princeton applied physics phd

Princeton Quantum Initiative

Quantum Science and Engineering PhD Program

PQI launched a new PhD program in Quantum Science and Engineering, with the first cohort starting in fall 2024.

Find full information about the program structure and requirements  from Princeton Graduate School. The application for the program can be found through the Graduate School portal .

The PhD program in Quantum Science and Engineering provides graduate training in a new discipline at the intersection of quantum physics and information theory. Just as the 20th century witnessed a technological and scientific revolution ushered in by our newfound understanding of quantum mechanics, the 21st century now offers the promise of a new class of technologies and lines of scientific inquiry that take full advantage of the more fragile and intricate consequences of quantum mechanics: coherent superposition, projective measurement, and entanglement. This field has broad implications ranging from many-body physics and the creation of new forms of matter to our understanding of the emergence of the classical world and our basic understanding of space and time.  It enables fundamentally new technological applications, including new types of computers that can solve currently intractable problems, communication channels whose security is guaranteed by the laws of physics, and sensors that offer unprecedented sensitivity and spatial resolution.

The Princeton Quantum Science and Engineering community is unique in its interdisciplinary breadth combined with foundational research in quantum information and quantum matter. Research at Princeton comprises every layer of the quantum technology stack, bringing together many body physics, materials, devices, new quantum hardware platforms, quantum information theory, metrology, algorithms, complexity theory, and computer architecture. This vibrant environment allows for rapid progress at the frontiers of quantum science and technology, with cross pollination among quantum platforms and approaches. The research community strongly values interdisciplinarity, collaboration, depth, and fostering a close-knit community that enables fundamental and impactful advances.

Our curriculum places students in an excellent position to build new quantum systems, discover new technological innovations, become leaders in the emergent quantum industry, and make deep, lasting contributions to quantum information science. The QSE graduate program aims to provide a strong foundation of fundamentals through a three-course core, as well as opportunities to explore the frontiers of current research through electives. First year students are also required to take a seminar course that is associated with the Princeton Quantum Colloquium, in which they closely read the associated literature and discuss the papers. Our curriculum has a unique emphasis on learning how to read and understand current literature over a large range of topics. The curriculum is complemented by many opportunities at PQI for scientific interaction and professional development. A major goal of the program is to help form a tight-knit graduate student cohort that spans disciplines and research topics, united by a common language. 

Most students enter the program with an undergraduate degree in physics, electrical engineering, computer science, chemistry, materials science, or a related discipline. When you apply, you should indicate what broad research areas you are interested in: Quantum Systems Experiment, Quantum Systems Theory, Quantum Materials Science, or Quantum Computer Science.

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• Decisions, Decisions

MIT Applied Physics vs Princeton Physics Ph.D.

• applied physics
• electrical engineering

By scarman February 11, 2018 in Decisions, Decisions

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Hello everyone.

I have been accepted to two really great physics schools for my Ph.D. - MIT and Princeton. However, the admission to MIT is through the EECS department’s applied physics route while Princeton is just traditional physics (I also applied to MIT’s physics program but have not heard back from them. Considering all the acceptances that were sent out on Friday, I will assume that I have been rejected).

My area of focus at the current moment is experimental condensed matter (CME) and quantum computing (QC). In this respect, MIT is stronger, but I am anxious about how the decision might affect a career path in academia.

Ultimately, I want to be a professor of physics somewhere. I do NOT want to be a professor of engineering (I don’t have anything against engineers, I just would prefer to teach pure physics topics over engineering topics). Consequently, I don’t want an applied physics degree if it is going to significantly hurt my chances of getting a great physics postdoc or teaching position in the future, even if the degree is from MIT.

I should also mention that I’m not entirely set on CME/QC - I very much enjoy these topics and most of my experience is in these areas, but I also have interests elsewhere. In particular, atomic physics (AMO, both experimental and theoretical) as well as condensed matter theory (CMT) seem fascinating to me. It does not seem likely that, if I were to do applied physics at MIT, I would be able to study theory. I’m sure I could squeeze in experimental AMO though. On the other hand, Princeton excels in theory altogether. 

As a disclaimer, I do not yet know of all of the academic restrictions at MIT’s applied physics route. That is, I don’t know whether or not I would be allowed to take pure physics courses (e.g., E&M, quantum, QFT if I go into CMT, etc) as an EECS student. This probably doesn’t matter too much if I go into experiment, but I better have access to these classes if I decide to go into theory (assuming I can even work with theorists as an EECS student).

Lastly, I don’t know anything about how happy Princeton’s graduate students are versus MIT’s graduate students are, but this is obviously a big factor into where I go (how will I be able to do great research if I’m miserable?)

Thank you you in advance for helping me come to a decision!

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Lots of research group websites have listings of where their alumni go. Checking those out should give you a good idea of career prospects if you choose either program. It's also a question you can ask PIs in person if you plan to visit.

Thinking harder about the research available at each institution might also help guide your decision. I can't speak on CME/CMT, but AMO is basically non-existent at Princeton (based on website, they only have two non-emeritus faculty + four postdocs). If you're seriously interested in keeping the AMO door open, then Princeton might not be the best.

Also, are these two schools the only options available to you? There are some programs of comparable caliber that are more likely to give you both the career prospects and the research flexibility that you want.

Best of luck!

