All Graduate courses are 3 credits except where noted.
See the registrar's web site for the current
course offerings. Select "Course Schedules" from the menu.
PEP 500
Physics Review *
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.
Prerequisites:
introductory mechanics and electromagnetism courses which employ
calculus and vector analysis. Typical text: Halliday, Resnick and
Walker, Fundamentals of Physics. No credit for Physics or Engineering
Physics majors.
PEP 501
Fundamentals of Atomic Physics *
Electrolysis, Brownian motion; charge and mass of electrons and ions;
Zeeman effect; photoelectric effect; reflection, refraction,
diffraction, absorption and scattering of X-rays; Compton effect;
diffraction of electrons; uncertainty principle; electron optics; Bohr
theory of atom; atomic spectra and electron distribution;
radioactivity; disintegration of nuclei; nuclear processes; nuclear
energy and fission. No credit for Physics majors. Typical text:
Weidner and lls, Elementary Modern Physics.
PEP 503
Introduction to Solid State Physics
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.
Prerequisites:PEP 242, PEP 542 or equivalent. Cross-listed with EE 503 and
MT 503.
PEP 506
Introduction to Astronomy and Cosmology
Theories of the universe, general relativity, Big Bang cosmology and
the inflationary universe; elementary particle theory and
nucleosynthesis in the early universe. Observational cosmology; galaxy
formation and galactic structure; stellar evolution and formation of
the elements. White dwarfs, neutron stars and black holes, planetary
systems and the existence of life in the universe.
PEP 507
Introduction to Microelectronics and Photonics
An overview of microelectronics and photonics science and
Technology. It provides the student who wishes to specialize in their
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. Cross-listed with EE 507 and MT 507.
PEP 509
Intermediate Waves and Optics
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.
Prerequisites:PEP 209,
PEP 542 or equivalent. Cross-listed with EE 509.
PEP 510
Modern Optics Lab
The course is designed to familiarize students with a range of optical
instruments and their applications. Included will be measurement of
aberrations in optical systems, thin-film properties, Fourier
transform imaging systems, nonlinear optics and laser beam
dynamics. Fall semester.
Prerequisites:PEP 509 or consent of the instructor. This course
may sometimes be offered in the spring term if space is available.
PEP 512
Introduction to Nuclear Physics and Nuclear Reactors
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; nuclear reactors.
PEP 515-516
Photonics I, II
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
.
Prerequisites:
either PEP 209 or PEP 509. Cross-listed with EE 515-516 and MT
515-516.
PEP 520
Computational Physics
Both numerical techniques and the elements of continuum mechanics are
covered. Numerical methods for integrating Newton's laws, the heat
equation, Poisson's equation and the fluid flow are
discussed. Topics also covered: discrete Fourier transform technique,
stability theory and the diagonalization of matrices, and Monte Carlo
methods. Course project offers students the opportunity to learn
specialized techniques in areas of interest. Spring semester. Typical
text: Potter, Computational Physics.
PEP 524
Introduction to Surface Science
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.
PEP 525
Techniques of Surface Analysis
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 spectroscopy; Auger,
photoelectron, LEED; ion spectroscopies; SIMS, IBS, field emission;
surface properties-area, roughness and surface tension. Alternate
years. (See MT 525.)
PEP 527
Mathematical Methods for Physics and Engineering I
Vector and tensor fields and transformation properties under rotation
of axes, vector identities, gradient, divergence, curl, tensor
contraction, geometric interpretation of symmetric and antisymmetric
tensors, divergence-Gauss' theorem for tensor fields and Stokes'
theorem, Helmholtz' theorem and scalar and vector
potentials. Applications to inertia tensor, particle mechanics,
transport, electromagnetism (Maxwell's equations), viscous fluid
dynamics (the Navier-Stokes equation, Euler equation, the Bernoulli
equation). Introduction to the Dirac delta-function and Green’s
function technique for solving linear inhomogeneous
equations. Orthogonal curvilinear coordinates (general, also
spherical, cylindrical). N-dimensional complex space and unitarity,
matrix notation, inverse of matrix, Pauli spin matrices, relativity,
Lorentz transformation. Tensors and pseudotensors in
n-dimensions. Similarity transformations and diagonalization of
Hermitian and unitary matrices, eigenvectors and eigenvalues of
Hermitian and unitary matrices, Schmidt
orthogonalization. Applications to coupled oscillators, rigid body
dynamics, etc. Linear independence and completeness. Functions of a
complex variable, analyticity, Cauchy’s theorem, Residue theorem,
Taylor and Laurent expansions, classification of singularities,
analytic continuation, Liouville’s theorem, multiple-valued
functions, contour integration, Jordan’s lemma, applications,
asymptotics. Fall Semester.
