# Physics (Ph) Graduate Courses (2020-21)

Ph 101.
Order-of-Magnitude Physics.
9 units (3-0-6):
third term.
Emphasis will be on using basic physics to understand complicated systems. Examples will be selected from properties of materials, geophysics, weather, planetary science, astrophysics, cosmology, biomechanics, etc. Offered in alternate years.
Instructor: Phinney.

Ay/Ph 104.
Relativistic Astrophysics.
9 units (3-0-6):
third term.
Prerequisites: Ph 1, Ph 2 ab.
This course is designed primarily for junior and senior undergraduates in astrophysics and physics. It covers the physics of black holes and neutron stars, including accretion, particle acceleration and gravitational waves, as well as their observable consequences: (neutron stars) pulsars, magnetars, X-ray binaries, gamma-ray bursts; (black holes) X-ray transients, tidal disruption and quasars/active galaxies and sources of gravitational waves. Not offered 2020-21.

Ph 105.
Analog Electronics for Physicists.
9 units:
first term.
Prerequisites: Ph 1 abc, Ma 2, or equivalent..
A laboratory course intended for graduate students, it covers the design, construction, and testing of simple, practical analog and interface circuits useful for signal conditioning and experiment control in the laboratory. No prior experience with electronics is required. Students will use operational amplifiers, analog multipliers, diodes, bipolar transistors, and passive circuit elements. Each week includes a 45 minute lecture/recitation and a 2½ hour laboratory. The course culminates in a two-week project of the student's choosing. Not offered 2020-21.

Ph 106 abc.
Topics in Classical Physics.
9 units (4-0-5):
first, second, third terms.
Prerequisites: Ph 2 ab or Ph 12 abc, Ma 2.
An intermediate course in the application of basic principles of classical physics to a wide variety of subjects. Ph 106 a will be devoted to mechanics, including Lagrangian and Hamiltonian formulations of mechanics, small oscillations and normal modes, central forces, and rigid-body motion. Ph 106 b will be devoted to fundamentals of electrostatics, magnetostatics, and electrodynamics, including boundary-value problems, multipole expansions, electromagnetic waves, and radiation. It will also cover special relativity. Ph 106 c will cover advanced topics in electromagnetism and an introduction to classical optics.
Instructors: Fuller, Golwala, Hutzler.

APh/Ph 115.
Physics of Momentum Transport in Hydrodynamic Systems.
9 units (3-0-6):
second term.
Prerequisites: ACM 95 or equivalent.
Contemporary research in many areas of physics requires some knowledge of the principles governing hydrodynamic phenomena such as nonlinear wave propagation, symmetry breaking in pattern forming systems, phase transitions in fluids, Langevin dynamics, micro- and optofluidic control, and biological transport at low Reynolds number. This course offers students of pure and applied physics a self-contained treatment of the fundamentals of momentum transport in hydrodynamic systems. Mathematical techniques will include formalized dimensional analysis and rescaling, asymptotic analysis to identify dominant force balances, similitude, self-similarity and perturbation analysis for examining unidirectional and Stokes flow, pulsatile flows, capillary phenomena, spreading films, oscillatory flows, and linearly unstable flows leading to pattern formation. Students must have working knowledge of vector calculus, ODEs, PDEs, complex variables and basic tensor analysis. Advanced solution methods will be taught in class as needed.
Instructor: Troian.

APh/Ph/Ae 116.
Physics of Thermal and Mass Transport in Hydrodynamic Systems.
9 units (3-0-6):
third term.
Prerequisites: ACM 95 or equivalent and APh/Ph 115 or equivalent.
Contemporary research in many areas of physics requires some knowledge of how momentum transport in fluids couples to diffusive phenomena driven by thermal or concentration gradients. This course will first examine processes driven purely by diffusion and progress toward description of systems governed by steady and unsteady convection-diffusion and reaction-diffusion. Topics will include Fickian dynamics, thermal transfer in Peltier devices, Lifshitz-Slyozov growth during phase separation, thermocouple measurements of oscillatory fields, reaction-diffusion phenomena in biophysical systems, buoyancy driven flows, and boundary layer formation. Students must have working knowledge of vector calculus, ODEs, PDEs, complex variables and basic tensor analysis. Advanced solution methods such as singular perturbation, Sturm-Liouville and Green's function analysis will be taught in class as needed.
Instructor: Troian.

