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Ph 1 abc
Classical Mechanics and Electromagnetism
9 units (405)

first, second, third terms
The first year of a twoyear course in introductory classical and modern physics. Topics: Newtonian mechanics in Ph 1 a; electricity and magnetism, and special relativity, in Ph 1 b, c. Emphasis on physical insight and problem solving. Ph 1 b, c is divided into two tracks: the Practical Track emphasizing practical electricity, and the Analytic Track, which teaches and uses methods of multivariable calculus. Students enrolled in the Practical Track are encouraged to take Ph 8 bc concurrently. Students will be given information helping them to choose a track at the end of fall term.
Instructors:
Cheung, Hsieh, Refael, Cissé
Ph 2 abc
Waves, Quantum Mechanics, and Statistical Physics
9 units (306)

first, second, third terms
Prerequisites: Ph 1 abc, Ma 1 abc.
An introduction to several areas of physics including applications in modern science and engineering. Topics include discrete and continuous oscillatory systems, wave mechanics, applications in telecommunications and other areas (first term); foundational quantum concepts, the quantum harmonic oscillator, the Hydrogen atom, applications in optical and semiconductor systems (second term); ensembles and statistical systems, thermodynamic laws, applications in energy technology and other areas (third term). Although best taken in sequence, the three terms can be taken independently.
Instructors:
Porter, Cheung, Adhikari
Ph 3
Introductory Physics Laboratory
6 units (033)

first, second, third terms
Prerequisites: Ph 1 a or instructor's permission.
Introduction to experimental physics and data analysis, with techniques relevant to all fields that deal in quantitative data. Specific physics topics include ion trapping, harmonic motion, mechanical resonance, and precision interferometry. Broader skills covered include introductions to essential electronic equipment used in modern research labs, basic digital data acquisition and analysis, statistical interpretation of quantitative data, professional record keeping and documentation of experimental research, and an introduction to the Mathematica programming language. Only one term may be taken for credit.
Instructors:
Black, Libbrecht
FS/Ph 4
Freshman Seminar: Astrophysics and Cosmology with Open Data
6 units (303)

first term
Astrophysics and cosmology are in the midst of a golden age of sciencerich observations from incredibly powerful telescopes of various kinds. The data from these instruments are often freely available on the web. Anyone can do things like study xrays from pulsars in our galaxy or gamma rays from distant galaxies using data from Swift and Fermi; discover planets eclipsing nearby stars using data from Kepler; measure the expansion of the universe using supernovae data; study the cosmic microwave background with data from Planck; find gravitational waves from binary black hole mergers using data from LIGO; and study the clustering of galaxies using Hubble data. We will explore some of these data sets and the science than can be extracted from them. A primary goal of this class is to develop skills in scientific computing and visualizationbring your laptop! Not offered 202122.
Ph 5
Analog Electronics for Physicists
9 units (054)

first term
Prerequisites: Ph1abc, Ma1abc, Ma2 taken concurrently.
A fastpaced laboratory course covering the design, construction, and testing of practical analog and interface circuits, with emphasis on applications of operational amplifiers. No prior experience with electronics is required. Basic linear and nonlinear elements and circuits are studied, including amplifiers, filters, oscillators and other signal conditioning circuits. Each week includes a 45 minute lecture/recitation and a 2½ hour laboratory. The course culminates in a twoweek project of the student's choosing.
Instructors:
Rice, Libbrecht
Ph 6
Physics Laboratory
9 units

second term
Prerequisites: Ph 2 a or Ph 12 a, Ma 2, Ph 3, Ph 2 b or Ph 12 b (may be taken concurrently), Ma 3 (may be taken concurrently).
A laboratory introduction to experimental physics and data analysis. Experiments use researchgrade equipment and techniques to investigate topics in classical electrodynamics, resonance phenomena, waves, and other physical phenomena. Students develop critical, quantitative evaluations of the relevant physical theories; they work individually and choose which experiments to conduct. Each week includes a 30minute individual recitation and a 3 hour laboratory.
Instructors:
Rice, Politzer
Ph 7
Physics Laboratory
9 units

