caltech theoretical physics phd

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Michael C. Cross

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.

New center positions UC Riverside as a leader in quantum vibronics

QuVet is funded by a $7.5M grant from the Department of Defense

Physicist Nathaniel Gabor at the University of California, Riverside, has been awarded a $7.5M grant from the Department of Defense, or DoD, to develop a Multidisciplinary University Research Initiatives, or MURI, center on campus. Called QuVET for the Center for Qu antum V ibronics in E nergy and T ime, the center’s co-principal investigators are leading scientists at UCR, Caltech, MIT, and Columbia University. 

“Vibronic,” a portmanteau of vibrational and electronic, refers to transitions between molecular energy states. Vibronic behavior is central to both biological and material systems and could impact future technology’s energy harvesting efficiency. Vibronic effects — vibrational transitions that accompany electronic transitions — occur in systems ranging from photosynthetic light-harvesting antennae to molecular gases and solid-state materials.

Gabor, a professor of physics and astronomy and the five-year grant’s principal investigator, believes the strong partnership with DoD laboratories and industry will position QuVET to be a scientific and technological epicenter for quantum vibronics. He said the visionary science QuVet represents could place UCR at the head of a new era of science, where biology, physics, and chemistry are explored through the lens of quantum mechanics.

“This is science at its best, bringing a lot of positive attention to UCR,” said Shan-Wen Tsai , chair of the Department of Physics and Astronomy. “QuVet will open up many good research opportunities for our undergraduate and graduate students.”

In the following Q&A, Gabor, a leader in the fields of quantum materials and photosynthetic light harvesting research, discusses his vision for the new center he will direct. Vivek Aji , a professor of physics and astronomy at UCR and the grant’s co-principal investigator, also shares his thoughts.

Q: Specifically, what research will QuVet focus on?

Gabor: At the length scales of atoms and molecules, atomic vibrations can strongly affect the wave-like behavior (quantum nature) of electrons. When vibrations and electrons interact, the resulting behavior can only be described as vibronic. We have assembled a team of physicists, chemists, biochemists, and biologists to overcome three critical challenges in achieving new technologies that harness quantum mechanics: 

(1) In many molecular and material systems, vibrations act to remove energy from electrons, decreasing the overall efficiency of energy transport. However, photosynthetic organisms have adapted to instead harness vibrations to enhance the efficient movement of energy. In new molecular and material systems, can we achieve the same outcome of photosynthesis in order to enhance transport towards ultimate efficiencies? 

(2) Tuning the interaction between atomic motion and electronic states via experimental control remains impossible, prevented by scientists’ inability to engineer materials at the atomic scale. Can emerging biochemical strategies and novel materials enable direct control over the wave-like behavior of electronic and vibrational excitations? 

(3) Design principles do not exist for next-generation quantum systems, which implement strong vibrational effects. How can we take inspiration from biology to develop new technologies based on exotic states in which vibrations directly affect electronic behavior?

Q: What will the collaboration with Caltech, MIT, and Columbia University scientists involve?

Aji: The QuVET team brings together leading researchers in disciplines ranging from quantum physics (UCR and Columbia) and quantum chemistry (Caltech and Columbia) to biophysics, biochemistry (MIT and UCR) and quantum materials (Columbia and UCR). Each member of the team brings unique expertise that strategically covers a broad scientific base. Since the center goals are ambitious and attempt to solve a major trans-disciplinary problem, it is important that each of the team members is a creative thinker and cross-disciplinary scientist.

Q: Why is now a good time for a center like this? 

Gabor: The theoretical understanding and experimental control of vibronic behavior is complicated by the wide range of physical processes that also occur in complex systems, such as the molecular light harvesting antennae of photosynthesis, where vibronic effects play the most important roles. Indeed, a complete quantum treatment of vibronic effects does not exist. 

