spectroscopies-Auger,
photoelectron, LEED; ion spectroscopies SIMS, IBS, field emission; surface
properties-area, roughness, and surface tension.

This course is an introduction to quantum mechanics for students in physics and engineering. Techniques discussed include solutions of the Schrodinger equation in one and three dimensions, and operator and matrix methods. Applications include infinite and finite quantum wells, barrier penetration and scattering in one dimension, the harmonic oscillator, angular momentum, central force problems, including the hydrogen atom, and spin. Fall semester. Typical text: Quantum Physics by Gasiorowicz

This course is meant as the first in a two-course sequence on non-relativistic quantum mechanics for physics graduate students, with an emphasis on applications to atomic, molecular, and solid state physics. Undergraduate students may take this course as a Technical Elective. Topics covered include: review of Schrödinger wave mechanics; operator algebra, theory of representation, and matrix mechanics; symmetries in quantum mechanics; spin and formal theory of angular momentum, including addition of angular momentum; and approximation methods for stationary problems, including time independent perturbation theory, WKB approximation, and variational methods. Typical text: Quantum Mechanics by E. Merzbacher.

Most processes in petroleum and chemical industries utilize catalytic reactions. Moreover, many emerging technologies in the energy sector and in green chemistry for sustainability rely on catalysis. This course provides the fundamentals of synthesis, characterization and testing of catalytic materials with an emphasis on metal and metal oxide nanoparticles, the most widely used class of catalysts. Methodologies for development of molecular-level reaction mechanisms, material structure-activity relations and kinetic models are described. The course is essential for anyone planning a career in the chemical industry. It is recommended for all professionals working with nanoparticles and also with diverse applications where the solid-gas interface is important.

Principles of environmental reactions with emphasis on aquatic chemistry; reaction and phase equilibria; acid-base and carbonate systems; oxidation-reduction; colloids; organic contaminants classes, sources, and fates; groundwater chemistry; and atmospheric chemistry.

A study of the chemical and physical operation involved in treatment of potable water, industrial process water, and wastewater effluent; topics include chemical precipitation, coagulation, flocculation, sedimentation, filtration, disinfection, ion exchange, oxidation, adsorption, flotation, and membrane processes. A physical-chemical treatment plant design project is an integral part of the course. The approach of unit operations and unit processes is stressed.

Deals with aspects of the technology of processing procedures involved in the fabrication of microelectronic devices and microelectromechanical systems (MEMS). Students will become familiar with various fabrication techniques used for discrete devices as well as large-scale integrated thin-film circuits. Students will also learn that MEMS are sensors and actuators that are designed using different areas of engineering disciplines and they are constructed using a microlithographically-based manufacturing process in conjunction with both semiconductor and micromachining microfabrication technologies

This course deals with the fundamentals and applications of nanoscience and nanotechnology. Size-dependent phenomena, ways and means of designing and synthesizing nanostructures, and cutting-edging applications will be presented in an integrated and interdisciplinary manner.

The goal of this course is to learn the basic concepts commonly utilized in the processing of advanced materials with specific compositions and microstructures. Solid state diffusion mechanisms are described with emphasis on the role of point defects, the mobility of diffusing atoms, and their interactions. Macroscopic diffusion phenomena are analyzed by formulating partial differential equations and presenting their solutions. The relationships between processing and microstructure are developed on the basis of the rate of nucleation and growth processes that occur during condensation, solidification, and precipitation. Diffusionless phase transformations observed in certain metallic and ceramic materials are discussed.

This course covers the environmental and health aspects of nanotechnology. It presents an overview of nanotechnology along with characterization and properties of nanomaterials. The course material covers the biotoxicity and ecotoxicity of nanomaterials. A sizable part of the course is devoted to discussions about the application of nanotechnology for environmental remediation along with discussions about fate and transport of nanomaterials. Special emphasis is given to risk assessment and risk management of nanomaterials, ethical and legal aspects of nanotechnology, and nano-industry and nano-entrepreneurship.

This course provides an overview and industrial perspectives regarding downstream separation in drug substance development and manufacturing. Basic principles and practical applications of unit operations most commonly employed in the pharmaceutical industry will be discussed, including extraction, absorption, membrane, distillation, crystallization, filtration, and drying. Examples will be discussed to illustrate the intrinsic relationship between process development, equipment selection, and scale-up success.

Upon completion of this course, students will be able to demonstrate an understanding of the major classes of engineering materials, their principal properties, and design requirements that serve as both the basis for materials selection, as well as for the ongoing development of new materials. This course is substantially differentiated from introductory materials courses by its very specific focus on materials whose use puts them in direct contact with physiological systems. Thus, the course begins with brief sections on inflammatory response, thrombosis, infection, and device failure. It then concentrates on developing the fundamental materials science and engineering concepts underlying the structure-property relationships in both synthetic and natural polymers, metals and alloys, and ceramics relevant to in vivo medical device technology.

