# Physics

**Paul M. Champion, PhD**

Professor and Chair

110 Dana Research Center

617.373.2902

617.373.2943 (fax)

__gradphysics@northeastern.edu__

**Mark Williams, PhD**

Professor and Director of Graduate Studies, ma.williams@northeastern.edu

**Nancy Wong**

Program Coordinator

n.wong@northeastern.edu

617.373.4240

The Northeastern Department of Physics performs advanced research in condensed matter, fundamental particles and fields, biophysics, and complexity. Students are expected to have demonstrated a graduate-level understanding of basic physics concepts upon completion of the MS degree. The program for the PhD degree consists of the required course work, a qualifying examination, a preliminary research seminar, the completion of a dissertation based upon original research performed by the student, and a dissertation defense upon completion of the dissertation. Based on these measures, students are expected to obtain a graduate-level understanding of basic physics concepts and demonstrate the ability to formulate a research plan, communicate orally a research plan, and conduct and present independent research.

## Physics Courses

**PHYS 5111. Astrophysics and Cosmology. 4 Hours.**

Introduces current ideas in astrophysics and cosmology, with emphasis on recent advances in this field. Topics include tools of the astronomer (telescopes, spectroscopy, and methods of distance measurement); the solar system; stellar properties (stellar spectra, stellar energy sources including gravitational or nuclear); Hertzsprung-Russell diagram; evolution of stars (birth, life, and ultimate collapse); our Milky Way galaxy; and extragalactic objects (galaxies, clusters of galaxies, radio galaxies, and quasars); cosmology (Olber’s paradox, recession of galaxies, big bang theory, cosmic background radiation, formation of galaxies, and the future of the universe).

**PHYS 5113. Introduction to Particle and Nuclear Physics. 4 Hours.**

Introduces the physics of atomic nuclei and elementary particles. Topics include classification of nuclei, strong and weak nuclear forces, mesons and nucleons, quarks and gluons, and unified theories of elementary particle interactions.

**PHYS 5114. Physics of Advanced Materials. 4 Hours.**

Explores the physical properties of materials and how such properties are essential for developing advanced applications. Models the fundamental properties of semiconductors, superconductors, and magnetic materials by elementary theories. Introduces the ideas motivating the need for a quantum theory of solids and uses these theories to explain the electronic, optical, and magnetic properties of advanced materials, with a direct relevance to their applications in nanoscale electronic devices, solar cells, laser diodes, quantum computers, etc.

**PHYS 5115. Quantum Mechanics. 4 Hours.**

Focuses on observations of macroscopic and microscopic bodies. Covers the uncertainty principle and wave-particle duality; probability amplitudes; Schrödinger wave theory and one-dimensional problems, Schrödinger equation in three dimensions; and angular momentum and the hydrogen atom.

**PHYS 5116. Complex Networks and Applications. 4 Hours.**

Introduces network science and the set of analytical, numerical, and modeling tools used to understand complex networks emerging in nature and technology. Focuses on the empirical study of real networks, with examples coming from biology (metabolic, protein interaction networks), computer science (World Wide Web, Internet), or social systems (e-mail, friendship networks). Shows the organizing principles that govern the emergence of networks and the set of tools necessary to characterize and model them. Covers elements of graph theory, statistical physics, biology, and social science as they pertain to the understanding of complex systems.

**PHYS 5117. Astrophysics. 4 Hours.**

Applies physics concepts to processes in celestial objects, particularly stars. Topics include tools of the astronomer (telescopes, spectroscopy, and methods of distance measurement); stellar properties; nuclear fusion reactions; hydrostatic equilibrium and stellar models; stellar evolution and the Hertzsprung-Russell diagram; morphology and dynamics of galaxies; and high-energy astrophysical phenomena. Not open to students who have completed PHYS 5111.

**PHYS 5118. General Relativity and Cosmology. 4 Hours.**

Introduces basic concepts in the general theory of relativity, including Riemannian geometry and Einstein’s field equations. These concepts are applied in studying the standard model of cosmology. Topics include thermodynamics in an expanding universe, dark matter and dark energy, and modern theories of cosmology. Not open to students who have completed PHYS 5111.