Ph/APh/EE/BE 118 abc.
Physics of Measurement.
9 units (3-0-6):
second, third terms.
Prerequisites: Ph 127, APh 105, or equivalent, or permission from instructor.
This course focuses on exploring the fundamental underpinnings of experimental measurements from the perspectives of responsivity, noise, backaction, and information. Its overarching goal is to enable students to critically evaluate real measurement systems, and to determine the ultimate fundamental and practical limits to information that can be extracted from them. Topics will include physical signal transduction and responsivity, fundamental noise processes, modulation, frequency conversion, synchronous detection, signal-sampling techniques, digitization, signal transforms, spectral analyses, and correlations. The first term will cover the essential fundamental underpinnings, while topics in second term will include examples from optical methods, high-frequency and fast temporal measurements, biological interfaces, signal transduction, biosensing, and measurements at the quantum limit. Part c not offered in 2020-21.
Instructor: Roukes.

CS/Ph 120.
Quantum Cryptography.
9 units (3-0-6):
first term.
Prerequisites: Ma 1b, Ph 2b or Ph 12b, CS 21, CS 38 or equivalent recommended (or instructor's permission).
This course is an introduction to quantum cryptography: how to use quantum effects, such as quantum entanglement and uncertainty, to implement cryptographic tasks with levels of security that are impossible to achieve classically. The course covers the fundamental ideas of quantum information that form the basis for quantum cryptography, such as entanglement and quantifying quantum knowledge. We will introduce the security definition for quantum key distribution and see protocols and proofs of security for this task. We will also discuss the basics of device-independent quantum cryptography as well as other cryptographic tasks and protocols, such as bit commitment or position-based cryptography. Not offered 2020-21.

Ph 121 abc.
Computational Physics Lab.
6 units (0-6-0):
first, second, third terms.
Many of the recent advances in physics are attributed to progress in computational power. In the advanced computational lab, students will hone their computational skills bu working through projects inspired by junior level classes (such as classical mechanics and E, statistical mechanics, quantum mechanics and quantum many-body physics). This course will primarily be in Python and Mathematica. This course is offered pass/fail.
Instructors: Simmons-Duffin, Refael.

Ph 125 abc.
Quantum Mechanics.
9 units (4-0-5):
first, second, third terms.
Prerequisites: Ma 2 ab, Ph 12 abc or Ph 2 ab, or equivalents.
A one-year course in quantum mechanics and its applications, for students who have completed Ph 12 or Ph 2. Wave mechanics in 3-D, scattering theory, Hilbert spaces, matrix mechanics, angular momentum, symmetries, spin-1/2 systems, approximation methods, identical particles, and selected topics in atomic, solid-state, nuclear, and particle physics. Chen.
Instructors: Wise, Y.

Ph 127 abc.
Statistical Physics.
9 units (4-0-5):
first, second terms.
Prerequisites: Ph 12 c or equivalent, and a basic understanding of quantum and classical mechanics.
A course in the fundamental ideas and applications of classical and quantum statistical mechanics. Topics to be covered include the statistical basis of thermodynamics; ideal classical and quantum gases (Bose and Fermi); lattice vibrations and phonons; weak interaction expansions; phase transitions; and fluctuations and dynamics.
Instructor: Motrunich.

Ph 129 abc.
Mathematical Methods of Physics.
9 units (4-0-5):
first, second terms.
Prerequisites: Ma 2 and Ph 2 abc, or equivalent.
Mathematical methods and their application in physics. First term focuses on group theoretic methods in physics. Second term includes analytic and numerical methods for solving differential equations, integral equations, and transforms, and other applications of real analysis. The term that covers probability and statistics in physics, part c, will not be offered in the 2020-21 academic year. Each part may be taken independently.
Instructors: X. Chen, Chatziioannou..