TheMostPowerfulApplicant

MIT Course 6 hands down

• 1 year later...

lessconfused

Can I ask, what decision did you end up making? I don't know if MIT EECS actually has Applied Physics anymore. The closest I see on the application is Materials and Devices. I'm also looking at Yale's Physics versus Applied Physics, so very curious about how to decide which to apply to. 

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Mae graduate courses, 501 (apc 501) mathematical methods of engineering analysis i.

A complementary presentation of theory, analytical methods, and numerical methods for the solution of problems in physics and engineering. Topics include an introduction to functional analysis, linear spaces and linear operators, including matrices, eigenproblems and Sturm-Liouville theory; basic ordinary differential equation (ODE) theory, Green’s functions for the solution of linear ODEs and Poisson’s equation, and the calculus of variations.

502 Mathematical Methods of Engineering Analysis II

A continuation of MAE 501. Complex variables, including contour integration using residues and conformal mapping; Fourier and Laplace transforms; linear partial differential equations (hyperbolic, parabolic and elliptic PDEs) and solution methods; traveling waves for nonlinear PDE; an introduction to numerical methods for ODEs and PDEs, and regular perturbation methods.

506 (APC 524) Software Engineering for Scientific Computing

The goal of this course is to teach basic tools and principles of writing good code, in the context of scientific computing. Specific topics include an overview of relevant compiled and interpreted languages, build tools and source managers, design patterns, design of interfaces, debugging and testing, profiling and improving performance, portability, and an introduction to parallel computing in both shared memory and distributed memory environments. The focus is on writing code that is easy to maintain and share with others. Students will develop these skills through a series of programming assignments and a group project.

507 (APC 523) Numerical Algorithms for Scientific Computing

A broad introduction to numerical algorithms used in scientific computing. The course will begin with a review of the basic principles of numerical analysis, including sources of error, stability and convergence of algorithms. The theory and implementation of techniques for linear and nonlinear systems of equations, and ordinary and partial differential equations will be covered in detail. Examples of the application of these methods to problems in physics, astrophysics and other disciplines will be given. Issues related to the implementation of efficient algorithms on modern high-performance computing systems will be discussed.

509, 510 Advanced Topics in Engineering Mathematics I, II

Selected topics in mathematical methods, with an emphasis on advances relevant to research activities represented in the department. Possible topics include analytical methods for differential equations, numerical solution of hyperbolic equations, and statistical methods.

511 Experimental Methods: Introduction to Electronics for Engineering and Science

A laboratory course that focuses on basic electronics techniques, digital electronics, and data acquisition and analysis. Topics include introduction to digital and analog electronics, digital-to-analog and analog-to-digital conversion, microcomputer sampling, and data analysis. There are four laboratory hours and two lecture hours per week. There is one project. Enrollment is limited.

512 Experimental Methods II

An exploration of experimental techniques in fluid mechanics and combustion. The course introduces experimentation, error analysis, and technical communication. Methods covered include pressure and temperature probes, flow visualization, hot-wire and laser anemometry, line reversal, Raman techniques, fluorescence, absorption, gas chromatography, and mass spectroscopy. There are three lecture hours and laboratory time per week.

519, 520 Advanced Topics in Experimental Methods I, II

Selected topics in experimental methods, with an emphasis on advances relevant to research activities represented in the department. Possible topics include dynamic data analysis; instrumentation and systems analysis, scanning probe techniques, and nanoscale materials property measurements.

521 Optics and Lasers

An introduction to principles of lasers. Topics include a review of propagation theory, interaction of light and matter, Fourier optics, a survey and description of operational characteristics of lasers, light scattering, and nonlinear optics. Some introductory quantum mechanics will be covered to give students an appreciation of the basic tools for the interaction of light with matter and nonlinear optical phenomena.

522 (AST564) Applications of Quantum Mechanics to Spectroscopy and Lasers

An intermediate-level course in applications of quantum mechanics to modern spectroscopy. The course begins with an introduction to quantum mechanics as a “tool” for atomic and molecular spectroscopy, followed by a study of atomic and molecular spectra, radiative, and collisional transitions, with the final chapters dedicated to plasma and flame spectroscopic and laser diagnostics. Prerequisite: one semester of quantum mechanics. (Offered in alternate years)

523 Electric Propulsion

Based on a review of pertinent atomic physics and electromagnetic theory, the particle and continuum representations of ionized gas dynamics are developed and applied to various electro-thermal, electrostatic, and electromagnetic acceleration mechanisms, each illustrated by various thruster designs, contemporary applications, and performances. (Offered in alternate years)

524 Plasma Engineering

The purpose of this course is to expose interested graduate and undergraduate students in engineering and the natural sciences to basic aspects of plasma physics and chemistry applicable to a variety of technologies, such as plasma propulsion, lasers, and materials processing. It involves extension of classical fluid mechanics, kinetic theory, statistical thermodynamics, and reaction engineering methods to relatively-low-temperature plasmas in electric and magnetic fields. (Offered in alternate years)

525 (AST 551) General Plasma Physics I

Characterization of the plasma state, Debye length, plasma and cyclotron frequencies, collision rates and mean free paths, atomic processes, adiabatic invariance, orbit theory, magnetic confinement of single charged particles, two-fluid description, magnetohydrodynamic waves and instabilities, heat flow, diffusion, finite-pressure effects, kinetic description, and Landau damping.

