Results for PHYSICS

Topics include measurements of temperature and sea level changes in the climate record of the Earth, satellite atmospheric spectroscopy, satellite gravity geodesy measurements of changes in water aquifers and glaciers, and ocean changes. The difference between weather fluctuations changes and climate change, climate models and their uncertainties in the context of physical, chemical and biological feedback mechanisms to changes in greenhouse gases and solar insolation will be discussed. Energy efficiency, transmission and distribution of electricity, energy storage, and the physics of harnessing fossil, wind, solar, geothermal, fission and fusion will be covered, along with prospects of future technological developments in energy use and production. Prerequisite: Physics 40 or Physics 60 series.

Lagrangian and Hamiltonian mechanics. Principle of least action, Euler-Lagrange equations. Small oscillations and beyond. Symmetries, canonical transformations, Hamilton-Jacobi theory, action-angle variables. Introduction to classical field theory. Selected other topics, including nonlinear dynamical systems, attractors, chaotic motion. Undergraduates register for Physics 110 (4 units). Graduates register for Physics 210 (3 units). Prerequisites: MATH 131P or PHYSICS 111. Recommended prerequisite: PHYSICS 130.

Elasticity, fluids, turbulence, waves, gas dynamics, shocks, and MHD plasmas. Examples from everyday phenomena, geophysics, and astrophysics.

Principles, ensembles, statistical equilibrium. Thermodynamic functions, ideal and near-ideal gases. Fluctuations. Mean-field description of phase-transitions and associated critical exponents. One-dimensional Ising model and other exact solutions. Renormalization and scaling relations. Prerequisites: PHYSICS 131, 171, or equivalents.

This course will cover order of magnitude or approximate, low-tech approaches to estimating physical effects in various systems. One goal is to promote a synthesis of understanding of basic physics (including quantum mechanics, electromagnetism, and physics of fluids) through solving various classic problems. Another goal will be to learn how to decide which terms in complicated equations can be omitted or simplified - and to obtain general features of the solution without solving them in their full complexity. We will be applying techniques such as scaling and dimensional analysis - with the overarching goal to develop physical intuition.

Special relativity: The principles of relativity, Lorentz transformations, four vectors and tensors, relativistic mechanics and the principle of least action. Lagrangian formulation, charges in electromagnetic fields, gauge invariance, the electromagnetic field tensor, covariant equations of electrodynamics and mechanics, four-current and continuity equation. Noether's theorem and conservation laws, Poynting's theorem, stress-energy tensor. Constant electromagnetic fields: conductors and dielectrics, magnetic media, electric and magnetic forces, and energy. Electromagnetic waves: Plane and monochromatic waves, spectral resolution, polarization, electromagnetic properties of matter, dispersion relations, wave guides and cavities. Prerequisites: PHYSICS 121 and PHYSICS 210, or equivalent; MATH 106 or MATH 116, and MATH 132 or equivalent.

Theoretical analysis of dynamical processes: dynamical systems, stochastic processes, and spatiotemporal dynamics. Motivations and applications from biology and physics. Emphasis is on methods including qualitative approaches, asymptotics, and multiple scale analysis. Prerequisites: ordinary and partial differential equations, complex analysis, and probability or statistical physics.

Fundamental concepts. Introduction to Hilbert spaces and Dirac's notation. Postulates applied to simple systems, including those with periodic structure. Symmetry operations and gauge transformation. The path integral formulation of quantum statistical mechanics. Problems related to measurement theory. The quantum theory of angular momenta and central potential problems. Prerequisite: PHYSICS 131 or equivalent.

Basis for higher level courses on atomic solid state and particle physics. Problems related to measurement theory and introduction to quantum computing. Approximation methods for time-independent and time-dependent perturbations. Semiclassical and quantum theory of radiation, second quantization of radiation and matter fields. Systems of identical particles and many electron atoms and molecules. Prerequisite: PHYSICS 230.

Scattering theory, partial wave expansion, Born approximation. Additional topics may include nature of quantum measurement, EPR paradox, Bell's inequality, and topics in quantum information science; path integrals and applications; Berry's phase; structure of multi-electron atoms (Hartree-Fock); relativistic quantum mechanics (Dirac equation). Undergraduates register for PHYSICS 134 (4 units). Graduate students register for PHYSICS 234 (3 units). Prerequisite: PHYSICS 131.