Prerequisites:
4 semesters undergraduate math courses.
PEP 528
Mathematical Methods for Physics and Engineering II
Introduction to Hilbert space, function vectors, completeness in the
strong and weak senses, expansion in complete orthonormal sets of
functions, Schmidt orthgonalization. The Weierstrass theorem and
completeness of eigenfunctions of a Hermitian operator. Dirac/dyadic
notation. Legendre polynomials, spherical harmonics, Fourier series
and integral, Laplace transform, multipole expansion. Ordinary
differential equations, ordinary point and iteration series solution
and power series method, Hermite equation, Schrödinger equation for
harmonic oscillator. Regular singular point and the method of
Frobenius, including the second solution, Bessel
equation. Sturm-Liouville systems and weighted complete orthonormal
sets of eigenfunctions, Green’s function determination and solution
of the inhomogeneous problem. Partial differential equations, heat
equation, wave equation, Poisson equation, solution by transform
techniques and Green’s function solution of inhomogeneous initial
value and boundary value problems. Linear integral equations,
iteration series solution, convergence, Kernels separable in several
parts, Hilbert-Schmidt theory, Fredholm theory, Volterra
equation. Spring semester.
Prerequisites:PEP 527.
PEP 538
Introduction to Mechanics
Particle motion in one dimension. Simple harmonic oscillators. Motion
in two and three dimensions, kinematics, work and energy, conservative
forces, central forces, scattering. Systems of particles, linear and
angular momentum theorems, collisions, linear spring systems, normal
modes. Lagrange’s equations, applications to simple
systems. Introduction to moment of inertia tensor and to Hamilton’s
equations.
PEP 540
Physical Electronics
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; Townsend discharge. Typical
text: Beck and Ahmed, An Introduction to Physical
Electronics.
PEP 541
Physics of Gas Discharges
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; discharge and
low-temperature plasma generation. Typical texts: J.R. Roth,
Industrial Plasma Engineering: Principles, Vol.1 , and
Y.P. Raizer, Gas Discharge Physics . Cross-listed with EE
541.
PEP 542
Electromagnetism
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, 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.
PEP 544
Introduction to Plasma Physics and Controlled Fusion
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,
thermonuclear reactions; the Lawson condition; magnetic confinement
fusion; laser fusion. Fall semester.
Prerequisites: PEP 542.
Typical text: F. Chen, Plasma Physics.
PEP 545
Plasma Processing
Basic plasma physics; some atomic processes; plasma diagnostics.
Plasma production; D.C. glow discharges, 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; ion implantation. Sputtering
systems; ion sources; electron sources; ion beam handling. Typical
texts: Chapman, Glow Discharge Processes ; Brodie, Muray,
The Physics of Micro-fabrication . Fall semester.
PEP 550
Fluid Mechanics
Description of principle flow phenomena: pipe and channel flows,
laminar flow, transition, turbulence; flow past an object-boundary
layer, wake, separation, vortices, drag; convection in horizontal
layers-conduction, convection, 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; transitions to
turbulence. Typical text: Tritton, Physical Fluid
Dynamics.
PEP 551
Advanced Physics Laboratory I
An experimental presentation of the evidence for atomic and nuclear
theories; typical experiments are: excitation potentials; electronic
charge; specific charge of the electron; the Balmer series; Zeeman
splitting; spectroscopic isotope shifts; the photovoltaic effect; the
Hall effect; gamma ray spectrometry; beta ray spectrometry; neutron
activation of nuclides; statistics of counting processes; optical and
X-ray diffraction; the Langmuir probe; nuclear magnetic
resonance. Fall semester, repeated second semester. By
arrangement. Laboratory fee $5. Typical texts: Young, Statistical
Treatment of Experimental Data; Melissinos, Experiments in
Modern Physics.
Prerequisites:PEP 222.
PEP 553
Introduction to Quantum Mechanics
This course is an introduction to Schrodinger wave mechanics for
students in physics and engineering with an emphasis on engineering
applications. This is a required course for all physics undergraduates
as well as students in the Microelectronics and Photonics
M.S./M.E. degree program and other professional M.S./M.E. degree
programs. Topics discussed include one dimensional infinite and finite
quantum wells, barrier penetration and scattering in one dimension,
linear harmonic oscillator, Kronig-Penney model, angular momentum,
central force problems including the hydrogen atom, and spin. Typical
texts: Introductory Quantum Mechanics by R. L. Liboff and
Quantum Mechanics Fundamentals and Applications to Technology
by J. Singh.