**PHYS 5260. Introduction to Nanoscience and Nanotechnology. 4 Hours.**

Focuses on reviewing the basic scientific concepts relevant to this field and also gives a broad overview of the current state-of-the-art in research and technology. Nanotechnology promises to transform twenty-first century technology by exploiting phenomena exhibited by nanoscaled materials. This technology is expected to have significant impact in diverse areas such as computers, electronics, health, etc. Successful technological advancement of this field requires that we have a fundamental understanding of the “science” of these materials. This course comprises a series of lectures on various topics: development of nanofabrication methods, advanced microscopy techniques, fabrication of novel nanomaterials, investigation of their fundamental properties and device applications. Provides a strong introduction for students interested in nanoscience and technology.

**PHYS 5318. Principles of Experimental Physics. 4 Hours.**

Designed to introduce students to the techniques of modern experimental physics. Topics include communication and information physics, signal processing and noise physics, applied relativity physics, detector techniques, semiconductor and superconductor physics, nanoscale microscopy and manipulation, and lasers and quantum optics.

**PHYS 5976. Directed Study. 1-4 Hours.**

Offers independent work under the direction of a member of the department on a chosen topic. Course content depends on instructor. May be repeated without limit.

**PHYS 5978. Independent Study. 1-4 Hours.**

Offers independent work under the direction of members of the department on a chosen topic. Course content depends on instructor. May be repeated without limit.

**PHYS 5984. Research. 1-4 Hours.**

Offers an opportunity to conduct research under faculty supervision. May be repeated without limit.

**PHYS 6960. Exam Preparation—Master’s. 0 Hours.**

Offers the student the opportunity to prepare for the master’s qualifying exam under faculty supervision.

**PHYS 6962. Elective. 1-4 Hours.**

Offers elective credit for courses taken at other academic institutions. May be repeated without limit.

**PHYS 6966. Practicum. 1-4 Hours.**

Provides eligible students with an opportunity for practical experience. May be repeated without limit.

**PHYS 7000. Qualifying Exam. 0 Hours.**

Provides eligible students with an opportunity to take the master’s qualifying exam.

**PHYS 7200. Methods of Advanced Problem Solving. 4 Hours.**

Designed to improve the ability of students to solve physics problems, which are of the same degree of difficulty as problems that often appear on the qualifying exam.

**PHYS 7210. Introduction to Research in Physics. 0 Hours.**

Offers a weekly seminar to introduce first- and second-year physics graduate students to research being done in the Physics department by advanced physics graduate students and faculty. May be repeated without limit.

**PHYS 7211. Introduction to Research 1. 1 Hour.**

Offered to first-year students during the fall semester, this one-unit course introduces new students to the various fields of current research undertaken in the department and elsewhere. Students attend seminars given by faculty and advanced graduate students engaged in cutting-edge research. Students are required to evaluate and provide constructive feedback to the seminar speakers. Students also present research articles, chosen through interactions with the faculty and with advanced graduate students. Students receive a letter grade.

**PHYS 7212. Introduction to Research 2. 1 Hour.**

Offered during the spring semester, this one-unit course introduces a first-year student to one of the fields of current research undertaken in the department. Students can select a particular thrust area and join the adviser’s group on a temporary basis. The purpose is to acquaint students with a group’s field of research, establish close ties with advanced graduate students, and gain some hands-on research experience. Students are expected to attend group meetings, participate in group projects, and in some cases complete a project of their own. Students receive a letter grade from the individual faculty member.

**PHYS 7221. Research 1. 1 Hour.**

Offered to second-year students in the fall semester, this one-unit seminar course helps students select a potential field of research for a PhD thesis topic. Students attend seminars given by faculty and advanced graduate students engaged in cutting-edge research. Students are required to evaluate and provide constructive feedback to the seminar speakers. Students also present research articles, chosen through interactions with faculty and with advanced graduate students. Students receive a satisfactory/unsatisfactory grade.

**PHYS 7222. Research 2. 1 Hour.**

Offered to second-year students in the spring semester, this is a one-unit seminar course. Students at this time are expected to have selected a PhD thesis topic and a thesis adviser. Students present seminars on material related to their proposed thesis topic. Faculty and advanced graduate students evaluate and provide constructive feedback to the seminar speakers. Students receive a satisfactory/unsatisfactory grade.