third term
Prerequisites: Ph6, Ph2b or Ph12b, Ph2c or Ph12c taken concurrently.
A laboratory course continuing the study of experimental physics introduced in Physics 6. The course introduces some of the equipment and techniques used in quantum, condensed matter, nuclear, and particle physics. The menu of experiments includes some classics which informed the development of the modern quantum theory, including electron diffraction, the SternGerlach experiment, Compton scattering, and the Mössbauer Effect. The course format follows that of Physics 6: students work individually and choose which experiments to conduct, and each week includes a 30 minute individual recitation and a 3 hour laboratory.
Instructors:
Rice, Politzer
Ph 8 bc
Experiments in Electromagnetism
3 units (030)

second, third terms
Prerequisites: Ph 1 a.
A twoterm sequence of experiments that parallel the material of Ph 1 bc. It includes measuring the force between wires with a homemade analytical balance, measuring properties of a 1,000volt spark, and building and studying a radiowave transmitter and receiver. The takehome experiments are constructed from a kit of tools and electronic parts. Measurements are compared to theoretical expectations.
Instructor:
Spiropulu
FS/Ph 9
Freshman Seminar: The Science of Music
6 units (204)

first term
This course will focus on the physics of sound, how musical instruments make it, and how we hear it, including readings, discussions, demonstrations, and student observations using sound analysis software. In parallel we will consider what differentiates music from other sounds, and its role psychically and culturally. Students will do a final project of their choice and design, with possibilities including a book review, analysis of recordings of actual musical instruments, or instrument construction and analysis. Freshmen only; limited enrollment.
Instructor:
Politzer
Ph 10
Frontiers in Physics
3 units (201)

first term
Open for credit to freshmen and sophomores. Weekly seminar by a member of the physics department or a visitor, to discuss his or her research at an introductory level; the other class meetings will be used to explore background material related to seminar topics and to answer questions that arise. The course will also help students find faculty sponsors for individual research projects. Graded pass/fail.
Instructor:
Spiropulu
FS/Ph 11 abc
Freshman Seminar: Beyond Physics
6 units (204)

second, third terms of freshman year and first term of sophomore year
Freshmen are offered the opportunity to enroll in this class by submitting potential solutions to problems posed in the fall term. A small number of solutions will be selected as winners, granting those students permission to register. This course demonstrates how research ideas arise, are evaluated, and tested and how the ideas that survive are developed. Weekly group discussions and oneonone meetings with faculty allow students to delve into cutting edge scientific research. Ideas from physics are used to think about a huge swath of problems ranging from how to detect life on extrasolar planets to exploring the scientific underpinnings of science fiction in Hollywood films to considering the efficiency of molecular machines. Support for summer research at Caltech between freshman and sophomore years will be automatic for students making satisfactory progress. Graded pass/fail. Freshmen only; limited enrollment.
Instructor:
Phillips
Ph 12 abc
Waves, Quantum Physics, and Statistical Mechanics
9 units (405)

first, second, third terms
Prerequisites: Ph 1 abc, Ma 1 abc, or equivalents.
A oneyear course primarily for students intending further work in the physics option. Topics include classical waves; wave mechanics, interpretation of the quantum wavefunction, onedimensional bound states, scattering, and tunneling; thermodynamics, introductory kinetic theory, and quantum statistics. Chen, Filippone, Patterson.
Instructor:
X
Ph 20
Computational Physics Laboratory I
6 units (060)

first, second, third terms
Prerequisites: CS 1 or equivalent.
Introduction to the tools of scientific computing. Use of numerical algorithms and symbolic manipulation packages for solution of physical problems. Python for scientific programming, Mathematica for symbolic manipulation, Unix tools for software development.
Instructors:
Mach, Weinstein
Ph 21
Computational Physics Laboratory II
6 units (060)

first, second, third terms
Prerequisites: Ph 20 or equivalent experience with programming.
Computational tools for data analysis. Use of python for accessing scientific data from the web. Bayesian techniques. Fourier techniques. Image manipulation with python.
Instructors:
Mach, Weinstein
Ph 22
Computational Physics Laboratory III
6 units (060)

first, second, third terms
Prerequisites: Ph 20 or equivalent experience with programming and numerical techniques.
Computational tools and numerical techniques. Applications to problems in classical mechanics. Numerical solution of 3body and Nbody systems. Monte Carlo integration.
Instructors:
Mach, Weinstein
Ph 50 ab
Caltech Physics League
3 units (102)