Biology, physics, and chemistry converge at the atomic and molecular scale, where quantum mechanics becomes vastly more important than at large scales. As our research technologies have advanced — and we collectively study molecules and materials at smaller and smaller length scales — more and more studies point to quantum mechanics as a means to understand emerging behaviors. Recently, it was discovered that the vibrational motion of atoms plays a critical role not only in the remarkably high efficiency of photosynthetic organisms, but also the efficiency of energy transfer in electronic materials. Our projects are among the first to explore the ability to engineer the interaction between vibrational motion and electronic states, heralding a new era of quantum science. 

We believe quantum vibronics will have a major impact on fundamental science and technology involving both the biology/biochemistry of quantum processes in light-sensing and the understanding of novel optoelectronic properties in quantum materials — two fields at the forefront of basic research within the DoD. 

Q: What sets this center apart from other centers like it elsewhere? 

Aji: Currently, no other center focuses strongly on vibronic effects and the possible future technologies that would result from a deep understanding of quantum vibronic phenomena.

QuVET takes such a strong multidisciplinary approach to the challenges we have described here. Vibronic effects occur in many places in nature and understanding them fully requires a very special combination of people and expertise.  

Q: What do you hope this center will achieve? 

Gabor: I hope this center marks a pivot towards trans-disciplinary science at UCR. With resources that are committed wisely, UCR could be the leader in emerging topics where quantum mechanics describes the interface between physics, chemistry, biology, and engineering.

Further, QuVET provides both undergraduate and graduate students with a unique opportunity to enter a fast-growing field — bio-inspired quantum vibronics — at its very outset and to steer its growth. The tightly integrated nature of the tasks will facilitate sharing of knowledge and resources between groups. Together with the strong collaborative ties between UCR, Caltech, Columbia, and MIT, this will create a multidisciplinary learning environment for students, fostering the development of young scientists with a unique blend of theoretical, materials and advanced spectroscopy expertise.

Header image shows Vivek Aji (left) and Nathaniel Gabor. (UCR/Stan Lim)

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PhD Position in Theoretical Physics

Job Information

Offer description.

Join our EU project to characterise colloidal gels for new sustainable materials. Make a real impact at the intersection of academic and industrial research!

Your job We seek an enthusiastic, capable PhD candidate who is interested in working on the numerical and theoretical characterization of colloidal gels – suspensions of micron-sized particles that stick together to form open network structures. You will become a part of the CoCoGel Marie Skłodowska-Curie Industrial Doctoral Network, together with 14 other PhD candidates, who will be working throughout Europe on bringing rational design to the structuring of colloidal gels. In this position, you will participate in the collaborative and training activities hosted by the CoCoGel network. You will be employed by Utrecht University, but as a part of the project, you will also be embedded in InProcess-LSP for a period of 18 months. InProcess-LSP is a Scaleup company that develops process analytical technology for the in-line characterisation of dense suspensions using optical coherence tomography (OCT). This technology was used, for example, to size the lipid nanoparticles used in the COVID-19 vaccine.

The core of the project is to push forward the capabilities of the fluid-dynamics solver for colloidal suspensions maintained by the De Graaf group and use this to further understanding of the behaviour of various experimental systems in the CoCoGel network. This solver is based on the Stokesian Dynamics algorithm and builds on the Google JAX framework. Elements that will need to be introduced are size polydispersity and frictional interactions, in addition the algorithm is to be optimised for sparse matrices. Beyond these computational physics aspects, you will study physically how the features of the gel are changed by subjecting the system to external perturbations. During your embedding in InProcess-LSP you will also learn the way in which particle size and features of the gel network may be extracted using OCT and connect this to the results from your simulation. As one of the few dedicated simulators within the CoCoGel consortium, you will be uniquely positioned to interact with many experimental groups and build toward a successful career either in academia or industry.

You will be working within the Institute for Theoretical Physics (ITP) for the duration of the PhD (Utrecht University, location Science Park). This includes a non-negotiable 18-month on-site stay at InProcess-LSP (located in Oss, the Netherlands).

You will work within a small team that specialises in hydrodynamics, statistical physics of soft-condensed-matter systems, and biophysics; presently having diverse research outlooks ranging from colloidal gelation, to tissue dynamics, to bacterial colony growth.

