caltech theoretical physics phd

Postdoctoral Fellowship Application

The Burke Institute has endowed fellowships for distinguished postdoctoral scholars in theoretical physics.

The support offered by these fellowships enables theorists to pursue innovative research. The success of the fellowship program is exemplified by the fact that over 95 percent of the more than 120 former fellows are holding distinguished academic positions .

The Walter Burke Institute for Theoretical Physics at the California Institute of Technology (Caltech) solicits applications for its Fellowship program. The Prize Fellowships at the Burke Institute offers an opportunity for outstanding recent and new Ph.D. recipients to perform research at Caltech for three years. They are selected by a faculty committee representing all areas of theoretical physics and astrophysics at Caltech and are provided with:

• flexibility, support, and freedom in choosing research direction within theoretical physics and astrophysics (including but not limited to theoretical astrophysics/cosmology, condensed matter theory, general relativity, particle/string theory, physical mathematics, and quantum information),
• an inclusive environment with faculty mentorship and activities organized by the Burke Institute to promote scientific exchanges and professional growth, and
• an annual stipend/salary and an annual research fund that are comparable to those of other prestigious fellowships.

The Burke Fellowship program significantly expands and strengthens the existing Prize Fellowship program at Caltech. The Prize Fellowship program has been successful with over 95 percent of the more than 120 former fellows holding distinguished academic positions .

We encourage all candidates to apply by November 15, 2023. Applicants should submit curriculum vitae (with email address and citizenship), a statement of research interests, and a list of publications to this application website. Applicants should also ensure that at least three letters of reference are submitted on their behalf to the website.

Email inquiries regarding the application process may be sent to [email protected] .

Visitors and Visiting Associates

Postdoctoral Scholars

Graduate Students

Research Staff

No results., administrative staff.

The Awakening of a Massive Black Hole

Observations from several telescopes, including the European Southern Observatory's Very Large Telescope (VLT) in the Atacama Desert in Chile, show a galaxy undergoing dramatic changes over the past several years. These dramatic changes in brightness began in December 2019, a phenomenon first noticed by the Zwicky Transient Facility (ZTF) , which operates from the 48-inch Samuel Oschin Telescope at Caltech's Palomar Observatory.

Various phenomena can cause a temporary increase in brightness in a galaxy, including supernova explosions or tidal disruptions (when a star is torn apart as it passes close to a supermassive black hole). But the behavior of this galaxy, called SDSS1335+0728, is novel, at least compared to previous observations. Rather than brightening temporarily, for dozens or a few hundred days, the galaxy is still growing brighter today, more than four years after the change was first observed.

The most likely explanation for this behavior is the turning on of a black hole at the center of SDSS1335+0728, though other explanations have not yet been ruled out. When supermassive black holes like this turn on, they are referred to as active galactic nuclei.

"We have found several million active galactic nuclei to date, and with the new generation of time-domain sky surveys like that at ZTF, we have found about 700 that are changing significantly in brightness," Matthew Graham, research professor of astronomy at Caltech and project scientist for ZTF, explains. "But up to now we have not observed any galactic nuclei that are in the actual process of turning on, of transitioning from a quiescent state to an active state with material falling into the supermassive black hole at the heart of the galaxy."

New observations from ESO's VLT and other locations show SDSS1335+0728 is radiating more ultraviolet, optical, and infrared light, and most recently, X-rays.

"As far as we can tell," Graham says, "there is nothing particularly unusual about this galaxy. We've just caught it at a somewhat unique moment. We expect most galaxies go through a phase like this since most galaxies have a supermassive black hole at their center. Further study of this galaxy will help us to better understand this process and also help us find other examples."

This research was published in Astronomy & Astrophysics under the title "SDSS1335+0728: The awakening of a ∼106M⊙ black hole."

Read the full story from ESO online.

Written by Cynthia Eller

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Freshman Theoretical Physicist: Admissions Info for CalTech/MIT/Harvard

• Thread starter phantom113
• Start date Mar 26, 2009
• Tags Physicist Theoretical Theoretical physicist
• Mar 26, 2009
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• Mar 27, 2009

You're going to need very good grades for those graduate programs. It's beyond just that though, each of those programs turn down many 4.0 students with perfect/near-perfect PGRE scores. You'll need grades, research, excellent letters of recommendation, and a top notch PGRE score. If you really enjoy the material, go for it.  