Energy as a consumable. Forms and interconvertability. World Joule budget. Equivalents in rivers, oil pipelines and nuclear weapons. Quantum mechanics of fire, batteries and fuel cells. Hydrocarbon and hydrogen synthesis. Fundamental limits to mechanical, electrical and magnetic strengths of materials. Flywheels, capacitors and high pressure tanks. Principles of AC and DC power transmission. Impossibility of pure electricity storage. Surge and peaking. Solar constant. Photovoltaic and thermal solar conversion. Physical limits on agriculture.

Radioactivity. Elementary nuclear processes. Energetics of fission and fusion. Cross-sections and resonances. Fissionable and fertile isotopes. Neutron budgets. Light water, heavy water and graphite reactors. World nuclear energy production. World reserves of uranium and thorium. Plutonium, reprocessing and proliferation. Half lives of fission decay products and actinides made by neutron capture. Nuclear waste. Three Mile Island and Chernobyl. Molten sodium breeders. Generation-IV reactors. Inertial confinement and magnetic fusion. Laser compression. Fast neutron production and fission-fusion hybrids. Prerequisities: Strong undergraduate background in elementary chemistry and physics. PHYSICS 240 and PHYSICS 252 recommended but not required. Interested undergraduates encouraged to enroll, with permission of instructor.

Elementary particles and the fundamental forces. Quarks and leptons. The mediators of the electromagnetic, weak and strong interactions. Interaction of particles with matter; particle acceleration, and detection techniques. Symmetries and conservation laws. Bound states. Decay rates. Cross sections. Feynman diagrams. Introduction to Feynman integrals. The Dirac equation. Feynman rules for quantum electrodynamics and for chromodynamics. Undergraduates register for PHYSICS 152. Graduate students register for PHYSICS 252. (Graduate students will be required to complete additional assignments in a format determined by the instructor.) Prerequisite: PHYSICS 130.

Radiative processes. Observed characteristics of stars and the Milky Way galaxy. Physical processes in stars and matter under extreme conditions. Structure and evolution of stars from birth to death. White dwarfs, planetary nebulae, supernovae, neutron stars, pulsars, binary stars, x-ray stars, and black holes. Galactic structure, interstellar medium, molecular clouds, HI and HII regions, star formation, and element abundances. Undergraduates register for PHYSICS 160. Graduate students register for PHYSICS 260. Pre-requisite: Physics 120 or permission of instructor. Recommended: Some familiarity with plotting and basic numerical calculations.

What do we know about the physical origins, content, and evolution of the Universe -- and how do we know it? Students learn how cosmological distances and times, and the geometry and expansion of space, are described and measured. Composition of the Universe. Origin of matter and the elements. Observational evidence for dark matter and dark energy. Thermal history of the Universe, from inflation to the present. Emergence of large-scale structure from quantum perturbations in the early Universe. Astrophysical tools used to learn about the Universe. Big open questions in cosmology. Undergraduates register for Physics 161. Graduates register for Physics 261. (Graduate students will be required to complete additional assignments in a format determined by the instructor.) Prerequisite: PHYSICS 120 or equivalent.

Einstein's General Theory of Relativity is a basis for modern ideas of fundamental physics, including string theory, as well as for studies of cosmology and astrophysics. The course begins with an overview of special relativity, and the description of gravity as arising from curved space. From Riemannian geometry and the geodesic equations, to curvature, the energy-momentum tensor, and the Einstein field equations. Applications of General Relativity: topics may include experimental tests of General Relativity and the weak-field limit, black holes (Schwarzschild, charged Reissner-Nordstrom, and rotating Kerr black holes), gravitational waves (including detection methods), and an introduction to cosmology (including cosmic microwave background radiation, dark energy, and experimental probes). Prerequisite: PHYSICS 121 or equivalent including special relativity.

Statistical methods constitute a fundamental tool for the analysis and interpretation of experimental physics data. In this course, students will learn the foundations of statistical data analysis methods and how to apply them to the analysis of experimental data. Problem sets will include data-sets from real experiments and require the use of programming tools to extract physics results. Topics include probability and statistics, experimental uncertainties, parameter estimation, confidence limits, and hypothesis testing. Students will be required to complete a final project.

