# Physics (Ph) Graduate Courses (2023-24)

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. Given in alternate years.
Not offered 2023-24.

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.
Instructor: Most.

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.
Instructors: Rice, Libbrecht.

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.

Ph 107.
Classical and Laser Optics.
9 units (3-0-6):
third term.
Prerequisites: Ph 2 ab or Ph 12 ab.
An introduction and overview of classical and laser optics. We will develop tools and concepts to understand the behavior of light, such as ray transfer matrix analysis, wave optics, diffraction, coherence, interference, and polarization. These tools will then be used to understand the action of optical elements, imaging, resonators, waveguides, fiber optics, Gaussian beams, interferometers, and other techniques and concepts commonly encountered in research settings.
Instructors: Hutzler, Adhikari.

APh/Ph 112 ab.
Noise and Stochastic Resonance.
9 units (3-0-6):
second term.
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 stochastic-based 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 color-based 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.
Part b not offered 2023-24.
Instructor: Troian.

Ph/APh/EE 118 c.
Physics of Measurement: Moonbounce and Beyond - Microwave Scattering for Communications and Metrology.
9 units (3-0-6):
third term.
Prerequisites: Ph 118a, and a course in microwave physics and engineering (e.g., Ph 118b, EE 153, or equivalent), or permission from the instructor.
In 1944, the possibility of bouncing radio waves off the moon was first discovered inadvertently. Since then, radio wave echoes have been recorded from other planets, asteroids, tropospheric disturbances, and airplanes aloft. Microwave scattering provides a rich platform enabling exploration of long-range microwave communications, remote sensing, and interesting astrophysical measurements. This class will cover the physics of microwave propagation and scattering, low-earth orbit (LEO) satellite trajectories and communications, moonbounce, and the principles of ultrasensitive instrumentation - for both transmitting and receiving - enabling remote sensing with microwaves. One formal lecture per week will cover the fundamentals. The second weekly class meeting will be an extended hands-on workshop - starting mid-afternoon and going on into the evening - to assemble all aspects of a high-power microwave scattering system operating at 23cm. Students will set up tracking software for satellites and planetary objects, assemble an ultrasensitive software-defined radio (SDR) system, implement 1kW microwave power amplification at 23cm, and explore antenna and feed horn theory and practice. Also implemented will be powerful weak signal communications methods pioneered by Prof. Joe Taylor (Physics, Princeton) enabling ultraweak signal extraction through GPS synchronization of remote sources and receivers. We will employ Caltech's fantastic resource for this project - a 6-meter diameter microwave dish atop Moore Laboratory. Prospective students are encouraged to obtain an FCC Technician license (or higher) prior to spring term to permit their operation of the system. For information see: http://www.its.caltech.edu/~w6ue/
Instructor: Roukes.

Ph/APh/EE/BE 118 ab.
Physics of Measurement.
9 units (3-0-6):
second term.
Prerequisites: Ph 127, APh 105, or equivalent, or permission from instructor.
This course explores the fundamental underpinnings of experimental measurements from the perspectives of information, noise, coupling, responsivity, and backaction. Its overarching goal is to enable students to develop intuition about a diversity of real measurement systems and the means to critically evaluate them. This involves developing a standard framework for estimating the ultimate and practical limits to information that can be extracted from a real measurement system. Topics will include the fundamental nature of information and signals, physical signal transduction and responsivity, the physical origin of noise processes, modulation, frequency conversion, synchronous detection, signal-sampling techniques, digitization, signal transforms, spectral analyses, and correlation methods. The first term will cover the essential underpinnings, while second-term topics will vary year-by-year according to interest. Among possible Ph118 b topics are: high frequency, microwave, and fast time-domain measurements; biological interfaces and biosensing; the physics of functional brain imaging; and quantum measurement.
Instructor: Roukes.

CS/Ph 120.
Quantum Cryptography.
9 units (3-0-6):
first term.
Prerequisites: Ma 1 b, Ph 2 b or Ph 12 b, 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 2023-24.
Instructor: Staff.

Ph 121 abc.
Computational Physics Lab.
6 units (0-6-0):
third term.
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 by 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.
Part a and part b not offered 2023-24.
Instructor: Motrunich.

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.
Instructors: Porter, Cheung.

Ph 127 ab.
Statistical Physics of Interacting Systems, Phases, and Phase Transitions.
9 units (4-0-5):
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 path-integral based quantum to classical statistical mechanics mapping, as well as dualities and topological-defects descriptions, with applications to magnets, superfluids, and gauge field theories.
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 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 2023-24.
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, and transport. In addition, the course will introduce topological band-structure 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: Ye.

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 136 a will focus on thermodynamics, statistical mechanics, random processes, and optics. Ph 136 b will focus on fluid dynamics, MHD, turbulence, and plasma physics. Ph 136 c will cover an introduction to general relativity. Given in alternate years.
Not offered 2023-24.