OK, here is perhaps a more concrete question for you all. While my strengths lie in the sciences I am taking about half of my classes in the humanities. It is easier to get a B- or above than in the sciences (you have to try to get a C in the humanities), however, it's also a lot harder (at least for me) to get straight A's in the humanity courses I take. Would grad schools see this as me having broad range of interests(I don't do poorly in the classes - B+ or A-) and not being afraid to challenge myself with something I may not be comfortable or would they see this as me not getting 3.8+ overall GPA and therefore I'm out(at places like caltech/MIT/harvard etc)? Thanks.  

You have to remember it's a competative process to get into graduate schoo.. They schools you're listing have very competative programs, so it's not a case of making some kind of minimum cut-off. Getting into graduate school is more about being the top candidate in the applicant pool. I strongly suspect for the the big name schools, you will be up against other students who have near perfect GPAs (both core and overall) and who distinguish themselves with additional merits such as research experience, publications, distinguished scholarships, impressive reference letters, etc. That being said, you can get what is likely an equivalent education from some of the less competative schools. One thing to keep in mind though is that if you're struggling to get a high mark in first year physics - it's not going to get easier. And stacking your courses to boost your overall GPA is not going to make you any better at physics. I think it's important to have some diversity in your degree, but selection committees know all the tricks.  

• Mar 31, 2009

I suspect Amherst has a respected undergrad physics program (I went to a very similar institution), but you will likely need something in the range of A- to A average to be competitive at top grad programs. Fortunately ultimately those grades are really only essential in upper level physics courses... don't let your grades from this year cut off any aspirations. And take full advantage of the small liberal arts college environment by talking to professors for advice!  

phantom113 said: Would grad schools see this as me having broad range of interests(I don't do poorly in the classes - B+ or A-) and not being afraid to challenge myself with something I may not be comfortable or would they see this as me not getting 3.8+ overall GPA and therefore I'm out(at places like caltech/MIT/harvard etc)?

I don't plan on getting C's in the other classes, more A-/B+ average. That shouldn't be a problem then?  

phantom113 said: I'm a freshman at Amherst College in my first college physics course (actually an E&M course). I was doing poorly at first (B-/B) but have gotten into the swing of things and am thoroughly enjoying the theory portion of the class(the experiments are also fun but are sometimes tedious). I have a few questions. What stats would be necessary for admission to CalTech/MIT/Harvard etc. for graduate school as a theoretical physicist (GPA, GRE, research, etc)? I am not sure what grade I will end up with in this class because of the first half of it so will that affect my chances badly as long as it's not a C+ or lower? I've also been doing reading with some theory and although the book is more for laymen, I think it is fascinating. Thanks for any information.

• Apr 1, 2009

khemix said: To get into those schools you have to be a genius. If you are gettings Bs in freshman you are not a genius in physics. The only excuse you have for gettings Bs are a) you never took physics in high school or b) you studied 1 hour a week. If this is all you are capable of with effort, let me hit you real hard and tell you that you will NEVER even make the cut off of those schools. Not because one C will screw your transcript; it won't. But because your grades in upper years won't be as good due to your lack of aptitude.

This previous thread might be enlightening... "Do first year undergrad marks matter when applying to grad school?" https://www.physicsforums.com/showthread.php?p=1993237#post1993237 (I've linked to my post in that thread... but read all of the replies.)  

• Apr 2, 2009

It is a lot harder than you might think to gain admission into a top graduate school. I had 1 B, straight A's otherwise, numerous national awards (Goldwater, Rhodes, etc.) and still got rejected from all the top 20 schools I applied to. I am pretty sure I had good letters of recommendation, too. It was a mix between the economy tanking and the competitive atmosphere (and crummy GRE scores). Everyone thinks that they will be the next great theorist at MIT or Caltech. In reality it's near impossible to do this. And the GRE is very, very important. Ignore anyone who tells you otherwise. A good score may not save you but a bad score will doom you.  

Related to Freshman Theoretical Physicist: Admissions Info for CalTech/MIT/Harvard

1. what are the admission requirements for caltech/mit/harvard's freshman theoretical physicist program.

The admission requirements for CalTech/MIT/Harvard's freshman theoretical physicist program vary slightly between each university, but generally include a strong academic record in high school, including advanced coursework in math and science, high standardized test scores (such as the SAT or ACT), and strong letters of recommendation. Additionally, a strong passion for and demonstrated interest in theoretical physics is highly valued.

2. Is it necessary to have prior research experience to be accepted into this program?

No, prior research experience is not necessary for admission into the freshman theoretical physicist program at CalTech, MIT, or Harvard. However, having research experience can strengthen your application and demonstrate your passion and commitment to the field.

3. Are international students eligible to apply for this program?

Yes, all three universities welcome applications from international students. However, international students may need to fulfill additional requirements, such as submitting English proficiency test scores.