**PHYS 7231. Research Seminar 1. 1 Hour.**

Offered in the fall semester, this one-unit seminar course is taken by students with advanced standing who have passed the qualifying exam and are registered for PHYS 9990 or PHYS 9996. Students are required to give oral presentations on current research topics (typically their thesis research). The course is designed to promote interactions between faculty, advanced graduate students, and beginning graduate students and to broaden their intellectual outlook from one that is simply focused in a specific research area. Gives students the opportunity to learn to give lively and understandable presentations, a necessary skill in their professional development and an important component of their experiential education. Student and faculty listeners give feedback via an “evaluation” form. Students receive a satisfactory/unsatisfactory grade based on their participation.

**PHYS 7232. Research Seminar 2. 2 Hours.**

Offered in the spring semester, this one-unit seminar course is taken by students with advanced standing who have passed the qualifying exam and are registered for PHYS 9990 or PHYS 9996. Advanced graduate students attend oral presentations on current research topics and/or thesis topics proposed by the second-year students who have just started their PhD thesis research and also give oral presentations on current research topics (typically their thesis research). The course is designed to promote interactions between faculty, advanced graduate students, and second-year graduate students and to broaden their intellectual outlook from one that is simply focused in a specific research area. Student and faculty listeners give feedback via an “evaluation” form. Students receive a satisfactory/unsatisfactory grade based on their participation.

**PHYS 7301. Classical Mechanics/Math Methods. 4 Hours.**

Covers mathematical methods of physics and classical mechanics. Topics include differential equations, boundary value problems, functions of a complex variable, linear vector spaces, Green’s functions, Lagrangian and Hamiltonian mechanics, linear oscillators, and scattering. May include additional topics as time permits.

**PHYS 7302. Electromagnetic Theory. 4 Hours.**

Analyzes Maxwell’s equations in vacuum and special relativity. Topics include electric and magnetic fields due to known sources with boundary conditions, radiation fields, bremsstrahlung, synchrotron radiation, the energy-momentum tensor for the electromagnetic field, fields in material media, boundary conditions at the interface between two media, and scattering of radiation. May include additional topics as time permits.

**PHYS 7305. Statistical Physics. 4 Hours.**

Briefly reviews thermodynamics. Topics include the principles of statistical mechanics and statistical thermodynamics; density matrix; theory of ensembles; Fermi-Dirac and Bose-Einstein statistics, application to gases, liquids, and solids; theory of phase transitions; and thermodynamics of electric and magnetic systems, transport phenomena, random walks, and cooperative phenomena.

**PHYS 7315. Quantum Theory 1. 4 Hours.**

Explores the experimental basis of quantum theory, the Schr÷dinger equation, and probability interpretation of wave mechanics. Topics include the uncertainty principle, application to one-dimensional problems, the harmonic oscillator, orbital angular momentum, and the central force problem.

**PHYS 7316. Quantum Theory 2. 4 Hours.**

Continues PHYS 7315. Topics include quantum theory of scattering; Born approximation; phase-shift analysis; introduction to S-matrix theory; general formulation quantum mechanics in Hilbert space; spin; identical particles and symmetrization principle; time-independent and time-dependent perturbation theory; semiclassical theory of radiation and atomic spectra; addition of angular momentum; Wigner-Eckart theorem; quantum theory of radiation; and absorption, emission, and scattering of photons. Also introduces free particle Dirac equation.

**PHYS 7321. Computational Physics. 4 Hours.**

Covers basic numerical methods for differentiation, integration, and matrix operations used in linear algebra problems, discrete Fourier transforms, and standard and stochastic ordinary and partial differential equations. Specific applications of these methods may include classical chaos, computation of eigenstates of simple quantum systems, classical phase transitions, boundary value problems, pattern formation, and molecular dynamics and classical/quantum Monte Carlo methods to simulate the equilibrium and nonequilibrium properties of condensed phases.

**PHYS 7323. Elementary Particle Physics. 4 Hours.**

Presents a survey of the present state of elementary particle physics, suitable for all graduate students. Topics include overview of strong interactions and their connection to nuclear physics; nonrelativistic quark structure of strongly interacting particles (hadrons); color and the SU(3) Yang-Mills theory of strong interactions; coupling constant renormalization and asymptotic freedom; and the parton model of scattering. Covers weak interactions including phenomenology of the Fermi V-A theory; universality; and neutrino scattering. Studies the Glashow-Weinberg-Salam theory including unification of weak and electromagnetic interaction, neutral currents, the Higgs mechanism, quark masses and mixing, neutrino masses, and neutrino oscillation. Offers experimental support for the standard model. Also examines supersymmetry including the hierarchy problem and broken supersymmetry; role of supersymmetry in cosmology.