This course follows the introductory course and covers advanced topics in the design, modeling, and fabrication of micro and nano electromechanical systems. The materials will be broad and multidisciplinary including: review of micro and nano electromechanical systems, dimensional analysis and scaling, thermal, transport, fluids, microelectronics, feedback control, noise, and electromagnetism at the micro and nanoscales; the modeling of a variety of new MEMS/NEMS devices; and alternative approaches to the continuum mechanics theory. The goal will be achieved through a combination of lectures, case studies, individual homework assignments, and design projects carried out in teams.

The course covers recent advances in macromolecular science, including polyelectrolytes and water-soluble polymers, synthetic and biological macromolecules at surfaces, self-assembly of synthetic and biological macromolecules, and polymers for biomedical applications.

Topics at the interface of polymer chemistry and biomedical sciences, focusing on areas where polymers have made a particularly strong contribution, such as in biomedical sciences and pharmaceuticals. Synthesis and properties of biopolymers; biomaterials; nanotechnology smart polymers; functional applications in biotechnology, tissue and cell engineering; and biosensors and drug delivery.

This course will provide a comprehensive introduction to the rapidly developing field of nanomedicine and discuss the application of nanoscience and nanotechnology in medicine such as, in diagnosis, imaging and therapy, surgery, and drug delivery.

 As an introduction to micro/nano fluidics, course topics include basic fluid mechanical theories, experimental techniques, fabrication techniques and applications of micro/nano fluidics. The theory part will cover continuum fluid mechanics at micro/nano scales, molecular approaches, capillary effects, electrokinetic flows, acoustofluidics and optofluidics. The experimental part will cover micro/nano rheology and particle image velocimetry. The fabrication part will cover materials and machining techniques for micro/nano fluidic devices. The application part will cover micro/nano fluidic devices for flow control, life sciences and chemistry. As a term project, individual students are required to perform a case study for their own selected topic in micro/nano fluidics, to conduct a literature survey/summary and to propose/analyze their own new design idea of a micro/nano fluidic devices by utilizing the knowledge obtained throughout the course. 

A survey course covering the chemical, biological and material science aspects of interfacial phenomena. Applications to adhesion, biomembranes, colloidal stability, detergency, lubrication, coatings, fibers and powders - where surface properties play an important role.

This course describes the application of nano- and micro-fabrication methods to build tools for exploring the mysteries of biological systems. It is a graduate-level course that will cover the basics of biology and the principles and practice of nano- and microfabrication techniques, with a focus on applications in biomedical and biological research.

This advanced course covers the mechanism and biological role of signal transduction in mammalian cells. Topics included are extracellular regulatory signals, intracellular signal transduction pathways, role of tissue context in the function of cellular regulation, and examples of biological processes controlled by specific cellular signal transduction pathways.

This course is intended to introduce the concept of electronic energy band engineering for device applications. Topics to be covered are electronic energy bands, optical properties, electrical transport properties of multiple quantum wells, superlattices, quantum wires, and quantum dots; mesoscopic systems, applications of such structures in various solid state devices, such as high electron mobility, resonant tunneling diodes, and other negative differential conductance devices, double-heterojunction injection lasers, superlattice-based infrared detectors, electron-wave devices (wave guides, couplers, switching devices), and other novel concepts and ideas made possible by nano-fabrication technology. Fall semester. Typical text: M. Jaros, Physics and Applications of Semiconductor Microstructures; G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures.

This course deals with the principles of light interactions with biological and biomedical-relevant systems. The enabling aspects of nanotechnology for advanced biosensing, medical diagnosis, and therapeutic treatment will be discussed.

 Lectures by department faculty, guest speakers and doctoral students on recent research.

This graduate course will introduce the applications of multiscale theory and computational techniques in the fields of materials and mechanics. Students will obtain fundamental knowledge on homogenization and heterogeneous materials, and be exposed to various sequential and concurrent multiscale techniques. The first half of the course will be focused on the homogenization theory and its applications in heterogeneous materials. In the second half multiscale computational techniques will be addressed through multiscale finite element methods and atomistic/continuum computing. Students are expected to develop their own course projects based on their research interests and the relevant topics learned from the course.

Progress in the technology of nanostructure growth; space and time scales; quantum confined systems; quantum wells, coupled wells, and superlattices; quantum wires and quantum dots; electronic states; magnetic field effects; electron-phonon interaction; and quantum transport in nanostructures: Kubo formalism and Butikker-Landau formalism; spectroscopy of quantum dots; Coulomb blockade, coupled dots, and artificial molecules; weal localization; universal conductance fluctuations; phase-breaking time; theory of open quantum systems: fluctuation-dissipation theorem; and applications to quantum transport in nanostructures.

A participating seminar on topics of current interest and importance in Nanotechnology.