first, second terms
Prerequisites: Ph 1 abc.
This course serves as a physics club, meeting weekly to discuss and analyze realworld problems in physical sciences. A broad range of topics will be considered, such as energy production, space and atmospheric phenomena, astrophysics, nanoscience, and others. Students will use basic physics knowledge to produce simplified (and perhaps speculative) models of complex natural phenomena. In addition to regular assignments, students will also compete in solving challenge problems each quarter with prizes given in recognition of the best solutions. Not offered 202122.
Ph 70
Oral and Written Communication
6 units (204)

first, second, third terms
Provides practice and guidance in oral and written communication of material related to contemporary physics research. Students will choose a topic of interest, make presentations of this material in a variety of formats, and, through a guided process, draft and revise a technical or review article on the topic. The course is intended for senior physics majors. Fulfills the Institute scientific writing requirement.
Instructor:
Hitlin
Ph 77 abc
Advanced Physics Laboratory
9 units (054)

first, second, third terms
Prerequisites: Ph 7 or instructor's permission.
Advanced preparation for laboratory research. Dual emphasis on practical skills used in modern research groups and historic experiments that illuminate important theoretical concepts. Topics include advanced signal acquisition, conditioning, and data processing, introductions to widelyused optical devices and techniques, laserfrequency stabilization, and classic experiments such as magnetic resonance, optical pumping, and dopplerfree spectroscopy. Fundamentals of vacuum engineering, thinfilm sample growth, and cryogenics are occasionally offered. Special topics and studentled projects are available on request.
Instructors:
Black, Libbrecht
Ph 78 abc
Senior Thesis (Experiment)
9 units

first, second, third terms
Prerequisites: To register for this course, the student must obtain approval of the chair of the Physics Undergraduate Committee (Ken Libbrecht).
Open only to senior physics majors. Experimental research must be supervised by a faculty member, the student's thesis adviser. Two 15minute presentations to the Physics Undergraduate Committee are required, one near the end of the first term and one near the end of third term. The written thesis must be completed and distributed to the committee one week before the second presentation. Students wishing assistance in finding an adviser and/or a topic for a senior thesis are invited to consult with the chair of the Physics Undergraduate Committee, or any other member of this committee. A grade will not be assigned in Ph 78 untli the end of the third term. P grades will be given the first two terms, and then changed at the end of the course to the appropriate letter grade. Not offered on a pass/fail basis.
Ph 79 abc
Senior Thesis (Theory)
9 units

first, second, third terms
Prerequisites: To register for this course, the student must obtain approval of the chair of the Physics Undergraduate Committee (Ken Libbrecht).
Open only to senior physics majors. Theoretical research must be supervised by a faculty member, the student's thesis adviser. Two 15minute presentations to the Physics Undergraduate Committee are required, one near the end of the first term and one near the end of third term. The written thesis must be completed and distributed to the committee one week before the second presentation. Students wishing assistance in finding an adviser and/or a topic for a senior thesis are invited to consult with the chair of the Physics Undergraduate Committee, or any other member of this committee. A grade will not be assigned in Ph 79 until the end of the third term. P grades will be given the first two terms, and then changed at the end of the course to the appropriate letter grade. Not offered on a pass/fail basis.
Ph 101
OrderofMagnitude Physics
9 units (306)

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. Not offered 202122.
Ay/Ph 104
Relativistic Astrophysics
9 units (306)

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, Xray binaries, gammaray bursts; (black holes) Xray transients, tidal disruption and quasars/active galaxies and sources of gravitational waves.
Instructor:
Kasliwal
Ph 105
Analog Electronics for Physicists
9 units

first term
Prerequisites: Ph1abc, Ma2, 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 twoweek project of the student's choosing.
Instructors:
Rice, Libbrecht
Ph 106 abc
Topics in Classical Physics
9 units (405)

