Physics

University Exemplary Department

Beate Schmittmann, Department Chair

Professors: M. Blecher; L.N. Chang¹; J.R. Heflin; G.J.M. Indebetouw; L.E. Piilonen; M. Pitt; R.S. Raghavan; B. Schmittmann; J. Slawny; U.C. Taeuber; B. Vogelaar; R.K.P. Zia

Associate Professors: N. Arav; J.J. Heremans; D. Minic; T. Mizutani; M.J.F. Pleimling; A.L. Ritter; J.H. Simonetti; V. Soghomonian; T. Takeuchi

Assistant Professors: G.A. Khodaparast; R.V. Kulkarni; J. Link; K. Park; H.D. Robinson; E. Sharpe

Adjunct Professors: Z. Chang; Y. Liang; z. Toroczkai

Affiliated Faculty: L. Asryan²; S. Eubank³; L. Guido²; A. Onufriev⁴; M. Paul⁵

Career adviser: A.L. Ritter (231-5369)

¹Dean, College of Science
² Regular appointment with Materials Science and Engineering
³ Regular appointment with Virginia Bioinformatics Institute
⁴ Regular appointment with Computer science
⁵ Regular appointment with Mechanical Engineering

E-mail: gradphys@vt.edu

Web: www.phys.vt.edu

The graduate physics program course work and research lead to the M.S. (thesis optional) and/or to the Ph.D. Research specialization is available in experimental and/or theoretical aspects of astronomical, biophysics, condensed-matter, elementary-particle, mathematical, medium-energy, optical, and statistical physics, and in physics teaching. The department also has programs which are directed toward improvement in physics teaching and include the testing of model physics courses, development of multimedia techniques for learning enhancement, and creation of computer simulations.

The department offers an Applied and Industrial Physics Option which leads to a degree of M.S. in physics and prepares a student to apply broad physics principles to technological problems of interest to industry. The program combines courses with applied and technological relevance with a research project that is carried out either in an industrial laboratory or on campus. Additional emphasis is placed on enhancing the communication skills of the student and on preparing the student to work with a team. The requirements for the degree include a research project leading to a written report and the successful completion of a program of study. Courses in physics, chemistry, materials science engineering, and business may be combined to satisfy the course requirements for the degree. The program can be completed in four semesters.

Special Facilities

Experimental laboratories within the Department of Physics include facilities employing Raman scattering, far-infrared to near-ultraviolet spectroscopy, conventional and superconducting magnets, thin-film electron scattering, susceptometry, sol-gel studies, laser holography and spatial filtering, and pulsed laser nonlinear optical measurements such as harmonic generation and degenerate four-wave mixing, and clean-room. Other techniques and materials are available via collaborative programs with the Departments of Chemistry, Chemical Engineering, and Materials Science.

Facilities are maintained in the Department of Physics to prepare experiments and analyze data collected by the radio astronomy and medium/high energy nuclear/particle groups which are currently working at national and international research centers, including FermiLab, Brookhaven, TJNAF (Newport News), ORNL (Oak Ridge Laboratory), Gran Sasso (Italy), KEK (Japan), Los Alamos (New Mexico) Kimballton underground science and engineering facility, and National Radio Astronomy Observatory (including the VLA and VLBA). Also housed in the department is the university's Institute for Particle Physics and Astrophysics. Many theorists are members of the University Center for Stochastic Processes in Science and Engineering which, comprised of faculty from the departments of Chemistry, Electrical Engineering, Geosciences, Materials Engineering and Mathematics, promotes interdisciplinary research in a wide variety of topics, ranging from quantum field theory and phase transitions to wave propagation in random media.

The Department of Physics has numerous microcomputers, minicomputers, and workstations in research laboratories, and a computer room for physics graduate students and majors, as well as acccess to a 25-node Beowulf cluster for exclusive use of department personnel, a 220 processor Beowulf cluster, which is shared with select departments in the College of Engineering, and the university's System X with 2300 processors which was recently (November 2004) ranked seventh in the world and first among university facilities worldwide. Access to supercomputers is also available through national and international networks.

Admissions Requirements

Applicants for admission to the graduate program are required to take the GRE General and Physics tests. International students are also required to take the TOEFL. Ph.D. candidates are required to pass an oral preliminary examination (administered by the student's Ph.D. advisery committee). The student is expected to present the intended dissertation research and to demonstrate a firm grasp of the content of the core courses (PHYS 5354, 5405-6, 5455-6, 5705, 5714). Passing will officially admit the student to candidacy for the Ph.D. To complete the degree, the student's committee must accept a dissertation describing the student's research findings.