Prerequisites:
Ma 221 and PEP 242 or
equivalent.
PEP 554
Quantum Mechanics I
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; approximation
methods for stationary problems including time independent
perturbation theory, WKB approximation and variational
methods. Typical text: Quantum Mechanics by E. Merzbacher.
Prerequisites:PEP 553, PEP 538, and PEP 527 or equivalent.
PEP 555
Statistical Physics and Kinetic Theory
Kinetic theory: ideal gases, distribution functions, Maxwell-Boltzmann
distribution, Boltzmann equation, H-theorem and entropy, simple
transport theory. Thermodynamics: review of first and second laws,
thermodynamic potentials, Legendre transformation, 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, blackbody
radiation. Typical text: Reif, Statistical and Thermal
Physics.
PEP 561
Solid State Electronics for Engineering I
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. Cross-listed with EE 561 and MT 561.
PEP 562
Solid State Electronics for Engineering II
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; integrated
devices. Cross-listed with EE 562 and MT 562.
PEP 570
Guided-Wave Optics
Review of electromagnetic theory; derivation of Fresnels’
equations; guided-wave propagation by metallic and dielectric
waveguides including step-index optical fibers, graded-index fibers;
optical transmission systems; nonlinear effects in optical fibers,
solitons and fiber-optic gyroscope.
PEP 575
Fundamentals of Atmospheric Radiation and Climate
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.
Prerequisites:
undergraduate calculus, ordinary differential equations (Ma 221 or
equivalent) and basic modern physics (PEP 201 or PEP 242 or equivalent).
PEP 577
Laser Theory and Design
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; high power chemical, dye lasers, TEA
lasers, gas dynamic lasers. Design and operation of
semiconductor DFB, quantum well, quantum dot; argon ion,
helium neon, carbon dioxide, Nd:YAG, diode-pumped fiber
lasers. Parametric frequency conversion. Typical Textbook:
Svelto, Principles of Lasers, Fourth Edition
PEP 578
Laser Applications and Advanced Optics
Integrated optics, nonlinear optics, Pockels effect, Kerr effect,
harmonic generation, parametric devices, phase conjugate mirrors,
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, optical
communication. Scattering of light, Rayleigh, Mie, Brillouin, Raman
and Doppler shift scattering. Spring semester.
PEP 580
Electronic Materials and Devices
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.
PEP 585
Physical Design of Wireless Systems
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. Cross-listed with
EE/MT 585.
PEP 595
Reliability and Failure of Solid State Devices
This course
deals with the electrical, chemical, environmental and mechanical
driving forces that compromise the integrity and lead to the failure
of electronic materials and devices. Both chip and packaging level
failures will be modeled physically and quantified statistically in
terms of standard reliability mathematics. On the packaging level,
thermal stresses, solder creep, fatigue and fracture, contact
relaxation, corrosion and environmental degradation will be
treated.
Prerequisites:PEP 507. Cross-listed with MT/EE 595.
PEP 596
Microfabrication Techniques
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.
Prerequisites:PEP 507. Cross-listed with MT/EE 596.
NANO 600
Nanoscale Science and Technology
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.
PEP 601
Fundamentals of Data Transmitting
This course is the first part of the graduate certificate program
“Wireless Secure Network Design,” which also includes 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 to protect existing
wireless systems and how to 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.
Prerequisites:PEP 507 and PEP 585 or permission of instructor.
PEP 602
Secure and Robust Communications
This course presents an overview of areas of first responders',
military activities and use of different heterogeneous wireless
systems during large scale crises, such as natural disasters, acts of
terrorism and during homeland defense, financial and military
operations. The course includes an analysis of different wireless
network architectures from a security point of view. The course is the
second part of the graduate certificate program “Wireless Secure
Network Design” which also includes three other courses: PEP 601, 603 and 604.
Prerequisites:PEP 601.
PEP 603
Physical and Logical Security
This course presents an overview of different methods of
authentication and authorization in secure wireless networks. The
course focuses 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 also includes
three other courses: PEP 601, 602 and 604.
Prerequisites:PEP 601, PEP 602.
PEP 604
Secure Telecom Wireless System Design
This 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 major parts of the course. The
course also includes practical exercises and lab experiments. The
course is the last part of the graduate certificate “Wireless
Secure Network Design” which includes also three other courses: PEP
601, 602 and 603. Students who have successfully finished all four
courses will receive a graduate certificate in wireless secure network
design.