(Formerly numbered PHYSICS 366) Foundations of principled inference from data, primarily in the Bayesian framework, with applications in astrophysics and cosmology. Topics include probabilistic modeling of data, parameter constraints and model comparison, numerical methods including Markov Chain Monte Carlo, and connections to frequentist and machine learning frameworks. The course is organized around tutorial notebooks using Python and Numpy, providing hands-on experience with real data. Prerequisites: programming in Python at the level of CS 106A or PHYSICS 113; probability at the level of STATS 116, CS 109, or PHYSICS 166/266; or permission of instructor. Normally offered every 2 years.

Relativistic fermions, Weyl and Dirac equations, Majorana masses. Electroweak theory, neutrino cross sections, neutrino refraction in matter, MSW effect. Three-flavor oscillations, charge-parity violation, searches for sterile neutrinos, modern long- and short-baseline oscillation experiments. Seesaw mechanism, models of neutrino masses, lepton flavor violation. Neutrinoless double beta decay. Cosmological constraints on neutrino properties. Advanced topics, such as collective oscillations in supernovae or ultrahigh energy neutrinos, offered as optional projects. The material in this course is largely complementary to PHYS 269, focusing on particle physics aspects of neutrinos. Prerequisites: PHYSICS 121, 131 and 171 or equivalent. PHYS 230-231, 269, 152 and 161 or equivalent are helpful, but not required.

Basic neutrino properties. Flavor evolution in vacuum and in matter. Oscillations of atmospheric, reactor and beam neutrinos. Measurements of solar neutrinos; physics of level-crossing and the resolution of the solar neutrino problem. Roles of neutrinos in stellar evolution; bounds from stellar cooling. Neutrinos and stellar collapse; energy transport, collective flavor oscillations, neutrino flavor in turbulent medium. Ultra-high-energy neutrinos. The cosmic neutrino background, its impact on the cosmic microwave background and structure formation; cosmological bounds on the neutrino sector. Prerequisites/corerequisites: PHYSICS 121, 131 and 171 or equivalent. PHYS 230-231, 152 and 161 or equivalent are helpful, but not required. May be repeat for credit

The strange behavior of electrons in metals or semiconductors at length scales below 1 micron, smaller than familiar macroscopic objects but larger than atoms. Ballistic transport, Coulomb blockade, localization, quantum mechanical interference, persistent currents, graphene, topological insulators, 1D wires. After a few background lectures, students come to each class session prepared to discuss one or more classic review articles or recent experimental publications.Prerequisite: undergraduate quantum mechanics and solid state physics preferred; physicists, engineers, chemists welcome.

Electrons in low-dimensional and narrow-band systems often display novel and extreme properties - unconventional superconductivity quantum hall effects, quantum mechanical interference, and localization, interplay of correlation and topology, natural and engineered (e.g., twist stacking) narrow-band systems with rich and unexpected behavior. After a few background lectures, students come to each class session prepared to discuss one or more classic review articles or recent experimental publications. Prerequisite: undergraduate quantum mechanics and solid-state physics preferred; physicists, engineers, and chemists welcome.

Introduction to the physics of quantum optics and atoms in the ultracold setting. Quantum gases and photons are employed in quantum simulation, sensing, and computation. Modern atomic physics and quantum optics will be covered, including laser cooling and trapping, ultracold collisions, optical lattices, ion traps, cavity QED, BEC and quantum degenerate Fermi gases, and quantum phase transitions in quantum gases and lattices. Prerequisites: Undergraduate quantum and statistical mechanics courses.

Required of first-year Physics graduate students; suggested for junior or senior Physics majors for 1 unit. Review of research activities in the department and elsewhere at Stanford at a level suitable for entering graduate students.

Curricular practical training for students participating in an internship with a physics-related focus. Meets the requirements for curricular practical training for students on F-1 visas. Prior to the internship, students submit a concise description of the proposed project and work activities. After the internship, students submit a summary of the work completed and skills learned, including a reflection on the professional growth gained as a result of the internship. This course may be repeated for credit. Students are responsible for arranging their own internship/employment and faculty sponsorship. Register under faculty sponsor's section number.

