**Mark Williams, PhD**

Professor and Chair

110 Dana Research Center

617.373.2902

617.373.2943 (fax)

gradphysics@northeastern.edu

Physics PhD and Master of Science students at Northeastern University have the opportunity to explore, discover, and apply the fundamental principles that run the universe. The program specializes in several subfields that reflect the forefront research activities of the department. These specializations include biological physics, condensed matter physics, elementary particle physics, nanomedicine, nanophysics, and network science.

The Department of Physics also offers a Graduate Certificate in Nanomedicine. The certificate is designed for students, engineers, and physicians to develop competency and practical skills in the application of nanotechnology to problems in medicine. This program is appropriate for those working in or seeking careers in biotechnology, pharmaceutical, biomedical, or clinical fields.

## 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).

**Prerequisite(s): **PHYS 2303 with a minimum grade of D- or graduate program admission

**Attribute(s): ** NUpath Natural/Designed World

**PHYS 5113. Particle Physics. (4 Hours)**

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

**Prerequisite(s): **(PHYS 2303 with a minimum grade of D- ; PHYS 4115 with a minimum grade of D- ) or graduate program admission

**Attribute(s): ** NUpath Natural/Designed World

**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.

**Prerequisite(s): **(PHYS 2303 with a minimum grade of D- ; PHYS 3602 with a minimum grade of D- ; (PHYS 2305 with a minimum grade of D- or PHYS 4305 with a minimum grade of D- )) or graduate program admission

**Attribute(s): ** NUpath Natural/Designed World

**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.

**Prerequisite(s): **PHYS 2303 with a minimum grade of D- or graduate program admission

**Attribute(s): ** NUpath Natural/Designed World

**PHYS 5117. Advanced Astrophysics Topics. (4 Hours)**

Seeks to provide an understanding of our universe through the connection between cosmology and particle physics. Covers basic concepts of the modern universe, stellar structure and evolution, and dark matter theory while introducing recent astrophysical observations and experiments.

**Prerequisite(s): **(PHYS 2303 with a minimum grade of D- ; (PHYS 2305 with a minimum grade of D- or PHYS 4305 with a minimum grade of D- )) or graduate program admission

**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.

**Prerequisite(s): **(PHYS 2303 with a minimum grade of D- ; (PHYS 2305 with a minimum grade of D- or PHYS 4305 with a minimum grade of D- )) or graduate program admission

**PHYS 5125. Advanced Quantum Mechanics. (4 Hours)**

Introduces time-independent and time-dependent perturbation theory. Covers hydrogen fine structure, Zeeman effect, helium splitting, variational principle, adiabatic approximation, scattering theory, second quantization, and modern topics such as theory of quantum entanglement, quantum computing, and quantum biology.

**Prerequisite(s): **PHYS 4115 with a minimum grade of D- or graduate program admission

**PHYS 5126. Contagion on Networks. (4 Hours)**

Investigates how scientists have uncovered remarkable regularities in the spread of contagions on social networks. Focuses on how to model contagions and study them using empirical data based on primary readings. From memes associated with fake news to pathogens such as Ebola, numerous spreading processes can be modeled as contagions on social networks. However, seemingly trivial modifications to the classical models of contagion can dramatically alter their physics. For example, discontinuous phase transitions can occur due to complex contagions, hysteresis loops can emerge when individuals modify their behavior, and double phase transitions can appear in the presence of asymmetric percolation.

**Prerequisite(s): **PHYS 2303 with a minimum grade of D- or graduate program admission

**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.

**Prerequisite(s): **PHYS 2303 with a minimum grade of D- or graduate program admission

**Attribute(s): ** NUpath Natural/Designed World

**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.

**Prerequisite(s): **PHYS 2303 with a minimum grade of D- or graduate program admission

**Attribute(s): ** NUpath Analyzing/Using Data, NUpath Capstone Experience, NUpath Natural/Designed World, NUpath Writing Intensive

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

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

**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 7220. Methods for Teaching in the Introductory Physics Laboratory 1. (0 Hours)**

Introduces first-year physics graduate students to the role of teaching assistant (TA) in the laboratory. Designed to prepare TAs for the experiments they are required to teach undergraduate students. Focuses on improving their teaching and grading effectiveness.

**PHYS 7230. Methods for Teaching Introductory Physics Laboratory 2. (0 Hours)**

Continues PHYS 7220, offered to first-year graduate physics teaching assistants. Designed to prepare TAs for the experiments they teach to undergraduate students. Offers students an opportunity to improve their teaching and grading effectiveness.

**Prerequisite(s): **PHYS 7220 with a minimum grade of S

**PHYS 7240. Evidence-Based Physics Teaching. (0 Hours)**

Offers students an opportunity to obtain a hands-on knowledge and experience of the active learning strategies used in the physics classroom. Intended for students interested in pursuing a career involving physics education, including teaching, secondary or university level, and tenure-track positions, many of which include teaching responsibilities.

**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.

**Prerequisite(s): **PHYS 7315 with a minimum grade of C-

**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 7322. Nonequilibrium Physics. (4 Hours)**

Covers selected topics in nonequilibrium statistical mechanics and nonlinear physics to be selected by the instructor, with emphasis on classical theories of solids, fluids, and other more complex phases of matter. Topics may include Brownian motion, including Langevin and Fokker-Planck equations; linear response theory and transport phenomena; nonequilibrium phase transitions, including nucleation and phase-ordering kinetics; elasticity theory and fluid mechanics; and nonlinear dynamics and pattern formation.

**Prerequisite(s): **PHYS 7305 with a minimum grade of C

**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 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.

**Prerequisite(s): **PHYS 5116 (may be taken concurrently) with a minimum grade of C

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

Focuses 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. This is an interdisciplinary course.

**Prerequisite(s): **PHYS 5116 with a minimum grade of C ; PHYS 7331 with a minimum grade of C

**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.

**Prerequisite(s): **PHYS 5116 with a minimum grade of C- ; PHYS 7331 with a minimum grade of C-

**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.

**Prerequisite(s): **PHYS 5116 with a minimum grade of D- or PHYS 5116 with a minimum grade of C- (Graduate)

**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.

**Prerequisite(s): **PHYS 7324 with a minimum grade of C-

**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.

**Prerequisite(s): **PHYS 7731 with a minimum grade of C- ; PHYS 7321 with a minimum grade of C-

**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 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 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 Term 1. (0 Hours)**

Offers experimental and theoretical work for PhD candidates. Requires written thesis and final oral exam.

**Prerequisite(s): **PHYS 9000 with a minimum grade of S

**PHYS 9991. Dissertation Term 2. (0 Hours)**

Offers dissertation supervision by members of the department.

**Prerequisite(s): **PHYS 9990 with a minimum grade of S

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

Offers experimental and theoretical work for PhD candidates. Requires written thesis and final oral exam.

**Prerequisite(s): **PHYS 9991 with a minimum grade of S or Dissertation Check with a score of REQ