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. Each term can be taken independent of each other. The main emphasis is on laying the foundation for understanding current research that utilizes cold atoms and quantized light fields. First term: resonance phenomena, atomic structure, and the semi-classical interaction of atoms 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.
Instructors: Hutzler, Endres.

APh/Ph 138 ab.
Quantum Hardware and Techniques.
9 units (3-0-6):
third term, a and b offered in alternating years.
Prerequisites: Ph 125 abc or Ph 127 ab 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 modules covering various topics including solid state quantum bits, topological quantum matter, trapped atoms and ions, applications of near-term quantum computers, superconducting qubits. Topics will alternate from year to year.
Instructors: Faraon, Minnich.

Ph 139.
Introduction to Elementary Particle 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.

APh/Ph/MS 152.
Fundamentals of Fluid Flow in Small Scale Systems.
9 units (3-0-6):
second term.
Prerequisites: ACM 95/100 ab or equivalent.
Research efforts in many areas of applied science and engineering are increasingly focused on microsystems involving active or passive fluid flow confined to 1D, 2D or 3D platforms. Intrinsically large ratios of surface to volume can incur unusual surface forces and boundary effects essential to operation of microdevices for applications such as optofluidics, bioengineering, green energy harvesting and nanofilm lithography. This course offers a concise treatment of the fundamentals of fluidic behavior in small scale systems. Examples will be drawn from pulsatile, oscillatory and capillary flows, active and passive spreading of liquid dots and films, thermocapillary and electrowetting systems, and instabilities leading to self-sustaining patterns. Students must have working knowledge of vector calculus, ODEs, basic PDEs, and complex variables.
Not offered 2023-24.
Instructor: Troian.

APh/Ph/Ae/MS 153.
Fundamentals of Energy and Mass Transport in Small Scale Systems.
9 units (3-0-6):
third term.
Prerequisites: ACM 95/100 ab or equivalent.
The design of instrumentation for cooling, sensing or measurement in microsystems requires special knowledge of the evolution and propagation of thermal and concentration gradients in confined geometries, which ultimately control the degree of maximum energy and mass exchange. A significant challenge facing the microelectronics industry, for example, is mitigation of hot spots in densely packed high power chips for artificial intelligence to prevent thermal runaway. This course offers a concise treatment of the fundamentals of mass and energy transport by examining steady and unsteady diffusive and convective processes in small confined systems. Contrasts with macroscale behavior caused by the effects of small scale confinement and reduced dimensionality will be examined. Sample problems will be drawn from systems in applied physics, material science, electrical and bioengineering. Students must have working knowledge of vector calculus, ODEs, basic PDEs, and complex variables.
Instructor: Troian.

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. 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 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 6, 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):
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 decision-making during escape, one-shot learning, and large-capacity recognition memory.
Not offered 2023-2024.
Instructors: Meister, Rutishauser.

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 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 203.
Nuclear Physics.
9 units (3-0-6):
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.
Instructor: Filippone.

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, anomalies, the Weinberg-Salam model, and renormalization.
Instructor: Wise.

Ph/CS 219 abc.
Quantum Computation.
9 units (3-0-6):
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 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.
Instructors: Kitaev, Preskill.

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 223 a covers second quantization, Hartree-Fock theory of the electron gas, Mott insulators and quantum magnetism, spin liquids, bosonization, and the integer and fractional quantum Hall effect. Ph/APh 223 b continues with superfluidity and superconductivity; topics include the Bose-Hubbard model, Ginzburg-Landau theory, BCS theory, tunneling signatures of superconductivity, Josephson junctions, superconducting qubits, and topological superconductivity.
Instructor: Alicea.

Ph 229 abc.
Advanced Mathematical Methods of Physics.
9 units (3-0-6):
second, third 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 gauge-field theories and the theory of Riemann surfaces, with emphasis on applications to string theory.
Part c not offered 2023-24.
Instructor: Kapustin.

Ph 230 abc.
Elementary Particle Theory.
9 units (3-0-6):
first, second 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 not offered 2023-24.
Instructors: Simmons-Duffin, Ooguri.

Ph 232.
Introduction to Topological Field Theory.
9 units (3-0-6):
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 3-manifolds and 4-manifolds. 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.
Not offered 2023-24.

Ph 235 ab.
Theoretical Cosmology and Astroparticle Physics.
9 units (3-0-6):
first, second terms.
Prerequisites: General Relativity at the level of Ph 236 a, and Quantum Field Theory at the level of Ph 205 a.
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.
Instructor: Zurek.

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. Given in alternate years.
Part c not offered 2023-24.
Instructors: Chatziioannou, Teukolsky.

Ph 237.
Gravitational Radiation.
9 units (3-0-6):
third term.
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.
Instructor: Y. Chen.

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: Libbrecht.

Ph 250.
Introduction to String Theory.
9 units (3-0-6):
second term.
Prerequisites: Ph 205 or equivalent.
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.

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.