4. What sets the freshman theoretical physicist program at CalTech/MIT/Harvard apart from other universities?

The freshman theoretical physicist programs at CalTech, MIT, and Harvard are highly competitive and prestigious. These universities have renowned faculty members and cutting-edge research facilities, providing students with unique opportunities for hands-on experience and mentorship. Additionally, the small class sizes and close-knit communities at these universities allow for personalized attention and support for students.

5. Are there any specific courses or extracurricular activities that can strengthen an application for this program?

While there are no specific courses or activities that are required for admission, taking advanced math and science courses and participating in related extracurricular activities (such as math or science clubs, research projects, or science fairs) can demonstrate your passion and aptitude for theoretical physics. Additionally, showcasing any leadership roles or community service experience can also strengthen your application.

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Courses 2023-24

Classical Mechanics and Electromagnetism

The first year of a two-year 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.

Waves, Quantum Mechanics, and Statistical Physics

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.

Introductory Physics Laboratory

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.

First-Year Seminar: Astrophysics and Cosmology with Open Data

Analog electronics for physicists.

A fast-paced 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 two-week project of the student's choosing.

Physics Laboratory

A laboratory introduction to experimental physics and data analysis. Experiments use research-grade 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 30-minute individual recitation and a 3 hour laboratory.

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 Stern-Gerlach 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.

Experiments in Electromagnetism

A two-term 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 1,000-volt spark, and building and studying a radio-wave transmitter and receiver. The take-home experiments are constructed from a kit of tools and electronic parts. Measurements are compared to theoretical expectations.

First-Year Seminar: The Science of Music

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 analysis of recordings of actual musical instruments, instrument construction and analysis, and tests or surveys of people's abilities or preferences. First-year (undergraduate) only; limited enrollment.

Frontiers in Physics

Open for credit to first-year students and sophomores. Weekly seminar by a member of the physics department or a visitor, to discuss their 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.

First-Year Seminar: Beyond Physics

First-year students 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 one-on-one 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 an undergraduate's first and sophomore years will be automatic for students making satisfactory progress. Graded pass/fail. First-year (undergraduates) only; limited enrollment.

Waves, Quantum Physics, and Statistical Mechanics

A one-year course primarily for students intending further work in the physics option. Topics include classical waves; wave mechanics, interpretation of the quantum wave-function, one-dimensional bound states, scattering, and tunneling; thermodynamics, introductory kinetic theory, and quantum statistics.

Computational Physics Laboratory I

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. Offered first and second terms.

Computational Physics Laboratory II

Computational tools for data analysis. Use of python for accessing scientific data from the web. Bayesian techniques. Fourier techniques. Image manipulation with python. Offered second and third terms.

Computational Physics Laboratory III

Computational tools and numerical techniques. Applications to problems in classical mechanics. Numerical solution of 3-body and N-body systems. Monte Carlo integration. Offered third term only.

Caltech Physics League

This course serves as a physics club, meeting weekly to discuss and analyze real-world problems in physical sciences. A broad range of topics will be considered, such as energy production, space and atmospheric phenomena, astrophysics, nano-science, 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.

Oral and Written Communication

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.

Advanced Physics Laboratory

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 widely-used optical devices and techniques, laser-frequency stabilization, and classic experiments such as magnetic resonance, optical pumping, and doppler-free spectroscopy. Fundamentals of vacuum engineering, thin-film sample growth, and cryogenics are occasionally offered. Special topics and student-led projects are available on request.

Senior Thesis (Experiment)

Senior thesis (theory).

Open only to senior physics majors. Theoretical research must be supervised by a faculty member, the student's thesis adviser. Two 15-minute 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.

Order-of-Magnitude Physics

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.

Relativistic Astrophysics

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.

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.

Topics in Classical Physics

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.

Classical and Laser Optics

Noise and stochastic resonance.

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.

Physics of Measurement

Physics of measurement: moonbounce and beyond - microwave scattering for communications and metrology, quantum cryptography.

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.

Computational Physics Lab

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.

Quantum Mechanics

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.

Statistical Physics of Interacting Systems, Phases, and Phase Transitions

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.

Mathematical Methods of Physics

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.

Introduction to Condensed Matter

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.

Applications of Classical Physics

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.

Atoms and Photons

Quantum hardware and techniques.

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.

Introduction to Elementary Particle Physics

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.

Fundamentals of Fluid Flow in Small Scale Systems

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.

Fundamentals of Energy and Mass Transport in Small Scale Systems

Reading and independent study, research in physics, advanced experimental physics.

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.