527 Physics of Gases

Physical and chemical topics of basic importance in modern fluid mechanics, plasma dynamics, and combustion science: statistical calculations of thermodynamic properties of gases; chemical and physical equilibria; adiabatic temperatures of complex reacting systems; quantum mechanical analysis of atomic and molecular structure and atomic-scale collision phenomena; transport properties; reaction kinetics, including chemical, vibrational, and ionization phenomena; and propagation, emission, and absorption of radiation.

528 (AST 566) Physics of Plasma Propulsion

Focus of this course is on fundamental processes in plasma thrusters for spacecraft propulsion with emphasis on recent research findings. Start with a review of the fundamentals of mass, momentum & energy transport in collisional plasmas, wall effects, & collective (wave) effects, & derive a generalized Ohm’s law useful for discussing various plasma thruster concepts. Move to detailed discussions of the acceleration & dissipation mechanisms in Hall thrusters, mangetoplasmadynamic thrusters, pulsed plasma thrusters, & inductive plasma thrusters, & derive expressions for the propulsive efficiencies of each of these concepts.

529,530 Advanced Topics in Applied Physics I, II

Selected topics in applied physics, with an emphasis on advances relevant to research activities represented in the department. Possible topics include advanced plasma propulsion, linear and nonlinear wave phenomena, and x-ray lasers in biological investigations.

531 Combustion

Fundamentals of combustion: thermodynamics; chemical kinetics; explosive and general oxidative characteristics of fuels; premixed and diffusion flames; laminar and turbulent flame phenomena; ignition and flame stabilization; detonation, environmental combustion considerations; and coal combustion.

532 Combustion Theory

Theoretical aspects of combustion: the conservation equations of chemically-reacting flows; activation energy asymptotics; chemical and dynamic structures of laminar premixed and non-premixed flames; aerodynamics and stabilization of flames; pattern formation and geometry of flame surfaces; ignition, extinction, and flammability phenomena; turbulent combustion; boundary layer combustion; droplet, particle, and spray combustion; and detonation and flame stabilization in supersonic flows.

534 Energy Storage Systems

This is a survey course on energy storage systems with a focus on electrochemical energy storage. Fundamentals of thermodynamics will be reviewed and fundamentals of electrochemistry introduced. These fundamentals will then be applied to de-vices such as batteries, flywheels and compressed air storage. Device optimization with respect to energy density, power density, cycle life and capital cost will be considered.

536 (MSE 586) Synchrotron and Neutron Techniques for Energy Materials

Topics include an introduction to radiation generation at synchrotron and neutron facilities, elastic scattering techniques, inelastic scattering techniques, imaging and spectroscopy. Specific techniques include X-ray and neutron diffraction, small-angle scattering, inelastic neutron scattering, reflectometry, tomography, microscopy, and X-ray absorption spectroscopy. Emphasis is placed on data analysis and use of Fourier transforms to relate structure/dynamics to experiment data. Example materials covered include energy storage devices, sustainable concrete, CO2 storage, magnetic materials, mesostructured materials and nanoparticles.

539, 540 Advanced Topics in Combustion I, II

Selected topics in theoretical and experimental combustion, with an emphasis on advances relevant to research activities represented in the department. Possible topics include turbulent combustion, theoretical calculations of rate constants, plasma fuels and natural resources, and nuclear propulsion power plants.

541 (APC 571) Applied Dynamical Systems

Phase-plane methods and single-degree-of-freedom nonlinear oscillators; invariant manifolds, local and global analysis, structural stability and bifurcation, center manifolds, and normal forms; averaging and perturbation methods, forced oscillations, homoclinic orbits, and chaos; and Melnikov’s method, the Smale horseshoe, symbolic dynamics, and strange attractors. (Offered in alternate years)

542 Advanced Dynamics

Principles and methods for formulating and analyzing mathematical models of physical systems; Newtonian, Lagrangian, and Hamiltonian formulations of particle and rigid and elastic body dynamics; canonical transformations, Hamilton-Jacob-Jacobi Theory; and integrable and non-integrable systems. Additional topics are explored at the discretion of the instructor.

543 Advanced Orbital Mechanisms

An advanced course in orbital motion of earth satellites, interplanetary probes, and celestial mechanics. Topics include orbit specification, orbit determination, Lambert’s problem, Hill’s equations, intercept and rendezvous, air-drag and radiation pressure, Lagrange points, numerical methods, general perturbations and variation of parameters, earth-shape effects on orbits, Hamiltonian treatment of orbits, Lagrange's planetary equations, orbit resonances, and higher-order perturbation effects. (Offered in alternate years)

544 Nonlinear Control

Nonlinear control of dynamical systems, with an emphasis on the geometric approach. The course gives an introduction to differential geometry, nonlinear controllability and constructive controllability, nonlinear observability, state-space transformations and stability, followed by study of a selection of nonlinear control design methods, including techniques motivated by geometric mechanics.