Prerequisites:PEP 601, PEP 602, PEP 603.
PEP 607/608
Plasma Physics III *
Motion of charged particles in electromagnetic field; Boltzmann
equation for plasma; properties of magnetoplasmas; 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; universal instabilities. Typical text: Schmidt, Physics
of High Temperature Plasmas. Fall and spring semester.
Prerequisites: PEP 642, PEP 643 and PEP 555.
PEP 610
Advanced Modern Optics Lab *
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.
Prerequisites:PEP 510 or the consent of the instructor.
PEP 619
Solid State Devices
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.
Prerequisites:
EE 503 or equivalent. Cross-listed with EE 619.
PEP 621
Quantum Chemistry
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; applications to many-electron atoms and
molecules.
Prerequisites:
Ch 520 or PEP 554 or equivalent.
PEP 626
Optical Communication Systems
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. Cross-listed with EE 626, MT 626 and NIS 626.
PEP 630
Nonlinear Dynamics
Definition of dynamical systems; phase space, equilibrium states and
their classification; nonlinear oscillator without and with
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; chaos: fractal dimension, 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.
Prerequisites:PEP 528 or permission of the instructor.
PEP 642
Mechanics
Lagrangian and Hamiltonian formulations of mechanics, rigid body
motion, elasticity, mechanics of continuous media, small vibration
theory, special relativity, canonical transformations, perturbation
theory. Typical text: Classical Mechanics.
PEP 643
Electricity and Magnetism I
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; Laundau and Lifshitz,
Electrodynamics in Continuous Media.
Prerequisites:PEP 528 and PEP 542.
PEP 644
Electricity and Magnetism II
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 Laundau and Lifshitz,
The Classical Theory of Fields, Electrodynamics in Continuous
Media.
Prerequisites:PEP 643.
PEP 653
Quantum Mechanics II
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.
Prerequisites:PEP 554 and PEP 542 or
equivalent.
PEP 661/662
Solid State Physics III
Crystal symmetry. Space-group-theory analysis of normal modes of
lattice vibration, phonon dispersion relations; 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, Fermi surfaces. Transport theory, electrical
conduction, thermal properties, cyclotron resonance, de Haas van Alfen
and Hall effects. Dia-, para- and ferro-magnetism, magnon
spinwaves. Fall and spring semester. Typical texts: Callaway,
Quantum Theory of Solid State; Ashcroft and Mermin, Solid
State Physics; Kittel, Quantum Theory of
Solids. Recommended: PEP 503 and PEP 553-554.
PEP 667
Statistical Mechanics
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, renormalization group. Typical text: Huang,
Statistical Mechanics.
PEP 678
Physics
of Optical Communication Systems
The physics behind modern optical communication systems and high data
rate communication systems; information theory and light propagation
in optical fiber wave guide channels; semiconductor laser sources and
detectors; digital optical communication systems; quantum optical
information theory; coherence and quantum correlations; optical
solution-based communication; squeezed light and noise limitations;
coherent optical communication systems; de-phasing and de-coherence;
teleportation, cryptography and fractal optics.
Prerequisites:PEP 542, PEP 554, and PEP 503.
PEP 679
Fourier 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; coherent and
incoherent optical signal processing. Spring semester. Typical text:
Goodman, Introduction to Fourier Optics.
PEP 680
Quantum 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, nonlinear interactions. Offered in alternate
years. Typical text: Loudon, Quantum Theory of Light.
Prerequisites:PEP 542 or
equivalent, PEP 554 and PEP
509.
PEP 690
Introduction to VLSI Design
This course introduces students 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. Selected class projects may be
sent for fabrication. Cross-listed with CpE 690 and MT 690.
PEP 691
Physics and Applications of Semiconductor Nanostructures
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.
Prerequisites:
Basic knowledge in quantum mechanics and solid state physics (at the
levels of PEP 553, PEP
503).
PEP 700
Quantum Electron Physics and Technology Seminar
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. One-half credit per
semester. PEP 700 and PEP
701 may be taken for up to three credits. Pass/Fail.
PEP 701
Topics in Physics and Engineering Physics *
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-half credit per semester. PEP 700
and PEP 701 may be taken for up to three
credits. Pass/Fail.
PEP 704
Group Theory for Physicists in Solid State and Molecular Physics
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, between
representations and states. Point groups: full rotation group,
crystallographic point groups, spin-associated double groups. Crystal
field theory with and without spin; selection rules and character
tables, 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.