Neural Computation

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.

Special Topics in Physics

Topics will vary year to year and may include hands-on laboratory work, team projects and a survey of modern physics research.

Candidacy Physics Fitness

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.

Nuclear Physics

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.

Relativistic Quantum Field Theory

Quantum computation.

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.

Advanced Condensed-Matter Physics

Advanced mathematical methods of physics.

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.

Elementary Particle Theory

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.

Introduction to Topological Field Theory

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.

Theoretical Cosmology and Astroparticle Physics

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.

General Relativity

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.

Gravitational Radiation

Special topics in Gravitational-wave Detection. Physics of interferometers, limits of measurement, coherent quantum feedback, noise, data analysis.

Physics Seminar

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.

Introduction to String Theory

Thesis research.

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

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Apply to physics or astronomy PhD program?

Hi all, I'm a rising fourth-year undergraduate physics major from a large public research university (very strong in physics). Most of my undergraduate coursework is in physics with some (3-4) astro/planetary electives. I'm interested in studying theoretical/computational astrophysics. On the Caltech admissions sites, it notes that a larger proportion of graduate students studying theoretical astrophysics tend to come from the physics dept. rather than from astronomy. But I was wondering if anybody had any further insights or statistics on acceptance rates of either program, number of students accepted in each cycle, etc..., or just any general advice on whether I should apply to the physics or astronomy PhD programs. Is one program more competitive than the other? Since my undergraduate major is in physics and not astrophysics, would I have a better chance of applying to the physics program? Any advice is appreciated!

NASA Space Mission to Uncover Secrets of Exoplanets, Dark Energy, and More

NASA has recently selected a new satellite mission, called Landolt, that will put an artificial star in orbit around Earth. This artificial star, a source of light whose brightness is precisely known, will allow scientists to more accurately measure the brightness of actual stars, including those nearby to those exploding as supernova in far-off galaxies. By enabling better characterization of stars, the $19.5 million mission will lead to a better understanding of planets that orbit some of these stars. Additionally, it will provide new clues to the mystery of dark energy, a force or substance thought to be pushing our universe apart at ever-increasing speeds.

"Even with today's modern instruments, measurements of the true brightness of stars have only been known to a few percent," says David Ciardi, the deputy director for the NASA Exoplanet Science Institute (NExScI) at IPAC, an astronomy center based at Caltech. "Landolt will enable an improvement in those measurements by more than a factor of 10. Understanding the true brightness of stars allows us to understand the stars better, and, perhaps more importantly, understand the planets that orbit the stars better."

The mission, planned for launch in 2029, is led by a former IPAC scientist and Caltech alum Peter Plavchan BS '01), who is now an associate professor of physics and astronomy at George Mason University in Virginia.

IPAC will be responsible for archiving the mission's data and will contribute to the ground support through Caltech's Palomar Observatory. Additional partners include the National Institute of Standards and Technology, a world leader in measuring photon emissions, in addition to several other universities. Other Caltech team members include Jessie Christiansen, the NExScI chief scientist and the project scientist for the NASA Exoplanet Archive at NExScI, who helped propose the mission.

Named for late astronomer Arlo Landolt, who put together widely used catalogs of stellar brightness in 1973, 1982, and 1992, and who passed away in 2022, this mission will launch a light source into the sky with a known emission rate of photons. The team will observe the light source, or artificial star, next to real stars to make new stellar brightness catalogs. The artificial star will orbit 22,236 miles above Earth, far enough away to look like a star to telescopes on the ground. This orbit also allows the satellite to move at the same speed of the Earth's rotation, keeping it in place over the United States during its one-year primary mission.

Read the full story from George Mason University.

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Caltech Announces Newest Cohort of Leadership Chairs and Named Professorships

During the 2023–24 academic year, Caltech recognized two faculty members with distinguished leadership chairs for administrative positions and 13 faculty members with named professorships, the Institute's most distinguished award.

These honors provide faculty with additional resources to advance innovative research ideas while they continue to mentor and train future generations.

Each named professorship brings its own legacy. Many professorships, for instance, have long-standing histories and pass a tradition of discovery and exploration from one academic generation to the next, from one colleague to another. A professorship may also provide a faculty member with an opportunity to forge meaningful connections with the philanthropists who made the award possible.

Leadership chairs generate discretionary funds that enable Institute leaders to support emerging research projects and ideas with potential for scientific and societal impact, and to support Caltech's educational mission and outreach programs.

Caltech is pleased to present its newest cohort of leadership chairs and named professors.