**PHYS 7324. Condensed Matter Physics. 4 Hours.**

Explores condensed matter physics. Topics include Drude and Sommerfield models of electrons in metals, crystal structure, one-electron states in crystal lattices, Bloch’s theorem, semiclassical theory of conduction, semiconductors and semiconducting devices, effects of electron-electron interactions, lattice vibrations and the classical and quantum theories of specific heat, optical properties of solids, investigation of crystal structure and excited states of crystals by x-ray and neutron scattering, simple transport theory based on the Boltzmann equation, and magnetic properties of solids.

**PHYS 7325. Quantum Field Theory 1. 4 Hours.**

Introduces the principles of quantum field theory. Topics include canonical quantization of scalar and spinor fields, functional integral methods, perturbation theory, regularization and renormalization, and symmetry breaking. Emphasizes applications to particle physics and condensed matter phenomena.

**PHYS 7326. Quantum Field Theory 2. 4 Hours.**

Presents the quantum theory of gauge fields and their interactions, as well as advanced topics in quantum field theory. Additional topics covered may include Lie groups and Yang-Mills theory, asymptotic freedom, perturbation theory anomalies, and applications to phase transitions.

**PHYS 7331. Network Science Data. 4 Hours.**

Offers an overview of data mining and analysis and techniques in network science. Introduces students to network data analysis. Presents algorithms for the characterization and measurement of networks (centrality based, decomposition, community analysis, etc.) and issues in sampling and statistical biases. Reviews visualization algorithms and specific software tools. Offers students an opportunity to learn about working with real-world network datasets.

**PHYS 7332. Network Science Data 2. 4 Hours.**

Offers an interdisciplinary course focusing on practical exercises in real network data. Offers students an opportunity to learn how to retrieve network data from the real world, analyze network structures and properties, study dynamical processes on top of the networks, and visualize networks. The main programming language used in this course is the current industry standard.

**PHYS 7335. Dynamical Processes in Complex Networks. 4 Hours.**

Immerses students in the modeling of dynamical processes (contagion, diffusion, routing, consensus formation, etc.) in complex networks. Includes guest lectures from local and national experts working in process modeling on networks. Dynamical processes in complex networks provide a rationale for understanding the emerging tipping points and nonlinear properties that often underpin the most interesting characteristics of socio-technical systems. The course reviews the recent progress in modeling dynamical processes that integrates the complex features and heterogeneities of real-world systems.

**PHYS 7337. Statistical Physics of Complex Networks. 4 Hours.**

Covers applications of statistical physics to network science. Focuses on maximum-entropy ensembles of networks and on applicability of network models to real networks. Main topics include microcanonical, canonical, and grand canonical ensembles of networks, exponential random graphs, latent variable network models, graphons, random geometric graphs and other geometric network models, and statistical inference methods using these models. Covers applications of maximum-entropy geometric network models to efficient navigation in real networks, link prediction, and community structure inference.

**PHYS 7731. Biological Physics 1. 4 Hours.**

Introduces the major classes of biological macromolecules and the physics underlying their structure, interaction, and biological function. Emphasis is on physical techniques for characterizing the structure and dynamics of proteins. Students are required to present a written and oral report on a focused research topic in molecular biophysics, based on a critical review of current scientific literature. Topics may include introduction to biomolecular structure, aqueous solution physics and hydrophobic interactions, chemical thermodynamics and reaction dynamics, spectroscopic techniques, molecular force measurements, and protein dynamics.

**PHYS 7733. Topics: Elementary Particle Physics and Cosmology. 4 Hours.**

Covers unified theories including evidence for supersymmetric SU(5) unification of couplings, and the grand unified scale and proton decay. Discusses particle physics and cosmology including a brief introduction to Einstein’s theory of general relativity, candidates for dark matter, inflation and the primordial fluctuations, and the problem of the cosmological constant. Examines developments leading to string theory including normal mode expansion; open and closed strings; deduction of D-26 for bosonic and D-10 for superstrings; scattering amplitudes in strings; heterotic string; compactifications on the torus, orbifolds, and Calabi-Yau manifolds; 4-D strings; and superstring phenomenology. Explores physics with extra dimensions including gravity at small distances, branes, and new approaches to the hierarch problem. May be repeated without limit.