Study of the literature of any special topic. Preparation, presentation of reports. If taken under the supervision of a faculty member outside the department, approval of the Physics chair required. Prerequisites: 25 units of college physics, consent of instructor.

Weekly seminar/discussions on interactive techniques for teaching physics. Practicum which includes class observations, grading, and student teaching in current courses. Required of all Teaching Assistants prior to the first teaching assignment. Mandatory attendance at weekly in-class sessions during the first 5 weeks of the quarter; mandatory successful completion of all practicum activities. Students who do not hold a US Passport must complete the International Teaching/Course Assistant Screening Exam and be cleared to TA before taking the class. Details: https://language.stanford.edu/programs/efs/languages/english-foreign-students/international-teachingcourse-assistant-screening. Enrollment in PHYSICS 294 is by permission. To get a permission number please complete the form: https://forms.gle/AQarpxz5XVJzVE8i7. If you have not heard from us by the beginning of class, please come to the first class session.

This course will provide students with a basic knowledge of the relevant research in cognitive psychology and science education and the ability to apply that knowledge to enhance their ability to learn and teach science, particularly at the undergraduate level. Course will involve readings, discussion, and application of the ideas through creation of learning activities. It is suitable for advanced undergraduates and graduate students with some science background.

Designed for physics graduate students but open to all graduate students with a calculus-based physics background and some laboratory and coding experience. Students make and analyze observations using the telescopes at the Stanford Student Observatory. Topics covered include navigating the night sky, the physics of stars and galaxies, telescope instrumentation and operation, imaging and spectroscopic techniques, quantitative error analysis, and effective scientific communication. The course concludes with an independent project where student teams propose and execute an observational astronomy project of their choosing, using techniques learned in class to gather and analyze their data, and presenting their findings in the forms of professional-style oral presentations and research papers. Enrollment by permission. To get a permission number please complete form: https://forms.gle/KDarBRcZWJZG3qr66 form. If you have not heard from us by the beginning of class, please come to the first class session.

Required of graduate students. May be repeated for credit.

Lorentz Invariance. S-Matrix. Quantization of scalar and Dirac fields. Feynman diagrams. Quantum electrodynamics. Elementary electrodynamic processes: Compton scattering; e+e- annihilation. Loop diagrams. Prerequisites: PHYSICS 130, PHYSICS 131, or equivalents AND a basic knowledge of Group Theory.

Functional integral methods. Local gauge invariance and Yang-Mills fields. Asymptotic freedom. Spontaneous symmetry breaking and the Higgs mechanism. Unified models of weak and electromagnetic interactions. Prerequisite: PHYSICS 330.

Theory of renormalization. The renormalization group and applications to the theory of phase transitions. Renormalization of Yang-Mills theories. Applications of the renormalization group of quantum chromodynamics. Perturbation theory anomalies. Applications to particle phenomenology. Prerequisite: PHYSICS 331.

Symmetries, group theory, gauge invariance, Lagrangian of the Standard Model, flavor group, flavor-changing neutral currents, CKM quark mixing matrix, GIM mechanism, rare processes, neutrino masses, seesaw mechanism, QCD confinement and chiral symmetry breaking, instantons, strong CP problem, QCD axion. Prerequisite: PHYSICS 330.

This course provides an overview of the Standard Model of Particle Physics, motivations for extending the Standard Model (including naturalness, the hierarchy, the cosmological constant, and strong CP problems), discussions on Technicolor and Composite Models, Grand Unified Theories and SU(5), exploration of the Supersymmetric Standard Model (including gauge coupling unification and lessons from LEP and the LHC), re-evaluation of naturalness, the multiverse, and the landscape of string theory, as well as topics such as split supersymmetry, string theory, large extra dimensions, the strong CP problem, and the QCD axion.

Basic theory of production of radiation in stars, galaxies and diffuse interstellar and intergalactic media and and transfer of radiation throughout the universe. Magnetic fields, turbulence shocks and  particle acceleration and transport around magnetospheres of planets to clusters of galaxies. Application to  compact objects, pulsars and accretion in binary stars and super-massive black holes, supernova remnants, cosmic rays and active galactic nuclei  Prerequisite: PHYSICS 260 or equivalent.