Leadership Chairs

Bethany L. Ehlmann Professor of Planetary Science Allen V. C. Davis and Lenabelle Davis Leadership Chair, Keck Institute for Space Studies Director, Keck Institute for Space Studies

Division of Geological and Planetary Sciences

Bethany Ehlmann's research focuses on the mineralogy and chemistry of planetary surfaces, remote sensing techniques and instruments, astrobiology, and science policy and outreach. Her specific areas of interest include unraveling Mars's environmental history and understanding water in the solar system. Ehlmann is also the principal investigator of Lunar Trailblazer , a NASA mission to map the form, distribution, and abundance of water on the Moon and to understand the lunar water cycle.

Professor Ehlmann joined the Caltech faculty in 2011.

Viviana Gradinaru (BS '05) Lois and Victor Troendle Professor of Neuroscience and Biological Engineering Allen V. C. Davis and Lenabelle Davis Leadership Chair, Richard N. Merkin Institute for Translational Research Director, Center for Molecular and Cellular Neuroscience Director, Richard N. Merkin Institute for Translational Research

Division of Biology and Biological Engineering

Viviana Gradinaru is interested in brain and body circuits and how they malfunction in neuropsychiatric disorders. To study these systems, she has developed diverse neurotechnologies including optogenetic actuators to precisely control neuronal activity, tissue clearing and imaging methods to map transparent organs, and engineered adeno-associated viral vectors (AAVs) for targeted gene delivery . Technologies developed by Gradinaru are now used by thousands of laboratories worldwide, including through her company Capsida Biotherapeutics, a Caltech spin-off.

Professor Gradinaru joined the Caltech faculty in 2012.

Named Professorships

R. Michael Alvarez Flintridge Foundation Professor of Political and Computational Social Science Co-director, Ronald and Maxine Linde Center for Science, Society, and Policy

Division of the Humanities and Social Sciences

Michael Alvarez is an expert on electoral politics, from public opinion and political campaigns to election technology and administration and statistical and computational modeling. He is co-director of The Ronald and Maxine Linde Center for Science, Society, and Policy (LCSSP) , which brings researchers, policymakers, and other stakeholders together to focus on cutting-edge science policy and science ethics. Alvarez is also co-director of the Caltech/MIT Voting Technology Project.

Professor Alvarez joined the Caltech faculty in 1992.

James (Jamie) Bock Marvin L. Goldberger Professor of Physics Jet Propulsion Laboratory Senior Research Scientist

Division of Physics, Mathematics and Astronomy

Jamie Bock is a leader in developing new technologies and experiments to study the early universe. He is the principal investigator of NASA's SPHEREx mission , which is set to launch in 2025 and will trace large-scale structures in our universe to answer questions about the birth of our cosmos. He also co-leads the BICEP Array , which carries out precise measurements of CMB polarization from the South Pole to probe the explosive period of rapid growth in our universe called inflation.

Professor Bock joined the Caltech faculty in 2012.

Venkat Chandrasekaran Kiyo and Eiko Tomiyasu Professor of Computing and Mathematical Sciences and Electrical Engineering

Division of Engineering and Applied Science

Venkat Chandrasekaran is an applied mathematician who studies optimization and the information sciences with a focus on effectively extracting insights from data. Some of his group's contributions include tractable algorithms for inverse problems and latent variable modeling, characterizations of tradeoffs between computational and statistical efficiency, and a paradigm for dimension-free optimization. These methods have been applied to problems in water resources modeling, super-resolution imaging, dynamical systems analysis, network inference, and engineering design.

Professor Chandrasekaran joined the Caltech faculty in 2012.

Xie Chen Eddleman Professor of Theoretical Physics

Xie Chen is a condensed matter theorist who studies emergent phenomena in large quantum systems. Chen takes models and tools from quantum information theory to study novel phase and phase transitions in condensed matter systems, which often have interesting field theory implications, with the goal of revealing the universal structures hidden behind the complicated microscopic details.

Professor Chen joined the Caltech faculty in 2014.

Michael B. Elowitz Roscoe Gilkey Dickinson Professor of Biology and Bioengineering Investigator, Howard Hughes Medical Institute

Michael Elowitz specializes in the fields of synthetic biology and systems biology. His research demonstrates that biological behaviors can be programmed using custom designed molecular circuits; revealed the pervasive role of stochastic fluctuations—or "noise"—in gene expression; and identified a set of biological circuit designs underpinning cellular and multicellular development.

Professor Elowitz joined the Caltech faculty in 2003.