545 Special Topics (Fall 2015)- Lessons from Biology for Engineering Tiny Devices

Over millions of years of evolution nature invented many tiny sensors, machines and structures that are important for functions of cells and organisms. In this course we present a survey of problems at the interface of statistical mechanics, biology and engineering to discuss how cells move around, transport cargo and separate their genome during division, how microorganisms sense and swim in response to changing environment, how viruses assemble and infect other cells, how organs, such as brain and gut, obtain their shape, how animals obtain structural colors and how they camouflage, etc. Using this knowledge we study how to engineer and self-assemble tiny devices with DNA origami, how to design thin structures that can transform into specific shapes in response to external stimulus, how to make metamaterials with unusual properties, etc. (Offered in alternate years)

546 Optimal Control 

This course covers the main principles of optimal control theory applied to deterministic continuous-time problems and provide guidance on numerical methods for their solution. Fundamental results are reached starting with parameter optimization, the calculus of variations, and finally Pontryagin¿s principle(s), dynamic programming and the Hamilton-Jacobi-Bellman equation. Geometric and analytic properties of the formulations and solutions are highlighted. Numerical methods for direct and indirect optimal control problems are covered with applications. Emphasis is placed on intuition between the various aspects of the course.

547 (ELE521) Linear System Theory

Advanced topics in linear system analysis. The course gives a review of linear vector spaces and differential equations. It covers characterization of continuous and discrete time linear systems, transfer functions and state-space representations, properties of transition matrices, observability and controllability, minimal realizations, stability, feedback, and pole assignment.

548 (ELE 523) Nonlinear System Theory

Mathematical techniques useful in the analysis and design of nonlinear systems. This course covers topics in nonlinear dynamical systems including qualitative behavior, Lyapunov stability, input-output stability, passivity, averaging and singular perturbations. (offered in alternate years)

549, 550 Advanced Topics in Dynamics and Control I, II

Selected topics in dynamics and control, with an emphasis on advances relevant to research activities represented in the department. Possible topics include bifurcation theory, nonlinear mechanics, system identification, intelligent control, learning control, and applied aerodynamics.

551 Fluid Mechanics

An introduction to fluid mechanics. The course explores the development of basic conservation laws in integral and differential forms: one-dimensional compressible flows, shocks and expansion waves; effects of energy addition and friction; unsteady and two-dimensional flows and method of characteristics. Reviews classical incompressible flow concepts, including vorticity, circulation, and potential flows. Introduces viscous and diffusive phenomena.

552 Viscous Flows and Boundary Layers

The mechanics of viscous flows. The course explores the kinematics and dynamics of viscous flows; solution of the Navier Stokes equations; the behavior of vorticity; the boundary layer approximation; laminar boundary layer with and without pressure gradient; separation; integral relations and approximate methods; compressible laminar boundary layers; instability and transition; and turbulent boundary layers and self-preserving turbulent shear flows.

553 Turbulent Flow

Physical and statistical descriptions of turbulence; and a critical review of phenomenological theories for turbulent flows. The course examines scales of motion; correlations and spectra; homogeneous turbulent flows; inhomogeneous shear flows; turbulent flows in pipes and channels; turbulent boundary layers; calculation methods for turbulent flows (Reynolds stress equations, LES, DNS); and current directions in turbulence research.

555 Non-Equilibrium Gasdynamics

Noncontinuum description of fluid flow and Liouville and Boltzmann equations. The course examines molecular collisions; detailed balancing; Chapman-Enskog expansion for near-equilibrium flows; transport phenomena; flows with translational, vibrational and chemical non-equilibrium; shock structure; and shear and mixing layers with chemical reactions.

557 Simulation and Modeling of Fluid Flows

Numerical methods are applied to solve the equations that govern fluid motion. Fluid flow problems involve convection, diffusion, and source terms. The governing equations are non-linear and coupled. Finite-difference and finite volume methods are considered, together with concepts of accuracy, consistency, stability, convergence, conservation, and shock capturing. A range of current methods is reviewed with emphasis on multidimensional steady and unsteady compressible flows. Homework topics include writing codes to solve the conservation equation for a scalar, boundary layer flow, shock tube flow, application to curvilinear coordinates.

559 Advanced Topics in Fluid Mechanics

Selected topics in fluid mechanics, with an emphasis on advances relevant to research activities represented in the department. Possible topics include advanced computational fluid dynamics, turbulence in fluids and plasmas, hydrodynamic stability, low Reynolds number hydrodynamics, and capillary phenomena.

561 (MSE 501) Introduction to Materials

Emphasizes the connection between microstructural features of materials (e.g., grain size, boundary regions between grains, defects) and their properties, and how processing conditions control structure. Topics include thermodynamics and phase equilibria, microstructure, diffusion, kinetics of phase transitions, nucleation and crystal growth, phase separation, spinodal decomposition, glass formation, and the glass transition.

562 (MSE 540) Fracture Mechanics

Fracture involves processes at multiple time and length scales. This course covers the basic topics, including energy balance, crack tip fields, toughness, dissipation processes, and subcritical cracking. Fracture processes are then examined as they occur in some modern technologies, such as advanced ceramics, coatings, composites, and integrated circuits. The course also explores fracture at high temperatures and crack nucleation processes. (Offered in alternate years)

563 Instabilities in Fluids: Linear and Non-Linear Analysis of Waves and Patterns in the Environment

This course describes natural patterns arising from instabilities in nature, and discusses their importance in the environment. We analyze phenomena at various scales, as diverse as wave breaking at the ocean surface, internal mixing in the atmosphere and the ocean, volcanic plumes, convection cells in the atmosphere, the break-up of fluid ligaments or bubble bursting at an interface. The course details mathematical tools (linear and non-linear stability analysis, symmetry arguments, solutions to non-linear equations such as shocks and solitons), as well as present laboratory and numerical demonstration of the instabilities. 