Prerequisites:
Course equivalent to PEP 554 in quantum mechanics and associated
mathematics of operators and Hilbert spaces.
PEP 722
Molecular Spectroscopy
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,
uv-vis spectroscopy; laser spectroscopy and applications;
photoelectron spectroscopy; multi-photon processes.
Prerequisites:
Ch 520 or PEP 554 and PEP 509 or
equivalent.
PEP 739
Theory of Relativity *
Geometrical foundations of space-time theories, geometrical objects,
affine geometry, metric geometry; structure of space-time theories,
symmetry, conservation laws; Newtonian mechanics; special relativity;
foundations of general relativity, Mach’s principle, principle of
equivalence, principle of general covariance, Einstein’s equations;
solution of Einstein’s equations; experimental tests of general
relativity; conservation laws in general relativity, gravitational
radiation, motion of singularities; cosmology. Fall semester. Course
may be taken for up to six credits.
PEP 740
The Physics of Nanostructures
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; quantum transport
in nanostructures: Kubo formalism, 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; applications to quantum transport in
nanostructures.
Prerequisites:PEP 553 - 554 and
PEP 661 - 662.
PEP 750
Quantum Field Theory *
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.
PEP 751
Elementary Particles *
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.
PEP 754
Advanced Quantum Mechanics
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.
Prerequisites:PEP 653.
PEP 757
Quantum Field Theory Methods in Statistical and Many-Body Physics
Dirac notation; Transformation theory; Second quantization; Particle
creation and annihilation operators; Schrödinger, 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 continuum and
chemisorption; Dyson equation; T-matrix; impurity scattering;
self-consistent Born approximation; density-of-states; Green's
function matching; ensemble averages and statistical thermodynamics,
Bose and Fermi distributions, Bose condensation; thermodynamic
Green’s functions; Lehmann spectral representation;
periodicity/antiperiodicity in imaginary time and Matsubara Fourier
series/frequencies; analytic continuation to real time; multiparticle
Green’s functions and equations of motion with particle-particle
interactions; Hartree and Hartree-Fock approximations; collisional
lifetime effects; sum-of-ladder-diagrams integral equation;
nonequilibrium 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,
W. A. Benjamin and Horing, Advanced Quantum Mechanics for
Interacting and Mesoscopic Systems. Fall semester.
Prerequisites:PEP 242 or equivalent and a
good mathematical background in linear algebra and multivariate
calculus; PEP 554 will be a corequisite unless
waived by instructor.
PEP 758
Coupled Quantum Field Theory Methods in Condensed Matter Physics *
Dielectric response of solid-state plasmas; random phase
approximation; semiclassical and hydrodynamic models; elasmons;
shielding; electron-hole plasmon Landau damping; exchange and
correlation energy; atom-surface van der Waals attraction; charged
particle energy loss; electrodynamic response functions; dyadic
Green’s functions; dynamic, nonlocal conductivity and dielectric
tensors; polaritons of compound nanostructures; coupling of light with
3D, 2D and superlattice collective modes; electron(e) - hole (h) -
phonon (p) Hamiltonian for solids with e-e, h-h, e-p, h-p and e-h
interactions explained; Coupled electron-hole-phonon Green’s
functions of all orders and derivation of the fully-interacting
equations of motion for 1-electron and 1-hole Green’s functions and
for 2-electron and 2-hole Green’s functions, as well as the
electron-hole Green’s function with analysis of exciton states and
electron-hole scattering matrix; electron-phonon coupling effects on
electron propagation and polarons; phonons of periodic lattice in the
harmonic approximation, eigenvector expansion of phonon Green’s
functions for monatomic and ionic diatomic lattices, acoustic and
optical phonons, polarizability of a diatomic lattice; Phonon
Green’s function with coupling to dynamic nonlocal electron
screening, umklapp, coupled ion-electron oscillations, Bohm-Staver
phonon dispersion relation; generalized shield potential
approximation; electron and hole interaction operators; superfluid
field operators and the Gross-Pitaevski equations; Bogoliubov
approximation, superfluid Green’s functions and elementary
excitations; superconductivity-BCS Theory, anomalous Green’s
functions and Gorkov equations, gap, derivation of Ginzburg-Landau
equations. Typical text: Horing, Advanced Quantum Mechanics for
Interacting and Mesoscopic Systems; Mahan, Many-Particle
Physics, Plenum Press and recommended readings. Spring semester.
Prerequisites:PEP 757.
PEP 800
Special Topics in Physics
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,
particle physics. Limit of six credits for the master’s degree.
PEP 960
Research in Physics
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.