Intended as a complement to Ph 362 and Ph 364.nGalaxies (including their nuclei), clusters, stars and backgrounds in the contemporary universe. Geometry, kinematics, dynamics, and physics of the universe at large. Evolution of the universe following the epoch of nucleosynthesis. Epochs of recombination, reionization and first galaxy formation. Fluid and kinetic description of the growth of structure with application to microwave background fluctuations and galaxy surveys. Gravitational lensing. The course will feature interleaved discussion of theory and observation. Undergraduate exposure to general relativity and cosmology at the level of Ph 262 and Ph 161 will be helpful but is not essential.

Intended to complement PHYSICS 361, this course will cover the earlier period in cosmology up to and including nucleosynthesis. The focus will be on high energy, early universe physics. This includes topics such as inflation and reheating including generation of density perturbations and primordial gravitational waves, baryogenesis mechanisms, out of equilibrium particle production processes in the early universe e.g. both thermal and non-thermal production mechanisms for dark matter candidates such as WIMPs and axions, and production of the light nuclei and neutrinos. Techniques covered include for example out of equilibrium statistical mechanics such as the Boltzmann equation, and dynamics of scalar fields in the expanding universe. Other possible topics if time permits may include cosmological phase transitions and objects such as monopoles and primordial black holes. We will use quantum field theory, although it will hopefully be accessible for those without much background in that area. Suggested prerequisites: general relativity at the level of PHYSICS 262, some knowledge of cosmology and in particular the basics of FRW cosmology as in PHYSICS 361 for example, and some knowledge of quantum field theory e.g. at the level of PHYSICS 331 as a corequisite.

General relativistic theory of spinning black holes and neutron stars including accretion, jets and tidal capture. Direct and indirect observation of relativistic effects in active galactic nuclei and stellar sources. Linear theory of the generation and propagation of (non-primordial) gravitational radiation. Detection of gravitational waves by Michelson interferometers, pulsars and atom interferometers. Nonlinear emission by binary black holes. Nuclear equation of state and nucleosynthetic implications of neutron star binaries. Pre-requisite: Ph 262 or equivalent.

Modern astrophysics explores physical processes in remote environments that prescribe, apply, and explore fundamental processes under conditions that are far more extreme than those attainable in a terrestrial laboratory. These include the production and interaction of peta eV gamma rays, peta eV neutrinos, and zetta eV cosmic rays by black holes and the behavior of 100 giga Tesla magnetic field anchored by neutron stars. The connection between observations, experiments, and the underlying physics will be emphasized. This course is intended for graduate students but should be accessible to advanced undergraduates. An understanding of basic general relativity and introductory quantum electrodynamics will be helpful but is not essential.

Fermi liquid theory, many-body perturbation theory, response function, functional integrals, interaction of electrons with impurities. Prerequisite: APPPHYS 273 or equivalent.

Superfluidity and superconductivity. Quantum magnetism. Prerequisite: PHYSICS 372.

This course will examine the physics of the accelerated expansion of the early and late universe. Classically, this leads to horizons beyond which we cannot see. Quantum mechanically the cosmic horizon is responsible for the seeds of structure in the observed universe, whose details are sensitive to quantum gravity. It also represents vast numbers of microstates according to holographic calculations and the mathematical structure of string theory. This course will introduce relevant notions from observation, quantum field theory, general relativity, string theory, and other tools such as low-dimensional models, with the aim of developing a broad understanding of the phenomenon as currently understood along with an introduction to open research problems.

This course will cover the developing intersection between quantum information theory and the quantum theory of gravity. We will focus on the central roles of entanglement and computational complexity in black hole physics. Prerequisites: Basic knowledge of quantum mechanics, quantum field theory, and general relativity.