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. Ph106a will be devoted to mechanics, including Lagrangian and Hamiltonian formulations of mechanics, small oscillations and normal modes, central forces, and rigidbody motion. Ph106b will be devoted to fundamentals of electrostatics, magnetostatics, and electrodynamics, including boundaryvalue problems, multipole expansions, electromagnetic waves, and radiation. It will also cover special relativity. Ph106c will cover advanced topics in electromagnetism and an introduction to classical optics.
Instructors:
Fuller, Golwala
APh/Ph 112 ab
Noise and Stochastic Resonance
9 units (306)

second, third terms
Prerequisites: Ph 12 abc, ACM 95/100 ab and Ph 106 abc, equivalent background, or instructor's permission.
The presence of noise in experimental systems is often regarded as a nuisance since it diminishes the signal to noise ratio thereby obfuscating weak signals or patterns. From a theoretical perspective, noise is also problematic since its influence cannot be elicited from deterministic equations but requires stochasticbased modeling which incorporates various types of noise and correlation functions. In general, extraction of embedded information requires that a threshold be overcome in order to outweigh concealment by noise. However, even below threshold, it has been demonstrated in numerous systems that external forcing coupled with noise can actually boost very weak signatures beyond threshold by a phenomenon known as stochastic resonance. Although it was originally demonstrated in nonlinear systems, more recent studies have revealed this phenomenon can occur in linear systems subject, for example, to colorbased noise. Techniques for optimizing stochastic resonance are now revolutionizing modeling and measurement theory in many fields ranging from nonlinear optics and electrical systems to condensed matter physics, neurophysiology, hydrodynamics, climate research and even finance. This course will be conducted in survey and seminar style and is expected to appeal to theorists and experimentalists alike. Review of the current literature will be complimented by background readings and lectures on statistical physics and stochastic processes as needed.
Instructor:
Troian
APh/Ph 115
Physics of Momentum Transport in Hydrodynamic Systems
9 units (306)

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 selfcontained 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, selfsimilarity 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. Not offered 20212022.
Instructor:
Troian
APh/Ph/Ae 116
Physics of Thermal and Mass Transport in Hydrodynamic Systems
9 units (306)

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 convectiondiffusion and reactiondiffusion. Topics will include Fickian dynamics, thermal transfer in Peltier devices, LifshitzSlyozov growth during phase separation, thermocouple measurements of oscillatory fields, reactiondiffusion 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, SturmLiouville and Green's function analysis will be taught in class as needed. Not offered 20212022.
Instructor:
Troian
Ph/APh/EE/BE 118 ab
Physics of Measurement
9 units (306)

second, third terms
Prerequisites: Ph 127, APh 105, or equivalent, or permission from instructor.
This course explores the fundamental underpinnings of experimental measurements from the perspectives of coupling, responsivity, noise, backaction, and information. Its overarching goal is to enable students to develop intuition about, and to critically evaluate, a diversity of real measurement systems  and to provide a framework for estimating the ultimate 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, signalsampling techniques, digitization, signal transforms, spectral analyses, and correlation methods. The first term will cover the essential fundamental underpinnings, while topics in second term will focus their application to high frequency, microwave, and fast timedomain measurements where distributed approaches become imperative. The second term (in alternate years) may focus on topics that include either measurements at the quantum limit, biosensing and biological interfaces, of functional brain imaging. Not offered 202122.
Instructor:
Roukes
CS/Ph 120
Quantum Cryptography
9 units (306)

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 deviceindependent quantum cryptography as well as other cryptographic tasks and protocols, such as bit commitment or positionbased cryptography. Not offered 20212022
Ph 121 abc
Computational Physics Lab
6 units (060)

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 manybody physics). This course will primarily be in Python and Mathematica. This course is offered pass/fail.
Instructors:
SimmonsDuffin, Refael
Ph 125 abc
Quantum Mechanics
9 units (405)

first, second, third terms
Prerequisites: Ma 2 ab, Ph 12 abc or Ph 2 ab, or equivalents.
A oneyear course in quantum mechanics and its applications, for students who have completed Ph 12 or Ph 2. Wave mechanics in 3D, scattering theory, Hilbert spaces, matrix mechanics, angular momentum, symmetries, spin1/2 systems, approximation methods, identical particles, and selected topics in atomic, solidstate, nuclear, and particle physics. Chen.
Instructors:
Wise, Porter, Y
Ph 127 ab
Statistical Physics of Interacting Systems, Phases, and Phase Transitions
9 units (405)