564 (MSE 512) Structural Materials

Stress/strain behavior of materials; dislocation theory and strengthening mechanisms; yield strength; materials selection. Fundamentals of plasticity, Tresca and Von Mises yield criteria. Case study on forging: upper and lower bounds. Basic elements of fracture. Fracture mechanics. Mechanisms of fracture. The fracture toughness. Case studies and design. Fatigue mechanisms and life-prediction methodologies. (Offered in alternate years)

MSE 452 Phase Transformations and Evolving Microstructures in Hard and Soft Matter Systems

This course covers the fundamental principles of thermodynamics and phase transformation kinetics in hard and soft matter systems, such as metals and alloys, semiconductors, polymers, and lipid bilayer membranes. The course synthesizes descriptive observations, principles of statistical thermodynamics, and mathematical theories to address emergent physical, chemical, mechanical, and biological properties of multi-component, multiphase materials systems.

569, 570 Advanced Topics in Materials and Mechanical Systems I, II

Selected topics in materials and mechanical systems, with an emphasis on advances relevant to research activities represented in the department. Possible topics include high temperature protective coatings, multifunctional materials, MEMS, advanced computational methods in materials engineering.

571 Inspiring Young Engineers through Outreach

We study effective ways to inspire young students to think about science and engineering. Four concepts of modern engineering are identified and demonstration labs are built around them. The setups are built using modern yet simple tools and are accompanied by a video explaining how the concepts fit together in a larger picture. A field trip is made to a science exhibition to study methods to inspire and teach science to young people. At the end of the course the students perform demonstrations to students from Harlem Prep Elementary who will visit the MAE department. 

574 Unmaking the Bomb, not offered every year

This course covers the science and technology underlying existing and emerging nuclear security issues. It introduces the principles of nuclear fission, nuclear radiation, and nuclear weapons (and their effects) and develops the concepts required to model and analyze nuclear systems. The second half of the semester is centered around a hands-on team project.

575 (ECE 533) Data Assimilation

This course covers the theory and numerical algorithms of nonlinear filtering and smoothing, starting with the discrete-time linear Gaussian case and advancing through the general continuous-time nonlinear non-Gaussian case. Variants of Kalman and ensemble methods will be covered with derivations and sketches of important proofs. A review of the necessary elements from probability and stochastic processes is included. Following the theory, numerical algorithms are regularly demonstrated on a suite of problems that include aerospace and geoscience applications.

579, 580 Advanced Topics in Energy and Environment I, II

Selected topics in energy and the environment, with an emphasis on advances relevant to research activities represented in the department. Possible topics include combustion control and emissions, economic development and energy resources, and energy efficiency.

597, 598 Graduate Seminar in Mechanical and Aerospace Engineering

A seminar of graduate students and staff presenting the results of their research and recent advances in flights, space, and surface transportation; fluid mechanics; energy conversion; propulsion; combustion; environmental studies; applied physics; and materials sciences. There is one seminar per week and participation at presentations by distinguished outside speakers.

Graduate School

Applied and Computational Math

General information, program offerings:, department for program:, director of graduate studies:, graduate program administrator:.

The Program in Applied and Computational Mathematics offers a select group of highly qualified students the opportunity to obtain a thorough knowledge of branches of mathematics indispensable to science and engineering applications, including numerical analysis and other computational methods.

Program Offerings

Program offering: ph.d..

Students enroll in courses based on research topics that they choose in consultation with faculty.  Typically, students take regular or reading courses with their advisers in the three topic areas of their choice, completing the regular exams and course work for these courses.  

Students must choose three areas out of a list of the following six topic areas in which to take courses and be examined:

• Asymptotics, analysis, numerical analysis, and signal processing;
• Discrete mathematics, combinatorics, algorithms, computational geometry, and graphics;
• Mechanics and field theories (including computational physics/chemistry/biology);
• Optimization (including linear and nonlinear programming and control theory);
• Partial differential equations and ordinary differential equations (including dynamical systems);  
• Stochastic modeling, probability, statistics, and information theory

Additional topics may be considered with prior approval by the director of graduate studies.

The student should choose specific topics by the end of October. In consultation with the student, the director of graduate studies appoints a set of advisers from among the faculty and associated faculty. The adviser in each topic meets regularly with the student, monitors progress, and assigns additional reading material. Advisers are usually program faculty or associated faculty, but faculty members from other departments may serve as advisers with approval.

Additional pre-generals requirements

At the end of the first year, students will take a preliminary exam, consisting of a joint interview by their three first-year topic advisers. Each student should decide with their first-year advisers which courses are relevant for the examination areas.

Students should assess their level of preparation for the preliminary examination by reviewing homework and examinations from the previous year’s work.  Students who fail the preliminary examination may take the examination a second time with the support of the first-year advisers.

General exam

Before being admitted to the third year of study, students must pass the general examination. The general examination, or generals, is designed as a sequence of interviews with assigned professors covering three applied mathematics areas. The generals culminate in a seminar on a research topic, usually delivered toward the end of the fourth term.  A student who completes all program requirements (coursework, preliminary exams, with no incompletes) but fails the general examination may take it a second time. Students who fail the general examination a second time will have their degree candidacy terminated.