Ph 135.
Introduction to Condensed Matter.
9 units (3-0-6):
first term.
Prerequisites: Ph 125 ab or equivalent or instructor's permission.
This course is an introduction to condensed matter which covers electronic properties of solids, including band structures, transport, and optical properties. Ph 135 a is continued by Ph 223 ab in second and third terms.
Instructor: Refael.

Ph 136 abc.
Applications of Classical Physics.
9 units (3-0-6):
first, second, third terms.
Prerequisites: Ph 106 ab or equivalent.
Applications of classical physics to topics of interest in contemporary "macroscopic'' physics. Continuum physics and classical field theory; elasticity and hydrodynamics; plasma physics; magnetohydrodynamics; thermodynamics and statistical mechanics; gravitation theory, including general relativity and cosmology; modern optics. Content will vary from year to year, depending on the instructor. An attempt will be made to organize the material so that the terms may be taken independently. Ph 136a will focus on thermodynamics, statistical mechanics, random processes, and optics. Ph136b will focus on fluid dynamics, MHD, turbulence, and plasma physics. Ph 136c will cover an introduction to general relativity. Offered in alternate years.
Instructors: Phinney, Fuller, Teukolsky.

Ph/APh 137 abc.
Atoms and Photons.
9 units (3-0-6):
first, second terms.
Prerequisites: Ph 125 ab or equivalent, or instructor's permission.
This course will provide an introduction to the interaction of atomic systems with photons. The main emphasis is on laying the foundation for understanding current research that utilizes cold atoms and molecules as well as quantized light fields. First term: resonance phenomena, atomic/molecular structure, and the semi-classical interaction of atoms/molecules with static and oscillating electromagnetic fields. Techniques such as laser cooling/trapping, coherent manipulation and control of atomic systems. Second term: quantization of light fields, quantized light matter interaction, open system dynamics, entanglement, master equations, quantum jump formalism. Applications to cavity QED, optical lattices, and Rydberg arrays. Third term [not offered 2020-21]: Topics in contemporary research. Possible areas include introduction to ultracold atoms, atomic clocks, searches for fundamental symmetry violations, synthetic quantum matter, and solid state quantum optics platforms. The emphasis will be on reading primary and contemporary literature to understand ongoing experiments.
Instructors: Hutzler, Endres.

APh/Ph 138 ab.
Quantum Hardware and Techniques.
9 units (3-0-6):
second and third terms.
Prerequisites: Ph 125 abc or Ph 127 abc or Ph 137 ab or instructor's permission.
This class covers multiple quantum technology platforms and related theoretical techniques, and will provide students with broad knowledge in quantum science and engineering. It will be split into three-week modules covering: applications of near-term quantum computers, superconducting qubits, trapped atoms and ions, topological quantum matter, solid state quantum bits, tensor-product states. APh/Ph 138a will not be offered 2020-21. APh/Ph 138b
Instructors: Endres, Faraon, Hsieh, Painter.

Ph 139.
Introduction to High Energy Physics.
9 units (3-0-6):
second term.
Prerequisites: Ph 125 ab or equivalent, or instructor's permission.
This course provides an introduction to particle physics which includes Standard Model, Feynman diagrams, matrix elements, electroweak theory, QCD, gauge theories, the Higgs mechanism, neutrino mixing, astro-particle physics/cosmology, accelerators, experimental techniques, important historical and recent results, physics beyond the Standard Model, and major open questions in the field.
Instructor: Weinstein.

Ph 171.
Reading and Independent Study.
Units in accordance with work accomplished:
.
Occasionally, advanced work involving reading, special problems, or independent study is carried out under the supervision of an instructor. Approval of the instructor and of the student's departmental adviser must be obtained before registering. The instructor will complete a student evaluation at the end of the term. Graded pass/fail.

Ph 172.
Research in Physics.
Units in accordance with work accomplished:
.
Undergraduate students registering for 6 or more units of Ph 172 must provide a brief written summary of their work, not to exceed 3 pages, to the option rep at the end of the term. Approval of the student's research supervisor and departmental adviser must be obtained before registering. Graded pass/fail.