Christopher Martin Edward C. Stone Professor of Physics Director, Caltech Optical Observatories

Christopher Martin is a leader in the development of ground, balloon-based, and space experiments designed to study the intergalactic medium, a network of gas filaments that connects and feeds galaxies across the universe. Formerly, he was the principal investigator of the NASA Galaxy Evolution Explorer (GALEX) mission. Recently, he led the development of the Keck Cosmic Web Imager, or KCWI, at the W. M. Keck Observatory, which made the first direct measurements of the largest and most hidden portions of the cosmic web .

Professor Martin joined the Caltech faculty in 1993.

Niles A. Pierce John D. and Catherine T. MacArthur Professor of Applied and Computational Mathematics and Bioengineering Executive Officer for Biology and Biological Engineering

Niles Pierce is a co-founder of the fields of dynamic nucleic acid nanotechnology and molecular programming. He has developed principles, mechanisms, and algorithms that enable the rational design and construction of dynamic molecular function in a biological context. The Pierce Lab's hybridization chain reaction (HCR) bioimaging technology platform and NUPACK software suite for nucleic acid analysis and design are each used by thousands of laboratories, companies, researchers, entrepreneurs, and students worldwide.

Professor Pierce joined the Caltech faculty in 2000.

Mikhail Shapiro Max Delbrück Professor of Chemical Engineering and Medical Engineering Investigator, Howard Hughes Medical Institute

Division of Chemistry and Chemical Engineering

Mikhail Shapiro develops molecular technologies for noninvasive imaging and control of cellular function and uses those technologies to study basic biology and to create cellular diagnostics and therapeutics . His group takes advantage of naturally evolved biological structures with unique physical properties , using them as starting points for engineering to help image and manipulate cellular and molecular function.

Professor Shapiro joined the Caltech faculty in 2014.

Andrew Thompson John S. and Sherry Chen Professor of Environmental Science and Engineering Director, Ronald and Maxine Linde Center for Global Environmental Science Executive Officer for Environmental Science

Andrew Thompson's research uses a combination of sea-going oceanic observations, remote sensing data, and models to study how the ocean influences global climate through the transport of heat, dissolved gases, and nutrients. His research group is especially interested in the dynamics of polar regions and understanding how the ocean has contributed to recent changes to sea ice and ice sheets as well as the implications for future climate change.

Professor Thompson joined the Caltech faculty in 2011.

Adam Wierman Carl F Braun Professor of Computing and Mathematical Sciences Director, Information Science and Technology

Adam Wierman's current research investigates the networked systems that govern our world—such as the electrical grid , data centers, and transportation systems—and aims to identify ways to make these systems greener and more resilient . His group develops new mathematical tools for machine learning and applies them to design novel algorithms and markets in an effort to improve the sustainability and efficiency of systems.

Professor Wierman joined the Caltech faculty in 2007.

Early Career Professorships

Hannah Druckenmiller Assistant Professor of Economics William H. Hurt Scholar

Division of Humanities and Social Sciences

Hannah Druckenmiller is an environmental economist who is principally interested in understanding the environmental benefits and economic costs of natural resource protection, and novel ways to quantify these benefits and costs for the sake of future public policy. She is affiliated with the nonprofit Resources for the Future, the National Bureau of Economic Research, and Caltech's Linde Center for Science, Society, and Policy (LCSSP).

Professor Druckenmiller joined the Caltech faculty in 2023.

Georgia Gkioxari Assistant Professor of Computing and Mathematical Sciences and Electrical Engineering William H. Hurt Scholar

Georgia Gkioxari investigates computer perception and understanding with the goal of enhancing the ability of computer systems to recognize and conceptualize visual inputs with the help of machine learning. She aims to design visual perception models that bridge the gap between two-dimensional imagery and our four-dimensional world. She was recently selected as a Google Research Scholar in machine perception and received an Amazon Research Award in generative artificial intelligence.

Professor Gkioxari joined the Caltech faculty in 2023.

Lu Wei Assistant Professor of Chemistry Ronald and JoAnne Willens Scholar Investigator, Heritage Medical Research Institute

Lu Wei's research occupies the intersection of optical spectroscopy, chemical biology, and life science. Her group focuses on developing next-generation optical spectroscopy and microscopy . These can then be used to better understand dynamical biological processes, such as cellular metabolism, with enhanced spatial, temporal and molecular precision. Among other honors, Wei received the 2024 Margaret Oakley Dayhoff Award from the Biophysical Society and a Chan Zuckerberg Initiative Award.

Professor Wei joined the Caltech faculty in 2018.

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College of Science

Edtech-inspired physics and mathematics senior lands a spot at top-tier university

A long time ago in a galaxy not so far away — in Lake Oswego, Oregon — Joey Takach ordered a bunch of soundboards, accelerometers and other metal parts online. This aspiring Jedi was determined to build his own model lightsabers that hummed and glowed just like the Star Wars movies.