This course describes the origin and the present status of inflationary cosmology. The main topics include: The Big Bang theory and the theory of cosmological phase transitions. Formation of domain walls, cosmic strings, and monopolies. Problems of the Big Bang theory, and solving these problems in inflationary cosmology. Main conceptual steps: Starobinsky model, old inflation, new inflation, chaotic inflation, eternal inflation. Reheating of the universe after inflation. Inflationary perturbations and the large-scale structure formation. Inflationary gravitational waves. Popular inflationary models such as hybrid inflation, natural inflation, Higgs inflation, and alpha-attractors. Testing inflationary models. Theory of tunneling and stochastic approach to inflation. The problem of initial conditions. Inflation in supergravity and string theory. Wave function of the universe, quantum cosmology, multiverse, and string theory landscape. Suggested prerequisites: general relativity at the level of PHYSICS 262 and some knowledge of quantum field theory at the level of PHYSICS 331.

This seminar is for first-year graduate students interested in theoretical physics. It is driven by introductory-level student talks and focuses on recent foundational developments across the field. Typical areas of interest include cosmology, particle physics, string theory, quantum gravity, and condensed matter.

Many body quantum systems can display rich dynamical phenomena far from thermal equilibrium. Understanding the non-equilibrium dynamics of quantum matter represents an exciting research frontier at the interface of condensed matter and AMO physics, high energy theory and quantum information. This is particularly topical in light of experimental advances in building quantum simulators and intermediate-scale quantum computers, which naturally operate in far-from-equilibrium regimes. This course is intended to serve as an introduction to this active research area, assuming only a knowledge of quantum mechanics and statistical physics. Topics covered include: quantum thermalization, quantum chaos, many-body localization, quantum entanglement and its dynamics, Floquet theory and time crystals, quantum circuits, quantum simulation, and tensor network methods. Prerequisites: PHYSICS 113, PHYSICS 130, PHYSICS 131, PHYSICS 170, and PHYSICS 171.

We will begin by reviewing a modern perspective on the theory of conventional (BCS s-wave) and unconventional (e.g. d-wave) superconductors. We will then discuss a variety of issues that are of current interest, but which are either incompletely understood or entirely open problems in the field. Depending upon the interests of the class and the whims of the instructor, topics to be covered may include: quantum superconductor to insulator and superconductor to metal transitions, emergence of superconductivity from a non-Fermi liquid normal state, exotic superconducting phases of matter, interplay between superconductivity and other broken symmetry states (issues of ¿intertwined orders¿), and superconductivity in paradigmatic models of highly correlated electron systems, including problems in which there is an interplay between strong electron-electron and electron-phonon interactions. We will also touch on theoretical ideas - all of them currently still being explored and hence controversial - concerning theories of unconventional metallic states - i.e. metallic states that cannot be well described in the context of a theory of weakly interacting quasiparticles. While the subject matter of this course is motivated by ongoing experimental studies in a variety of quantum materials and devices, the principle focus of the class will be on a coherent understanding of what is known and on crisply identifying what is not known.

This course will discuss various research topics related to quantum information theory and its application in many-body systems. The course contains three main parts. In the first part, we will discuss the fundamentals of classical and quantum information theory, including concepts such as quantum channels and quantum measurements, physical quantities such as quantum relative entropy, and mutual information. We will also discuss quantum error correction and quantum teleportation. The second part will be an overview of entanglement properties in various many-body systems, such as free fermions and free bosons, stabilizer states, conformal field theory, random states, etc. In the third part, I will give a brief overview of the relation of quantum information with spacetime and quantum gravity.

Open only to Physics graduate students, with consent of instructor. Work is in experimental or theoretical problems in research, as distinguished from independent study of a non-research character in 190 and 293.

This course will be an introduction to topological quantum computation (TQC), which has recently emerged as an exciting approach to constructing fault-tolerant quantum computers. We start with a review of some basics of quantum computing, 2D topological phases of matter, Abelian/non-Abelian anyons, etc. Then we introduce the concept of TQC and study some examples such as the toric/surface code and Levin-Wen string-net model. We continue to talk about the mathematical theory of anyons including modular tensor categories, braid groups, 6j-symbols, Pentagon Equations. We study the issue of universality for different systems. Lastly, we show the equivalence of TQC with standard circuit model. Additional topics include complexity classes, Jones polynomials, topological field theories, etc. Prerequisite: Basic knowledge of quantum mechanics and condensed matter physics. Some knowledge of category theory and representation theory is useful but is not required. The course will run the first five weeks.