As a PhD candidate, you will primarily focus on the development of numerical methods for the study of colloidal gels, which include hydrodynamic interactions and carrying out the physics-focused research that is based on the numerical methods that you help develop. You are also expected to participate in assisting with classes (10-15% workload). Participation within the ITN training network conforms to EU legislation.

Requirements

We are seeking a motivated researcher, who can balance the research requirements expected of a Dutch PhD with the opportunities that are afforded by working in an industry-academia collaboration. You must have a M.Sc. in Physics or in an associated field by the start of the programme. It is important that you are proficient in English and have good communication skills, as the CoCoGel project requires substantial coordination and collaboration. Experience with computational fluid dynamics and good knowledge of classical statistical physics are considered very valuable, the ability to program in C or C++ or a comparable language is needed to make progress in the project. You are expected to actively pursue a research PhD and contribute to the network activities of the CoCoGel ITN.

To qualify for this position, you cannot have resided or carried out your main activity (work, studies, etc.) in the Netherlands for more than 12 months in the 36 months preceding the recruitment start date.

Additional Information

• a position for four years;
• a full-time gross monthly salary between €2,770 and €3,539 in the case of full-time employment (salary scale P under the Collective Labour Agreement for Dutch Universities (CAO NU);
• 8% holiday pay and 8.3% year-end bonus;
• a pension scheme, partially paid parental leave and flexible terms of employment based on the CAO NU.

In addition to the terms of employment laid down in the CAO NU, Utrecht University has a number of schemes and facilities of its own for employees. This includes schemes facilitating professional development , leave schemes and schemes for sports and cultural activities , as well as discounts on software and other IT products. We also offer access to additional employee benefits through our Terms of Employment Options Model. In this way, we encourage our employees to continue to invest in their growth. For more information, please visit Working at Utrecht University .

As Utrecht University, we want to be a home for everyone. We value staff with diverse backgrounds, perspectives and identities, including cultural, religious or ethnic background, gender, sexual orientation, disability or age. We strive to create a safe and inclusive environment in which everyone can flourish and contribute.

If you are enthusiastic about this position, just apply via the 'Apply now' button! Please enclose:

• your letter of motivation;
• your curriculum vitae;
• the names, telephone numbers, and email addresses of at least two references.

If this specific opportunity isn’t for you, but you know someone else who may be interested, please forward this vacancy to them.

For more information, please contact Joost de Graaf at [email protected] and have a look at the attached general advert for the CoCoGel network.

Do you have a question about the application procedure? Please send an email to [email protected] .

Candidates for this vacancy will be recruited by Utrecht University.

Work Location(s)

Where to apply.

Verifying the work of quantum computers

New method uses classical computers to check accuracy of complex quantum systems.

Quantum computers of the future may ultimately outperform their classical counterparts to solve intractable problems in computer science, medicine, business, chemistry, physics, and other fields. But the machines are not there yet: They are riddled with inherent errors, which researchers are actively working to reduce. One way to study these errors is to use classical computers to simulate the quantum systems and verify their accuracy. The only catch is that as quantum machines become increasingly complex, running simulations of them on traditional computers would take years or longer.

Now, Caltech researchers have invented a new method by which classical computers can measure the error rates of quantum machines without having to fully simulate them. The team describes the method in a paper in the journal Nature .

"In a perfect world, we want to reduce these errors. That's the dream of our field," says Adam Shaw, lead author of the study and a graduate student who works in the laboratory of Manuel Endres, professor of physics at Caltech. "But in the meantime, we need to better understand the errors facing our system, so we can work to mitigate them. That motivated us to come up with a new approach for estimating the success of our system."

In the new study, the team performed experiments using a type of simple quantum computer known as a quantum simulator. Quantum simulators are more limited in scope than current rudimentary quantum computers and are tailored for specific tasks. The group's simulator is made up of individually controlled Rydberg atoms -- atoms in highly excited states -- which they manipulate using lasers.