"When I was really young, I wanted to be an astrophysicist, but I didn't really know what that meant. I’ve always been a huge Star Wars fan, so fantasizing about creating technology that might resemble something from that played a significant role in what I chose to study,” he said.

Building lightsabers while in high school wasn’t out of the ordinary for Takach. He loved putting together different types of gadgets for fun, and drew inspiration from the type of work his mother did in the engineering field.

When it was time to decide his next steps in his academic career, he applied to Oregon State University to study electrical engineering. The presidential scholarship helped him avoid student debt and made studying at Oregon State especially appealing.

But then his trajectory changed entirely. Instead of focusing on the mechanics of building lightsabers, he became fascinated by something bigger: getting closer to objective reality itself. And being able to model what happens in real life using mathematical equations to make sense of everyday experiences was just as captivating.

Takach plays with some of his favorite equations.

"When I started to take more physics classes, I thought, 'Wow, this physics stuff is really cool,' and it just clicked,” Takach said. One thing led to another, his passion grew and he pivoted entirely.

"Not to say that math isn’t beautiful, but I think that applying math to something real is what is most important."

Takach is graduating this summer with a double major in physics and mathematics. "The coolest thing about the math department is how flexible it is. And in the physics department, everyone's really friendly and there's lots of interaction between students," he said.

In the fall, Takach is moving forward with a Ph.D. program at University of California, Berkeley, focusing on particle physics and phenomenology. This involves looking for things that can be observed and may not be obvious experimentally. Instead of testing a hypothesis, phenomenologists choose a mathematical theory and try to “tease out” observations. After they decide what the observable effects are, they tell experimentalists to go looking for them in real life applications.

By chance, physics meets education technology

Takach found a lot of faculty support that allowed him to make an impact early on in his academic career. In his first year, one of his main advisors, Associate Department Head David Craig became his go-to resource for knowledge.

“I did the naive freshman thing and went to Craig because he was one of the resident theoretical physicists here. He directed me to a bunch of stuff to study in my free time and what books to read. He also motivated me to start learning on my own, and helped me learn how to attack those high-level concepts early without waiting to be in a class.”

Takach’s journey didn’t stop there. Last summer, he landed an internship at University of California, Davis, where he gained experience working with computational physics and quantum field theories in the realm of particle physics.

At Oregon State, he worked on campus as a peer advisor for the Science Success Center and as a learning assistant for the Techniques of Theoretical Mechanics course in the physics department.

His passion blossomed when he learned how to utilize the power of Python, a computer programming language, to create educational videos about high-level physics concepts and make the content more accessible to students who haven’t learned it.

Takach presents a vector video simulation using the Python programming language.

“Getting an early start and giving kids the opportunities to learn more as early as they can is so important. It becomes second-nature if they start early enough,” he said.

Inspired by YouTuber 3Blue1Brown, who made animated mathematics content, Takach created his own video to help more students have access to an engaging, easier-to-grasp learning experience. His goal was to teach about an advanced mathematics topic: curl.

In vector mathematics, curl is a concept that involves measuring the rotational or swirling behavior of a vector field. A vector is a direction with a specified measurement, such as how fast a golf ball moves forward when hit with a golf club. Imagine a bunch of arrows pointing in the direction that the ball is moving – the longer the arrows, the stronger the force in that direction.

“There are tons of people online that make these kinds of videos. Making this content accessible to younger people is essential because the amount of science you need to know in order to advance in a field is very daunting,” Takach said.

He sent his video to Physics Professor Emeritus Corinne Manogue, the leader behind the Paradigms in Physics project funded by the National Science Foundation. This physics education project led to the creation of 19 new physics courses and focused on shifting the curricula from traditional lectures to active engagement for students at Oregon State.

She hired Takach to make more educational videos that were aligned with the physics curriculum, including quantum mechanics. The videos were intended to improve the learning experience for future physics students.

“The most concrete thing that I want to have an impact on is teaching. I love sharing the experience of learning something for the first time. It happens so frequently – it's the weirdest experience and when you share that with someone, It’s motivating, fulfilling and fun,” he said.

Physics Associate Professor Elizabeth Gire also had a positive influence on his academic career. After she taught one of his first upper-division physics courses, he left feeling inspired. "She really, really cares about the students and how much everyone's learning. I think that rubbed off on me. The way she goes about teaching and encouraging people to work together is definitely something to look up to and had a big impression on me.”