first, second terms
Prerequisites: Ph 12 c or equivalent; quantum mechanics at the level of Ph 125 ab is required for Ph 127 b; may be taken concurrently.
An advanced course in statistical physics that focuses on systems of interacting particles. Part a will cover interacting gases and spin models of magnetism, phase transitions and broken symmetries, classical field theories, and renormalization group approach to collective phenomena. Part b will introduce the pathintegral based quantum to classical statistical mechanics mapping, as well as dualities and topologicaldefects descriptions, with applications to magnets, superfluids, and gauge field theories.
Instructor:
Motrunich
Ph 129 abc
Mathematical Methods of Physics
9 units (405)

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 methods such as complex analysis, differential equations, integral equations and transforms, and other applications of real analysis. Third term covers probability and statistics in physics. Each part may be taken independently. Part c not offered 20212022. Chen, Chatziioannou.
Instructor:
X
Ph 135
Introduction to Condensed Matter
9 units (306)

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, and transport. In addition, the course will introduce topological bandstructure effects, covering Berry phase, the Thouless pump, and topological insulators. Ph 135 is continued by Ph/APh 223 ab in the winter and spring terms.
Instructor:
Refael
Ph 136 abc
Applications of Classical Physics
9 units (306)

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. Not offered 202122.
Ph/APh 137 abc
Atoms and Photons
9 units (306)

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 semiclassical 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 20212022]: 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 (306)

third term, a and b offered in alternating years
Prerequisites: Ph 125abc or Ph 127ab or Ph137ab 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 threeweek modules covering: applications of nearterm quantum computers, superconducting qubits, trapped atoms and ions, topological quantum matter, solid state quantum bits, tensorproduct states.
Instructors:
Faraon, Minnich
Ph 139
Introduction to Elementary Particle Physics
9 units (306)

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, astroparticle 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 (045)

second, third terms
Prerequisites: Ph 6, Ph 106 a, Ph 125 a or equivalents.
A oneterm 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 (306)

third term
Prerequisites: introductory neuroscience (Bi 150 or equivalent); mathematical methods (Bi 195 or equivalent); scientific programming.
This course aims at a quantitative understanding of how the nervous system computes. The goal is to link phenomena across scales from membrane proteins to cells, circuits, brain systems, and behavior. We will learn how to formulate these connections in terms of mathematical models, how to test these models experimentally, and how to interpret experimental data quantitatively. The concepts will be developed with motivation from some of the fascinating phenomena of animal behavior, such as: aerobatic control of insect flight, precise localization of sounds, sensing of single photons, reliable navigation and homing, rapid decisionmaking during escape, oneshot learning, and largecapacity recognition memory.
Instructors:
Meister, Rutishauser
Ph 198
Special Topics in Physics
Units in accordance with work accomplished
Topics will vary year to year and may include handson laboratory work, team projects and a survey of modern physics research.
Instructor:
Staff
Ph 199
Frontiers of Fundamental Physics
9 units (306)

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 firstyear graduate students who are not in particle physics, although students in particle physics are welcome to attend. Not offered 20212022.
Ph 201
Candidacy Physics Fitness
9 units (306)

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 203
Nuclear Physics
9 units (306)

third term
Prerequisites: Ph 125 or equivalent.
An introduction and overview of modern topics in nuclear physics, including models and structure of nucleons, nuclei and nuclear matter, the electroweak interaction of nuclei, and nuclear/neutrino astrophysics. Not offered 20212022.
Instructor:
Filippone
Ph 205 abc
Relativistic Quantum Field Theory
9 units (306)

first, second, third terms
Prerequisites: Ph 125.
Topics: the Dirac equation, second quantization, quantum electrodynamics, scattering theory, Feynman diagrams, nonAbelian gauge theories, Higgs symmetrybreaking, the WeinbergSalam model, and renormalization.
Instructors:
Kapustin, Zurek, Wise
Ph/CS 219 abc
Quantum Computation
9 units (306)