Ph 177.
Advanced Experimental Physics.
9 units (0-4-5):
second, third terms.
Prerequisites: Ph 7, Ph 106 a, Ph 125 a or equivalents.
A one-term laboratory course which will require students to design, assemble, calibrate, and use an apparatus to conduct a nontrivial experiment involving quantum optics or other current research area of physics. Students will work as part of a small team to reproduce the results of a published research paper. Each team will be guided by an instructor who will meet weekly with the students; the students are each expected to spend an average of 4 hours/week in the laboratory and the remainder for study and design. Enrollment is limited. Permission of the instructors required.
Instructors: Rice, Hutzler.

CNS/Bi/Ph/CS/NB 187.
Neural Computation.
9 units (3-0-6):
first term.
Prerequisites: familiarity with digital circuits, probability theory, linear algebra, and differential equations.
Programming will be required. This course investigates computation by neurons. Of primary concern are models of neural computation and their neurological substrate, as well as the physics of collective computation. Thus, neurobiology is used as a motivating factor to introduce the relevant algorithms. Topics include rate-code neural networks, their differential equations, and equivalent circuits; stochastic models and their energy functions; associative memory; supervised and unsupervised learning; development; spike-based computing; single-cell computation; error and noise tolerance. Not Offered 2020-21.
Instructor: Perona.

Ph 198.
Special Topics in Physics.
Units in accordance with work accomplished:
.
Topics will vary year to year and may include hands-on laboratory work, team projects and a survey of modern physics research.
Instructor: Staff.

Ph 199.
Frontiers of Fundamental Physics.
9 units (3-0-6):
third term.
Prerequisites: Ph 125 ab, Ph 106 ab, or equivalent.
This course will explore the frontiers of research in particle physics and cosmology, focusing on the physics at the Large Hadron Collider. Topics include the Standard Model of particle physics in light of the discovery of the Higgs boson, work towards the characterization and measurements of the new particle's quantum properties, its implications on physics beyond the standard model, and its connection with the standard model of cosmology focusing on the dark matter challenge. The course is geared toward seniors and first-year graduate students who are not in particle physics, although students in particle physics are welcome to attend. Not offered 2020-21.

Ph 201.
Candidacy Physics Fitness.
9 units (3-0-6):
third term.
The course will review problem solving techniques and physics applications from the undergraduate physics college curriculum. In particular, we will touch on the main topics covered in the written candidacy exam: classical mechanics, electromagnetism, statistical mechanics and quantum physics, optics, basic mathematical methods of physics, and the physical origin of everyday phenomena.
Instructor: Endres.

Ph 205 abc.
Relativistic Quantum Field Theory.
9 units (3-0-6):
first, second, third terms.
Prerequisites: Ph 125.
Topics: the Dirac equation, second quantization, quantum electrodynamics, scattering theory, Feynman diagrams, non-Abelian gauge theories, Higgs symmetry-breaking, the Weinberg-Salam model, and renormalization.
Instructors: Gukov, Zurek, Kapustin.

Ph 217.
Introduction to the Standard Model.
9 units (3-0-6):
first term.
Prerequisites: Ph 205 abc and Ph 236 abc, or equivalent.
An introduction to elementary particle physics and cosmology. Students should have at least some background in quantum field theory and general relativity. The standard model of weak and strong interactions is developed, along with predictions for Higgs physics and flavor physics. Some conjectures for physics beyond the standard model are introduced: for example, low-energy supersymmetry and warped extra dimensions. Not offered 2020-21.

Ph/CS 219 abc.
Quantum Computation.
9 units (3-0-6):
first, second terms.
Prerequisites: Ph 125 ab or equivalent.
The theory of quantum information and quantum computation. Overview of classical information theory, compression of quantum information, transmission of quantum information through noisy channels, quantum error-correcting codes, quantum cryptography and teleportation. Overview of classical complexity theory, quantum complexity, efficient quantum algorithms, fault-tolerant quantum computation, physical implementations of quantum computation. Part c not offered in 2020-21.
Instructors: Preskill, Kitaev.