Looking back, one of Takach’s favorite memories at Oregon State is living with his friends for three years. "Two of my best friends from high school are still my roommates now. They’ve been a great support system.”

During his free time, Joey loves to dive into music and plays several instruments, including guitar, bass, viola and violin. When the sun comes out, he enjoys hiking, backpacking and traveling. After completing his Ph.D. in California, Takach dreams of becoming a physics professor. “Learning and teaching for as long as possible is the most ideal for me. I need the connection to what is actually real. Not to say that math isn’t beautiful, but I think that applying math to something real is what is most important.”

Takach contributes to the beauty of mathematics and reality of physics on a chalkboard.

Read more stories about: students , mathematics , physics , student success , graduation , mathematics major , physics major

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• MyU : For Students, Faculty, and Staff

CM Theory Seminar Recordings

The Condensed Matter Theory Seminar is held every Wednesday at 1:25 in the Physics and Nanotechnology Building. Please see the calendar below for our upcoming seminars.

Our full catalogue of recordings is available on FTPI's YouTube Channel @FineTheoryInstitute

2023 | 2022

Patrick A. Lee (Massachusetts Institute of Technology and California Institute of Technology)

Strongly Driven Superconductors: What the Data tell us about Cuprates and Organicx

In the past decade, Cavalleri's group has reported "superconducting-like" behavior up to several times Tc in HiTc cuprates, the organic superconductors and K3C60. I will review some of the data and focus on the first two systems. In collaboration with M. Michael and E. Demler, I undertook a new analysis of the YBCO data. The goal is to find the minimal set of assumptions which can explain the observations. Unlike earlier discussions, we find that intense drive does not enhance the in-plane pair correlation or the inter-bilayer correlation. However, in order to explain the data, short range order within the plane and  correlation between members within the bi-layer are required in the equilibrium state. The implication is that pairing correlation survives up to the pseudogap scale. Therefore the pseudogap is a pairing gap. For the organic superconductor, I will also discuss a proposal with Zhehao Dai that the observed enhanced gap under drive is an induced Mott gap rather than a pairing gap.

Liang Fu (Massachusetts Institute of Technology)

Mott, Chern and Wigner Insulators in Semiconductor Heterostructures

The advent of moire superlattices in van der Waals heterostructures opens a new venue for exploring quantum phases of matter with unprecedented tunability. I will describe various kinds of quantum phases at integer fillings in semiconductor bilayer systems at zero magnetic field, including Mott and Chern insulators at the filling of one charge per unit cell, as well as Wigner solids at higher integer fillings.

**There were technical issues with the video recording of this seminar, so only audio is available.**

Dan Stamper-Kurn (University of California, Berkeley)

Many-body Physics of Atoms in Optical Lattices and Optical Cavities

Ultracold atomic gases allow us to create a variety of many-body quantum systems, which we might regard as synthetic quantum materials. In some of these systems, we encounter many of the properties pertinent to condensed-matter systems. In that vein, I will present experiments on atoms in optical lattices where we test a scaling hypothesis that relates phase transitions occurring in different lattice configurations and examine transport and equilibration of itinerant particles in geometrically frustrated bands. I will also share some results obtained from experiments on atoms placed within optical cavities, where they interact strongly with an optical field. This field can serve both as a precise probe, e.g. allowing us to examine non-equilibrium thermodynamics of a mesoscopic system, and also as a dynamical component within a hybridized atom + matter quantum system. I hope to spark some discussion where we can generate some new ideas on applications of quantum simulation, on feedback-controlled quantum matter, and on phase transitions in open quantum systems.

Erez Berg (Weizmann Institute)

What does the Wiedemann-Franz Law Tell Us About Non-Fermi Liquids?

The Wiedemann-Franz (WF) law, stating that the Lorenz ratio L=κ/Tσ between the electronic thermal and electrical conductivities in a metal approaches a universal constant L_0 at low temperatures, is often taken to be a signature of fermionic Landau quasi-particles. In contrast, we show that various models of weakly disordered non-Fermi liquids, where the fermionic quasi-particles are either marginally defined or ill-defined, also obey the WF law at T→0. Instead, we argue that the behavior of the leading correction to the WF law at low temperature distinguishes different types of strange metals. In particular, in a solvable model of a marginal Fermi liquid, we find that the leading low-temperature deviation of L-L_0 scales as T, in contrast to a Fermi liquid where it is proportional to T^2. Moreover, by invoking a quantum Boltzmann equation approach, we demonstrate that this behavior is generic in a class of marginal- and non-Fermi liquids characterized by a weakly momentum-dependent inelastic scattering rate.

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