first, second, third 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 errorcorrecting codes, quantum cryptography and teleportation. Overview of classical complexity theory, quantum complexity, efficient quantum algorithms, faulttolerant quantum computation, physical implementations of quantum computation.
Instructors:
Preskill, Kitaev
Ph/APh 223 ab
Advanced CondensedMatter Physics
9 units (306)

second, third terms
Prerequisites: Ph 135 or equivalent, or instructor's permission.
Advanced topics in condensedmatter physics, with emphasis on the effects of interactions, symmetry, and topology in manybody systems. Ph/APh 223a covers second quantization, HartreeFock theory of the electron gas, Mott insulators and quantum magnetism, spin liquids, bosonization, and the integer and fractional quantum Hall effect. Ph/APh 223b will continue with BCS theory of superconductivity, GinzburgLandau theory, elements of unconventional and topological superconductors, theory of superfluidity, BoseHubbard model and bosonic Mott insulators, and some aspects of quantum systems with randomness.
Instructor:
Alicea
Ph 229 abc
Advanced Mathematical Methods of Physics
9 units (306)

first, second terms
Prerequisites: Ph 129 abc or equivalent.
Advanced topics in geometry and topology that are widely used in modern theoretical physics. Emphasis will be on understanding and applications more than on rigor and proofs. First term will cover basic concepts in topology and manifold theory. Second term will include Riemannian geometry, fiber bundles, characteristic classes, and index theorems. Third term will include anomalies in gaugefield theories and the theory of Riemann surfaces, with emphasis on applications to string theory. Part c will not be offered in 20212022.
Instructors:
Ooguri, Kapustin
Ph 230 abc
Elementary Particle Theory
9 units (306)

first, third terms
Prerequisites: Ph 205 abc or equivalent.
First term: Standard model, including electroweak and strong interactions, symmetries and symmetry breaking (including the Higgs mechanism), parton model and quark confinement, anomalies. Second and third terms: more on nonperturbative phenomena, including chiral symmetry breaking, instantons, the 1/N expansion, lattice gauge theories, and topological solitons. Other topics include topological field theory, precision electroweak, flavor physics, conformal field theory and the AdS/CFT correspondence, supersymmetry, Grand Unified Theories, and Physics Beyond the Standard Model. Part c will not be offered in 20212022.
Instructors:
Zurek, Gukov
Ph 232
Introduction to Topological Field Theory
9 units (306)

first term
Prerequisites: Ph 205.
Topological field theories are the simplest examples of quantum field theories which, in a sense, are exactly solvable and generally covariant. During the past twenty years they have been the main source of interaction between physics and mathematics. Thus, ideas from gauge theory led to the discovery of new topological invariants for 3manifolds and 4manifolds. By now, topological quantum field theory (TQFT) has evolved into a vast subject, and the main goal of this course is to give an accessible introduction to this elegant subject.
Instructor:
Gukov
Ph 235 ab
Theoretical Cosmology and Astroparticle Physics
9 units (306)

first term
Prerequisites: General Relativity at the level of Ph 236a, and Quantum Field Theory at the level of Ph 205a.
Cosmology in an expanding universe, inflation, big bang nucleosynthesis, baryogenesis, neutrino and nuclear astrophysics. Second term: Cosmological perturbation theory and the cosmic microwave background, structure formation, theories of dark matter. Not offered 20212022.
Instructor:
Zurek
Ph 236 abc
General Relativity
9 units (306)

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 spacetime, cosmology and brane worlds. Offered in alternate years. Part c will not be offered in 20212022.
Instructors:
Chatziioannou, Teukolsky
Ph 237
Gravitational Radiation
9 units (306)

third term
Prerequisites: Ph 106 b, Ph 12 b or equivalents.
Special topics in Gravitationalwave Detection. Physics of interferometers, limits of measurement, coherent quantum feedback, noise, data analysis. Chen.
Instructor:
Y
Ph 242 ab
Physics Seminar
4 units (202)

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 firstyear graduate students in physics.
Instructor:
Patterson
Ph 250
Introduction to String Theory
9 units (306)

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 worldsheet formulation, then basic elements of the target space physics, after which we will discuss interesting phenomena/applications, such as Tduality, Dbranes, anomalies, building semirealistic models of particle physics from string compactifications, etc. Not offered 20212022.
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.
Published Date:
July 28, 2022