Special Degree Requirements

The experiences gained by physics graduate students in carrying out the duties attached to graduate project assistantships, graduate research assistantships, graduate teaching assistantships, and graduate assistantships are viewed by the department as essential ingredients in the training required for the physics master's and doctoral degrees. It is therefore required that on-campus master's students hold an assistantship (of one or more of the indicated types) for at least two semesters and on-campus doctoral students for at least eight semesters (past the bachelor's degree) during their programs of study.

A brochure detailing the graduate physics program may be requested from the Graduate Programs Coordinator by calling (540) 231-8728.

Graduate Courses (Phys)

5354: CLASSICAL MECHANICS

Theory of classical Lagrangian and Hamiltonian mechanics of particles and rigid bodies, including canonical transformations and Hamilton-Jacobi theory. Consent required. (3H,3C).

5405-5406: CLASSICAL ELECTROMAGNETISM

Classical theory of electromagnetism and its applications. 5405: Electrostatics and magnetostatics; Maxwell's equations and electromagnetic waves; wave guides, apertures, and antennae. 5406: Special relativity and Lagrangian and Hamiltonian formulations; Lienard-Wiechert potentials, motion, radiation, and energy loss be charged particles; self-fields and radiative damping; magnetic monopoles and field theories. Consent required. Co: 5714. (3H,3C).

5455-5456: QUANTUM MECHANICS

General principles of nonrelativistic quantum mechanics from the point of view of advanced dynamics, with applications to problems of atomic and nuclear structure. Consent required. (3H,3C).

5504: NUCLEAR & PARTICLE PHYSICS

Properties of nuclei, two-nucleon systems, nuclear force, nuclear models, nuclear reactions, alpha and beta decay, and fission. Relativistic kinematics, invariance principles, quantum numbers, strange particles, weak interactions, formation and production reactions, and symmetries. Consent required. (3H,3C).

5555-5556: SOLID-STATE PHYSICS

Solidity, crystal structure, k-space, quantum mechanics of covalent bonding, phonon excitations, thermal energy, the nearly-free-electron approximation, Bloch electrons, E(k) energy bands in semiconductors and metals, density of states, optical properties of solids, donors and acceptors in semiconductors, excitons, plasmons, polaritons, electrical properties, magnetic materials, the percolation model and phase transitions, metal-insulator transitions, and amorphous solids. Consent required. (3H,3C).

5604: FOURIER OPTICS AND HOLOGRAPHY

Principles of scalar diffraction theory, Fresnel, and Fraunhofer diffraction, coherent optical imaging systems, optical filtering and optical data processing, and holography. Pre: 4614. (3H,3C).

5614: INTRODUCTION TO QUANTUM ELECTRONICS

Theory of laser oscillation, optical resonators, interaction of radiation and atomic systems, giant pulsed lasers, laser systems, wave propagation in nonlinear media, modulation of optical radiation, noise in optical detection and generation, and interaction of light and sound. Pre: 4614. (3H,3C).

5705-5706: STATISTICAL MECHANICS

Theory of classical and quantum statistical mechanics. Derivation of thermodynamics. 5705: ensembles, fluctuations and ideal gas systems. 5706: modern developments and advanced topics. Pre: 5456. (3H,3C).

5714: METHODS OF THEORETICAL PHYSICS

Selected topics in mathematical physics. Review of analytic function theory. Matrices, spectral theory of operators in Hilbert Space with applications to quantum mechanics. Solution of partial differential equations of mathematical physics, boundary-value problems, and special functions. Distribution theory and Green's functions. Consent required. (3H,3C).

5794: COMPUTATIONAL PHYSICS

Survey of computational methods in physics. Applications of Fourier analysis, curve fitting, solving differential equations, solving integral equations, Monte Carlo simulations, symbolic mathematics, and graphic simulations in mechanics, electromagnetism, nuclear physics, atomic physics, molecular physics, and condensed matter physics. Pre: 4455. (3H,3C).

5894: FINAL EXAMINATION

Pass/Fail only. (3H,3C).

5904: PROJECT & REPORT

Variable credit course.

5944: SEMINAR

Pass/Fail only. (1H,1C).

5974: INDEPENDENT STUDY

Pass/Fail only. Variable credit course.

5984: SPECIAL STUDY

Variable credit course.

5994: RESEARCH & THESIS

Variable credit course.

6354: ADVANCED CLASSICAL DYNAMICS

Conservative systems: Geometry of phase space, integrable

systems, perturbation theory and introduction to Kolmogorov-Arnold-Moser (KAM) theory. Dissipative systems: local bifurcation theory and introduction to chaos. Pre: 5354. (3H,3C).