Qualifying for the M.A.

The Master of Arts degree is normally an incidental degree on the way to full Ph.D. candidacy but may also be awarded to students who, for various reasons, leave the Ph.D. program. Students who have successfully completed all courses undertaken during their graduate study, have satisfactorily resolved all incompletes (if any), and have passed the preliminary exam may be awarded an M.A. degree.  Upon learning the program’s determination of their candidacy to receive the M.A., students apply for the master's degree online through the advanced degree application system. 

Dissertation and FPO

The doctoral dissertation must consist of either a mathematical contribution to some field of science or engineering or the development or analysis of mathematical or computational methods useful for, inspired by, or relevant to science or engineering.

The Ph.D. is awarded after the candidate’s doctoral dissertation has been accepted and the final public oral examination sustained.

• Amit Singer

Director of Undergraduate Program

• Paul Seymour

Executive Committee

• Noga M. Alon, Mathematics
• René A. Carmona, Oper Res and Financial Eng
• Emily Ann Carter, Mechanical & Aerospace Eng
• Maria Chudnovsky, Mathematics
• Peter Constantin, Mathematics
• Amit Singer, Mathematics
• Howard A. Stone, Mechanical & Aerospace Eng
• Romain Teyssier, Astrophysical Sciences
• Jeroen Tromp, Geosciences
• Ramon van Handel, Oper Res and Financial Eng

Associated Faculty

• Ryan P. Adams, Computer Science
• Amir Ali Ahmadi, Oper Res and Financial Eng
• Michael Aizenman, Physics
• Yacine Aït-Sahalia, Economics
• William Bialek, Physics
• Mark Braverman, Computer Science
• Carlos D. Brody, Princeton Neuroscience Inst
• Adam S. Burrows, Astrophysical Sciences
• Roberto Car, Chemistry
• Bernard Chazelle, Computer Science
• Jianqing Fan, Oper Res and Financial Eng
• Jason W. Fleischer, Electrical & Comp Engineering
• Mikko P. Haataja, Mechanical & Aerospace Eng
• Gregory W. Hammett, PPPL Theory
• Isaac M. Held, Atmospheric & Oceanic Sciences
• Sergiu Klainerman, Mathematics
• Naomi E. Leonard, Mechanical & Aerospace Eng
• Simon A. Levin, Ecology & Evolutionary Biology
• Luigi Martinelli, Mechanical & Aerospace Eng
• William A. Massey, Oper Res and Financial Eng
• Assaf Naor, Mathematics
• Jonathan W. Pillow, Princeton Neuroscience Inst
• H. Vincent Poor, Electrical & Comp Engineering
• Frans Pretorius, Physics
• Herschel A. Rabitz, Chemistry
• Peter J. Ramadge, Electrical & Comp Engineering
• Jennifer Rexford, Computer Science
• Clarence W. Rowley, Mechanical & Aerospace Eng
• Szymon M. Rusinkiewicz, Computer Science
• Frederik J. Simons, Geosciences
• Jaswinder P. Singh, Computer Science
• Ronnie Sircar, Oper Res and Financial Eng
• Mete Soner, Oper Res and Financial Eng
• John D. Storey, Integrative Genomics
• Sankaran Sundaresan, Chemical and Biological Eng
• Ludovic Tangpi, Oper Res and Financial Eng
• Robert E. Tarjan, Computer Science
• Corina E. Tarnita, Ecology & Evolutionary Biology
• Salvatore Torquato, Chemistry
• Olga G. Troyanskaya, Computer Science
• Matt Weinberg, Computer Science
• Noga M. Alon
• Maria Chudnovsky
• Peter Constantin
• Romain Teyssier
• Jeroen Tromp

Associate Professor

• Ramon van Handel

For a full list of faculty members and fellows please visit the department or program website.

Permanent Courses

Courses listed below are graduate-level courses that have been approved by the program’s faculty as well as the Curriculum Subcommittee of the Faculty Committee on the Graduate School as permanent course offerings. Permanent courses may be offered by the department or program on an ongoing basis, depending on curricular needs, scheduling requirements, and student interest. Not listed below are undergraduate courses and one-time-only graduate courses, which may be found for a specific term through the Registrar’s website. Also not listed are graduate-level independent reading and research courses, which may be approved by the Graduate School for individual students.

AOS 576 - Current Topics in Dynamic Meteorology (also APC 576)

Apc 503 - analytical techniques in differential equations (also ast 557), apc 523 - numerical algorithms for scientific computing (also ast 523/cse 523/mae 507), apc 524 - software engineering for scientific computing (also ast 506/cse 524/mae 506), apc 599 - summer extramural research project, ast 559 - turbulence and nonlinear processes in fluids and plasmas (also apc 539), cbe 502 - mathematical methods of engineering analysis ii (also apc 502), cbe 554 - topics in computational nonlinear dynamics (also apc 544), mae 501 - mathematical methods of engineering analysis i (also apc 501/cbe 509), mae 502 - mathematical methods of engineering analysis ii (also apc 506), mae 541 - applied dynamical systems (also apc 571), mat 522 - introduction to pde (also apc 522), mat 572 - topics in combinatorial optimization (also apc 572), mat 585 - mathematical analysis of massive data sets (also apc 520), mat 586 - computational methods in cryo-electron microscopy (also apc 511/mol 511/qcb 513), mse 515 - random heterogeneous materials (also apc 515/chm 559), orf 550 - topics in probability (also apc 550).