**PHYS 7734. Topics: Condensed Matter Physics. 4 Hours.**

Covers selected advanced topics in the theory of solids to be chosen each time by the interested students and instructor. Topics may include theory of normal metals, Hartree-Fock and random phase approximations, optical and transport properties, solid-state plasmas, Raman spectroscopy, quasiparticles and collective excitations, quantum solids, and amorphous solids. May be repeated without limit.

**PHYS 7735. Nonlinear Dynamics. 4 Hours.**

Offers various topics, depending on the instructor. Covers introduction to the Hamilton-Jacobi equation; action-angle variables, and Liouville’s integrability theorem; nonlinear oscillators; chaos in Hamiltonian systems; and continuous media via the sine-Gordon equation, solitons/antisolitons, and nonsolitonic solutions, Lagrangian derivation of the field equations, and Klein-Gordon equation.

**PHYS 7736. Material Physics. 4 Hours.**

Studies the physical properties and applications of materials. Topics include crystalline and amorphous materials, metals, ceramics, glasses, polymers, materials characterization methods, such as x-ray diffraction, microscopies (optical, tunneling, and electron), susceptibilities (electric, magnetic), electronic transport in metals, semiconductors, superconductors, diffraction, defects, dislocations, specific heat, phonons, and thermal and electrical conductivities.

**PHYS 7741. Biological Physics 2. 4 Hours.**

Continues PHYS 7731. The first part of the course provides a foundation necessary to construct and implement models of neurons and networks of neurons. Topics include Hodgkin-Huxley form of the kinetical equations, single neuron models, dynamics of synapses, plasticity of synaptic strength, and neuromodulators. The second part covers nonlinear time series analysis and nonlinear dynamics in neuroscience. The goal is to provide a set of tools to analyze and model large multidimensional data sets encountered in many biological/neuroscience experiments. Topics include data testing of nonlinearity construction of linear and nonlinear models; spike sorting using independent component analysis and clustering algorithms; and analysis of continuous time series.

**PHYS 7962. Elective. 1-4 Hours.**

Offers elective credit for courses taken at other academic institutions. May be repeated without limit.

**PHYS 7976. Directed Study. 1-4 Hours.**

Offers independent work under the direction of a member of the department on a chosen topic. Course content depends on instructor. May be repeated without limit.

**PHYS 7978. Independent Study. 1-4 Hours.**

Offers independent work under the direction of members of the department on a chosen topic. Course content depends on instructor. May be repeated without limit.

**PHYS 7990. Thesis. 1-4 Hours.**

Undertakes a master’s thesis in a selected topic in experimental or theoretical physics. Written thesis required. May be repeated without limit.

**PHYS 7996. Thesis Continuation. 0 Hours.**

Offers continued thesis work conducted under the supervision of a departmental faculty.

**PHYS 8960. Exam Preparation—Doctoral. 0 Hours.**

Offers the student the opportunity to prepare for the PhD qualifying exam under faculty supervision.

**PHYS 8966. Practicum. 1-4 Hours.**

Provides eligible students with an opportunity for practical experience. May be repeated without limit.

**PHYS 8982. Readings. 1-4 Hours.**

Offers reading course, or theoretical or experimental work, under individual faculty supervision. May be repeated without limit.

**PHYS 8984. Research. 1-4 Hours.**

Offers an opportunity to conduct research under faculty supervision. May be repeated without limit.

**PHYS 8986. Research. 0 Hours.**

Offers an opportunity to conduct full-time research under faculty supervision. May be repeated without limit.

**PHYS 9000. PhD Candidacy Achieved. 0 Hours.**

Indicates successful completion of the doctoral comprehensive exam.

**PHYS 9984. Advanced Research. 1-8 Hours.**

Provides an opportunity for advanced students to work with an individual instructor on a topic related to current research. The instructor and student negotiate a written agreement as to what topic(s) are covered and what written or laboratory work forms the basis for the grade. Viewed as a lead-in to thesis research. May be repeated without limit.

**PHYS 9986. Research. 0 Hours.**

Offers an opportunity to conduct full-time research under faculty supervision. May be repeated without limit.

**PHYS 9990. Dissertation. 0 Hours.**

Offers experimental and theoretical work for PhD candidates. Requires written thesis and final oral exam. May be repeated once.

**PHYS 9996. Dissertation Continuation. 0 Hours.**

Offers experimental and theoretical work for PhD candidates. Requires written thesis and final oral exam. May be repeated without limit.