6455-6456: ADVANCED QUANTUM THEORY

Classical field theory; Noether's theorem and symmetries; second quantization and many-body formalism; free quantum Klein-Gordon, Dirac, and Maxwell fields; and interacting fields, S-matrix and covariant perturbation theory. Feynman diagrams; quantum electrodynamics; renormalization; path-integral formulation; non-Abelian gauge theories; and elements of electro-weak theory. Pre: 5354, 5406, 5456. (3H,3C).

6504: THEORETICAL NUCLEAR PHYSICS

Basic concepts and methods of theoretical nuclear physics for energies up to 1 GeV. General nuclear properties, nuclear force, conserved quantitites, symmetries, and nuclear models. Pre: 5406, 5456. (3H,3C).

6555-6556: ADVANCED SOLID-STATE PHYSICS

Applications of field-theory techniques to many-body aspects of solid-state physics. 6555: Green functions, Feynman diagrams, lattice Hamiltonian, neutron scattering, electron gas, Fermi-liquid theory, and linear-response theory. 6556: Electron-phonon interaction in metals and semiconductors, polarons, optical properties, excitons, superconductivity, and excitations in magnetic materials. Pre: 5456, 5555. (3H,3C).

6655,6656: ADVANCED ASTROPHYSICS

Concepts and methods of astrophysics. 6655: Stellar structure and evolution; radiative and convective energy transfer; white dwarfs, neutron stars and black holes; stellar nucleosynthesis. 6656: Interstellar medium; star formation; galaxies and large scale structure; active galactic nuclei and quasars. Pre: 5406, 5456. (3H,3C).

6675-6676: GENERAL RELATIVITY & COSOMOLOGY

6675: Differential geometry; equivalence principle; general theory of relativity; classical tests; post-Newtonian approximation; special solutions. 6676: Black holes; observational basis of cosmology; relativistic model universes; nucleosynthesis; cosmoic background radiation; dark matter; inflation. Pre: 5354, 5406. (3H,3C).

6714: SELECTED TOPICS IN THEORETICAL PHYSICS

Topics of current interest in theoretical physics as announced in Timetable. May be repeated for credit with permission. Consent required. (3H,3C).

6725-6726: ELEMENTARY PARTICLE PHYSICS

Symmetry principles, quark model, scattering-theory and particle-theory processes, weak interactions, quantum chromodynamics, spontaneous symmetry breaking, and unified field theories. Consent required. Co: 6455, 6456. (3H,3C).

6725-6726: ELEMENTARY PARTICLE PHYSICS

6755-6756 (MATH 6755- 6756): MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS

Advanced course in mathematical physics which encompasses the frontiers of research in quantum theory. Content varies from year to year and includes scattering theory, spectral and perturbation theory, and many-body quantum dynamics. This course frequently taken concurrent with thesis research. The course alternates with Math 6745-6746 and may be taken a second time with instructor's consent. Pre: 5456, MATH 6256. (3H,3C).

7994: RESEARCH & DISSERTATION

Variable credit course.

Advanced Undergraduate Courses (PHYS)

The following 4000-level courses have been approved for graduate credit:

4315-4316: MODERN EXPERIMENTAL PHYSICS

Representative apparatus, techniques, and phenomena of contemporary research. Includes electrical measurements, computers, thermometry, vacuum deposition, machine shop, nuclear spectra, experimentation related to major developments of modern physics. Pre: 3314. (6L,2C).

4404: MAGNETICS

Macroscopic magnetic phenomena and utilization of magnetic fields and materials. Criteria for materials selection and device design of electromagnets, transformers, relays, permanent magnets, motors, shielding, recording, and other energy and information storage techniques. Pre: 2306, MATH 2214. (3H,3C).

4455-4456: INTRODUCTION TO QUANTUM MECHANICS

Experimental bases; postulates; conservation theorems and symmetry; one-dimensional and two-dimensional problems; angular momentum and problems in three dimensions; matrix mechanics and spin; applications to atomic and molecular physics; perturbation theory; scattering. Pre: 3356, 3406. (3H,3C).

4504: INTRODUCTION TO NUCLEAR AND PARTICLE PHYSICS

Structure and properties of atomic nuclei and elementary particles, theoretical interpretations based on elementary quantum mechanics. Symmetries; various nuclear models; interactions at small distances; classification of elementary particles. Consent required. Co: 4456. (3H,3C).

4554: INTRODUCTION TO SOLID STATE PHYSICS

Basic concepts of solid state physics including crystal structure, lattice vibrations, electron states, energy bands, semiconductors, metals. Consent required. Co: 4456. (3H,3C).

4714: INTRODUCTION TO BIOPHYSICS

Selected topics from the general area of biomechanics, bioelectricity, radiation biophysics, molecular biophysics, and thermodynamics and transport in biological systems. Emphasis on the physical aspects of biological phenomena and biophysical measurement techniques and instrumentation. Pre: 2206 or 2306. (3H,3C).