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Department of Physics

Pre-Doctoral Fellowship

Princeton University’s culture and unique characteristics are strengthened by its diversity. As articulated in the University’s Statement on Diversity and Inclusion, which was included in the University’s Report of the Trustee Ad Hoc Committee on Diversity, dated September 2013, “Princeton University is a community devoted to excellence in education and scholarship. We believe that only by including people with a broad range of experiences and perspectives are we able to realize our potential—to expand our capacity for teaching and learning, to increase opportunities for innovative research, and to equip students for lives of service and leadership in an increasingly pluralistic society. Thus, the goals of excellence and diversity are inextricably linked.”

The Physics Department has partnered with the Graduate School to offer a one-year fully funded fellowship that includes an offer of regular admission to the Physics PhD program the following year.

The Physics Pre-Doctoral Fellowship Program has the following features:

• Advanced undergraduate classes or graduate classes in statistical mechanics, quantum mechanics, electromagnetism, classical mechanics and other advanced topics.
• Participate in independent research with one of the research groups. See the department web sites for information on research activities in the departments.

Eligibility 

Members of groups who contribute to the University’s diversity—including members of groups that have been historically and are presently underrepresented in the academy (e.g., racial and ethnic minorities, individuals from first generation/low income backgrounds, etc.) and those who have made active contributions to enhancing access, diversity, and inclusion in the sponsoring departments field—are especially encouraged to apply. Applicants must be legally authorized to work/study in the United States at the time of submitting the application and for the duration of the program.  

If you would like more information on this fellowship and how to apply   please click on this link which will direct you to the Graduate school website .

Further Information  on program features please contact Professor Simone Giombi (DGS) (Physics Department, [email protected] ).

Princeton Center for Complex Materials

Jiachen Yu earned his PhD from the Department of Applied Physics, Stanford University, under the advising of Prof. Benjamin Feldman. At Princeton, he will be working with Prof. Ali Yazdani  (IRG-A) on imaging novel quasiparticles in graphene using STM, as well as developing new low temperature scanning probe techniques. Start: Fall 2023

About the Program

The P4 (Prospective Physics PhD Preview) program is a transformative workshop that empowers participants to engage in physics research, discover ideal graduate programs, and cultivate a compelling graduate application. Along the way, the P4 Scholars will interact with graduate students, postdocs, and faculty from Princeton’s Physics Department. The workshop will run between  February 15-17, 2024 .

Eligibility :

• Students on track to apply for the fall 2024 application cycle or beyond.
• Students who have not participated in P4 before. 
• Students interested in ANY Physics PH.D program. Applications for P4 2024 are now closed.

Please feel free to reach out to  [email protected]  with any questions, comments, or concerns.

Office of the Dean for Research

Dean for research peter schiffer assumes role as vice president for princeton plasma physics laboratory.

Peter Schiffer. Photo by Sameer A. Khan

Peter Schiffer, Princeton’s dean for research and the Class of 1909 Professor of Physics, will succeed David McComas as Princeton University’s vice president for the Princeton Plasma Physics Laboratory (PPPL),  a U.S. Department of Energy national laboratory managed by Princeton University. Schiffer will maintain his dean for research role. The transition will take place on Sept. 2. 

McComas will conclude his PPPL leadership role to focus on the successful completion and launch of NASA’s Interstellar Mapping and Acceleration Probe (IMAP). McComas is the principal investigator for the IMAP mission, which is scheduled to launch from Cape Canaveral next year to advance understanding of the space environment in our solar neighborhood.

“I am grateful to David McComas for stewarding the University’s relationship with the Plasma Physics Laboratory and the Department of Energy so conscientiously over the past eight years,” said Princeton President Christopher L. Eisgruber. “Dave’s outstanding scientific acumen, administrative skill, and personal integrity have benefited us tremendously over the course of his tenure. I wish him well as he devotes himself full-time to his research program, and I look forward to working with Peter Schiffer as he adds this new role to his portfolio.”

David McComas

Photo by Sameer A. Khan/Fotobuddy

As PPPL vice president since 2016, McComas has served as a liaison between senior University leadership, the laboratory and the Department of Energy. At Princeton, his executive leadership has included service as a member of the President’s cabinet and the Executive Compliance Committee. 

PPPL conducts essential research using plasma — the fourth state of matter — to solve some of the world’s toughest science and technology challenges, including the development of fusion energy as a clean, safe and virtually limitless power source.

“I feel great about the contributions I made in overseeing PPPL as a University vice president, but I also feel that after eight and a half years, it’s time for me to focus on my other primary job,” he said. “PPPL is vital to the national interest, and it’s also vital to the national interest that we get IMAP launched and working perfectly. It’s critical for NASA heliophysics and space science, and as the principal investigator, I’m responsible for the entire mission.”

Since coming to Princeton, McComas has been a half-time vice president and half-time professor of astrophysical sciences. As he transitions to a full-time role on the astrophysics faculty, he will continue leading his roughly 35-person research team, teaching his unique  space physics  undergraduate lab, and serving as the mission leader for IMAP and other NASA missions and instruments. After he steps down as vice president, McComas will be a special adviser to the provost and continue to serve on the boards of directors for both PPPL and Brookhaven National Laboratory.