One key feature of the simulator, and of all quantum computers, is entanglement -- a phenomenon in which certain atoms become connected to each other without actually touching. When quantum computers work on a problem, entanglement is naturally built up in the system, invisibly connecting the atoms. Last year, Endres, Shaw, and colleagues revealed that as entanglement grows, those connections spread out in a chaotic or random fashion, meaning that small perturbations lead to big changes in the same way that a butterfly's flapping wings could theoretically affect global weather patterns.

This increasing complexity is believed to be what gives quantum computers the power to solve certain types of problems much faster than classical computers, such as those in cryptography in which large numbers must be quickly factored.

But once the machines reach a certain number of connected atoms, or qubits, they can no longer be simulated using classical computers. "When you get past 30 qubits, things get crazy," Shaw says. "The more qubits and entanglement you have, the more complex the calculations are."

The quantum simulator in the new study has 60 qubits, which Shaw says puts it in a regime that is impossible to simulate exactly. "It becomes a catch-22. We want to study a regime that is hard for classical computers to work in, but still rely on those classical computers to tell if our quantum simulator is correct." To meet the challenge, Shaw and colleagues took a new approach, running classical computer simulations that allow for different amounts of entanglement. Shaw likens this to painting with brushes of different size.

"Let's say our quantum computer is painting the Mona Lisa as an analogy," he says. "The quantum computer can paint very efficiently and, in theory, perfectly, but it makes errors that smear out the paint in parts of the painting. It's like the quantum computer has shaky hands. To quantify these errors, we want our classical computer to simulate what the quantum computer has done, but our Mona Lisa would be too complex for it. It's as if the classical computers only have giant brushes or rollers and can't capture the finer details.

"Instead, we have many classical computers paint the same thing with progressively finer and finer brushes, and then we squint our eyes and estimate what it would have looked like if they were perfect. Then we use that to compare against the quantum computer and estimate its errors. With many cross-checks, we were able to show this 'squinting' is mathematically sound and gives the answer quite accurately."

The researchers estimated that their 60-qubit quantum simulator operates with an error rate of 91 percent (or an accuracy rate of 9 percent). That may sound low, but it is, in fact, relatively high for the state of the field. For reference, the 2019 Google experiment, in which the team claimed their quantum computer outperformed classical computers, had an accuracy of 0.3 percent (though it was a different type of system than the one in this study).

Shaw says: "We now have a benchmark for analyzing the errors in quantum computing systems. That means that as we make improvements to the hardware, we can measure how well the improvements worked. Plus, with this new benchmark, we can also measure how much entanglement is involved in a quantum simulation, another metric of its success."

The Nature paper titled "Benchmarking highly entangled states on a 60-atom analog quantum simulator" was funded by the National Science Foundation (partially via Caltech's Institute for Quantum Information and Matter, or IQIM), the Defense Advanced Research Projects Agency (DARPA), the Army Research Office, the U.S. Department of Energy's Quantum Systems Accelerator, the Troesh postdoctoral fellowship, the German National Academy of Sciences Leopoldina, and Caltech's Walter Burke Institute for Theoretical Physics. Other Caltech authors include former postdocs Joonhee Choi and Pascal Scholl; Ran Finkelstein, Troesh Postdoctoral Scholar Research Associate in Physics; and Andreas Elben, Sherman Fairchild Postdoctoral Scholar Research Associate in Theoretical Physics. Zhuo Chen, Daniel Mark, and Soonwon Choi (BS '12) of MIT are also authors.

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Story Source:

Materials provided by California Institute of Technology . Original written by Whitney Clavin. Note: Content may be edited for style and length.

Journal Reference :

• Adam L. Shaw, Zhuo Chen, Joonhee Choi, Daniel K. Mark, Pascal Scholl, Ran Finkelstein, Andreas Elben, Soonwon Choi, Manuel Endres. Benchmarking highly entangled states on a 60-atom analogue quantum simulator . Nature , 2024; DOI: 10.1038/s41586-024-07173-x

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