Ph/APh 223 ab.
Advanced Condensed-Matter Physics.
9 units (3-0-6):
second, third terms.
Prerequisites: Ph 135 or equivalent, or instructor's permission.
Advanced topics in condensed-matter physics, with emphasis on the effects of interactions, symmetry, and topology in many-body systems. Ph/Aph 223a covers second quantization, Hartree-Fock theory of the electron gas, Mott insulators and quantum magnetism, bosonization, quantum Hall effects, and symmetry protected topological phases such as topological insulators. Ph/APh 223b will continue with BCS theory of superconductivity, Ginzburg-Landau theory, elements of unconventional and topological superconductors, theory of superfluidity, Bose-Hubbard model and bosonic Mott insulators, and some aspects of quantum systems with randomness.
Instructors: Alicea, Kitaev.

Ph 229 ab.
Advanced Mathematical Methods of Physics.
9 units (3-0-6):
second term.
Prerequisites: Ph 205 abc or equivalent.
A course on conformal field theory and the conformal bootstrap. Students should have some background in quantum field theory. Topics will include the renormalization group, phase transitions, universality, scale vs. conformal invariance, conformal symmetry, operator product expansion, state-operator correspondence, conformal blocks, the bootstrap equations, bootstrap in d=2 dimensions, numerical bootstrap methods in d>2, analytical bootstrap methods, introduction to AdS/CFT. Possible additional topics (time permitting) include superconformal field theories, entanglement entropy, monotonicity theorems, and conformal perturbation theory.
Instructor: Kapustin.

Ph 230 ab.
Elementary Particle Theory.
9 units (3-0-6):
first, third terms.
Prerequisites: Ph 205 abc or equivalent.
Advanced methods in quantum field theory. First term: introduction to supersymmetry, including the minimal supersymmetric extension of the standard model, supersymmetric grand unified theories, extended supersymmetry, supergravity, and supersymmetric theories in higher dimensions. Second term: Advanced topics will be chosen from nonperturbative phenomena in non-Abelian gauge field theories, including quark confinement, chiral sym-metry breaking, anomalies, instantons, the 1/N expansion, lattice gauge theories, and topological solitons.
Instructors: Zurek, Ooguri.

Ph 236 abc.
General Relativity.
9 units (3-0-6):
first, second terms.
Prerequisites: a mastery of special relativity at the level of Goldstein's Classical Mechanics, or of Jackson's Classical Electrodynamics.
A systematic exposition of Einstein's general theory of relativity and its applications to gravitational waves, black holes, relativistic stars, causal structure of space-time, cosmology and brane worlds. Offered in alternate years. Not offered 2020-21.

Ph 237.
Gravitational Radiation.
9 units (3-0-6):
.
Prerequisites: Ph 106 b, Ph 12 b or equivalents.
Special topics in Gravitational-wave Detection. Physics of interferometers, limits of measurement, coherent quantum feedback, noise, data analysis. Not offered 2020-21.

Ph 242 ab.
Physics Seminar.
4 units (2-0-2):
first, second terms.
An introduction to independent research, including training in relevant professional skills and discussion of current Caltech research areas with Caltech faculty, postdocs, and students. One meeting per week plus student projects. Registration restricted to first-year graduate students in physics.
Instructor: Patterson.

Ph 250.
Introduction to String Theory.
9 units (3-0-6):
second term.
Prerequisites: Ph 205 or equivalent.
This year, we offer a lighter version of the course. It will cover a condensed version of the world-sheet formulation, then basic elements of the target space physics, after which we will discuss interesting phenomena/applications, such as T-duality, D-branes, anomalies, building semi-realistic models of particle physics from string compactifications, etc.
Instructor: Gukov.

Ph 300.
Thesis Research.
Units in accordance with work accomplished:
.
Ph 300 is elected in place of Ph 172 when the student has progressed to the point where research leads directly toward the thesis for the degree of Doctor of Philosophy. Approval of the student's research supervisor and department adviser or registration representative must be obtained before registering. Graded pass/fail.

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