“Dave’s expertise has been timely, important and valued,” said Princeton Provost Jennifer Rexford, who is also the Gordon Y.S. Wu Professor in Engineering. “PPPL’s research mission, working toward an efficient and clean energy source, is critically important for humanity. Dave is a deep scientist in his own right, and he also understands all the engineering and operational issues involved in working at the leading edge of technology.”

Schiffer was the logical choice to succeed him as vice president for PPPL, Rexford said.

She noted that the scope of research at PPPL has diversified in the past several years, incorporating research into microelectronics, quantum sensors and devices, and sustainability science. 

“The widening of the research going on at the Lab has increased opportunities for connection with campus,” she said. “That stronger connection benefits from going through the Office of the Dean for Research.” 

Leadership at PPPL

Over the past eight years, McComas has worked with University and PPPL leadership to strengthen the connections between the Lab and the campus. “PPPL is an important part of the future of the University,” McComas said. “The University is interested in advances that make a huge difference for humanity, and it has a very long view of things. That’s exactly what fusion energy needs.” 

McComas is a renowned space physicist and the principal investigator on multiple NASA instruments and missions. He holds seven patents and has published more than 800 peer-reviewed papers with more than 50,000 citations. Prior to coming to Princeton, he served in a variety of leadership roles at Los Alamos National Laboratory and the Southwest Research Institute.

In addition to overseeing PPPL’s research mission, he has secured two contract extensions with the DOE and led the international search that that brought the renowned fusion scientist Sir Steven Cowley to PPPL as its director.

“Dave has been a steadfast partner during a period of rapid expansion at the Laboratory,” said Cowley, who is also a professor of astrophysical sciences at the University. “PPPL is tackling global issues in the nation’s interest, contributing to a sustainable future while driving scientific innovation forward. Dave’s inventive mindset, coupled with his strong organizational leadership, has been an asset to PPPL during a critical time.” 

With fusion energy at an inflection point, “it’s an exciting time at PPPL,” McComas said. Unprecedented numbers of public-private partnership grants are helping to advance fusion science and engineering at the Lab, he said, adding that the growing number of private companies working in the sector indicates that investors are confident that technologies are advancing toward bringing fusion energy to the national grid.

McComas and IMAP

Several months ago, as McComas saw both of his major responsibilities — PPPL and IMAP — coming to critical points, he felt that it was time to focus his energies on the space physics to which he has devoted his academic career.

IMAP’s mission is to explore our solar neighborhood, by decoding the messages in particles captured from the Sun and from beyond our cosmic shield, the heliopause. After  its launch , IMAP will provide extensive new observations of the inner and outer heliosphere and answer two of the most important topics in space physics today: how energetic particles are accelerated in the solar wind, and how the solar wind interacts with the local interstellar medium. 

The roughly $750 million IMAP mission carries 10 cutting-edge scientific  instruments and will launch from Cape Canaveral in 2025 on a Falcon 9 Heavy rocket. In addition to resolving fundamental scientific questions, IMAP will make real-time observations of the space environment a million miles sunward of the Earth, providing critical advance warning of impending space weather events. 

In his career, McComas has led the TWINS and IBEX space physics missions as well as instruments for numerous other missions, including Parker Solar Probe to the sun, the Advanced Composition Explorer to study spaceborne energetic particles, Ulysses to view the sun from outside the ecliptic, New Horizons to and past Pluto, Juno to Jupiter, and Cassini to Saturn.

Among many other honors, he has received the  Arctowski Medal from the National Academy of Sciences, the  Distinguished Scientist Award from the Scientific Committee on Solar-Terrestrial Physics of the International Science Council, and the NASA Exceptional Public Service Medal. He is a fellow of the American Physical Society, the American Geophysical Union and the American Association for the Advancement of Science. 

Schiffer and PPPL

With an active research program in the Department of Physics in addition to his administrative roles, Schiffer is an eminent condensed matter physicist who holds a Ph.D. from Stanford University and a B.S. from Yale.

Prior to coming to Princeton in 2023, he served as a member of the faculty and an administrator at Yale University, the University of Illinois at Urbana-Champaign, and Pennsylvania State University. He currently also serves on the governing board of the American Physical Society and previously served as a senior fellow with the Association of American Universities.

Schiffer leads the Office of the Dean for Research, which supports the Princeton research enterprise by expanding access to funding and other resources, building research relationships with external partners, facilitating regulatory and policy compliance, and supporting innovation, entrepreneurship and the development of intellectual property. 

He said he looks forward to continuing PPPL’s long legacy of research in the nation’s service, expanding its academic affiliation with the University and building on its importance as a regional economic hub. “Princeton has been the steward of the Lab since it was founded back in the ’50s,” Schiffer said. “It is part of the University’s scientific legacy and tradition to have PPPL as a critical part of our overall research portfolio; it provides research opportunities for undergrads, graduate students and postdocs. With its hundreds of employees and global scientific reputation, PPPL also has a big economic footprint within our community.”

He continued: “PPPL is a very important part of Princeton’s intellectual ecosystem, and we’re honored to have the opportunity to manage the Lab for the nation and support the great science that comes out of it.”