Condensed Matter Physics Lecture

[Jayme Bostic]

Acourse on electromagnetism, starting from the Maxwell equations and describing their application to electrostatics, magnetostatics, induction, light and radiation. The course also covers the relativistic form of the equations and electromagnetism in materials.

An introduction to the quantum Hall effect. The first half uses only quantum mechanicsand is at a levelsuitable for undergraduates. The second half covers more advanced field theoretic techniques of Chern-Simonsand conformal field theories.

An introduction to fluid mechanics, aimed at undergraduates. The course covers the basic flows arising from the Euler and Navier-Stokes equations, including discussions of waves, stability, and turbulence.

An introduction to statistical mechanics and thermodynamics,aimed at final year undergraduates. After developing the fundamentals of the subject, the course covers classical gases, quantum gases and phase transitions.

An introduction to general relativity, aimed atfirst year graduate students. It starts with a gentle introduction to geodesics in curvedspacetime. The course then describes the basics of differential geometry before turning tomore advanced topics in gravitation.

These notes provide an introduction to the fun bits of quantum field theory, in particular those topics relatedto topology and strong coupling. They are aimed at beginning graduate students and assumea familiarity with the path integral.

An elementary course on elementary particles. This is, by some margin, the least mathematically sophisticated of all my lecture notes, requiring little more than high school mathematics. The lectures provide a pop-science, but detailed, account of particle physics and quantum field theory. These lectures were given at the CERN summer school.

A course on particle physics that most definitely uses more than high school mathematics. The lectures describe the mathematical structure of the Standard Model, and explore features of the stong and weak forces. There are also sections on spontaneous symmetry breaking and anomalies.

An introduction to N=1 supersymmetry in d=3+1 dimensions, aimed at first year graduate students. The lectures describe how to construct supersymmetric actions before unpacking the details of their quantum dynamics and dualities.

The fascinating world of topological aspects of condesned matter systems is exposed in a 13 weeks lecture series. The course starts with the introduction of the most celebrated topological phase: the quantum Hall effect discovered in 1980. In the following chapters we develop the theoretical concepts that underpin the field of topological condensed matter physics. All topics are explained with the combination of abstract concepts and tangible illustatrations using the standard toy models. We finish the course by using our acquired knowledge to approach the magic of the fractional quantum Hall phases.

Learning goals:

- We know the pumping argument of Laughlin and the concept of spectral flow.

- We know that there is always a delocalized state in each LL.

- We know that σxy is given by the Chern number.

- We understand why the Chern number is an integer.

Learning goals:

- We understand the Bogoliubov-de-Gennes representation of a mean-field superconducting Hamiltonian and its relation to a Majorana fermion representation.

- We know one-dimensional topological superconductors, their topological invariant, boundary modes and topological classification.

- We understand how interactions reduce the topological classification from Z to Z 8 in one-dimensional topological superconductors.

Learning goals:

- We know the three symmetries on which the table of topological insulators is based.

- We know how, in principle, one can build the table.

- We know how to derive the indices for each symmetry group.

- We know how to make use of the table in real life.

Learning goals:

- We understand how the topological classification of insulators and the bulk-boundary correspondence is enhanced by including crystalline symmetries.

- We know how topological invariants such as mirror-graded winding numbers and the mirror Chern number are defined.

- We have an understanding of higher-order topological insulators.

Learning goals:

- We understand what we mean by Wannierizablity.?

- We know how to think of a band as a representation of the space group.

- We know how to construct elementary band representations.

- We can use the Bilbao server to analyze bands according to their symmetry properties.

Learning goals:

- We know Weyl semimetals, their Fermi arc surface states and chiral anomaly.

- We have an overview of other types of symmetry-enforced degeneracies in band structures, including point-like degeneracies of several bands and nodal lines.

Dr. Richard Prange did his graduate studies at the University of Chicago, where he worked with recent Nobelist Yoichiro Nambu, among others. He accepted a position at the University of Maryland in 1961.

Until his retirement in 2000, he played a vital role in the life of the Physics department. He led a substantial reform of its undergraduate major program and served energetic and innovative terms as chair of crucial departmental entities, including the Salary, Priorities, and Appointment, Promotion and Tenure committees. His was an important and highly-respected voice in all departmental deliberations.

Dr. Prange was the editor of a well-known book on the Quantum Hall Effect, but his interests reached well beyond condensed matter, into every substantive aspect of theoretical physics, including some pioneering work on quantum chaos. He was at complete ease discussing subjects as disparate as ferromagnetism and the cosmological constant. His interests also included history and travel.

Professor Cao's research focuses on the intersection of quantum gravity, quantum information, and quantum many-body physics. Topics of interest include emergent spacetime and gravity in the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, quantum computing, especially quantum error correction, and tensor network methods. The research style ranges from formal theory to close collaboration with experiments.

Professor Cheng's research interests are in soft condensed matter systems, including both biological and synthetic polymers, nanoparticles, nanocomposites, and membranes. The group uses molecular dynamics simulations and theoretical models based on statistical mechanics to study phenomena including supramolecular and supramacromolecular self-assembly (for example, microtubules as shown in the left figure), nanoparticle self-assembly, evaporation, capillarity, wetting, adhesion, and friction.

Prof. Dua's research is in condensed matter physics and quantum information science. His current dominant interests are topological order, quantum error correction, quantum control, and the physics and applications of deep learning. The research style involves formal theory and numerical computations and discussions with quantum computing laboratories about practical implementations. Check out his recent papers here and feel free to contact him at ad...@vt.edu to discuss exciting and important open questions.

Professor Ivanov's work is focused primarily on the areas of topological materials, quantum defects, and strongly correlated materials, studying these systems using a variety of theoretical and computational models. His recent work includes: studying the collective behavior of large numbers of Weyl points in real materials; the interplay of normal-state topology and unconventional superconductivity; simulation of color-center defects in various materials including silicon and diamond to study their dynamics and properties for applications in quantum sensing, quantum communication, and single photon generation.

Prof. Kaplan's research interests are in theoretical soft matter and biological physics. In close connection to experiments, his group develops theories and simulations to elucidate the interplay between the material composition, dynamics, form, and emergent function in living systems and their synthetic analogs.

Professor Park's research interests are theoretical and computational studies of electronic, magnetic, and transport properties of spin-orbit-coupled nanostructures and their interactions with local and external environmental factors. A few recent examples include: electron-vibron coupling effects in electron tunneling via a single-molecule magnet, spin dynamics for magnetic nanoparticles, and topological insulators with non-magnetic or magnetic interfaces. For these calculations we use density-functional theory (DFT), Monte Carlo simulations, and effective model Hamiltonian with parameters obtained from DFT.

Professor Pleimling's research interests are in condensed matter and non-equilibrium systems. Specific research interests include: out-of-equilibrium dynamical behavior of complex systems; aging phenomena and dynamical scaling; stochastic population dynamics; statistical mechanics of flux lines in superconductors; disordered systems; critical phenomena in confined geometries. These systems are explored using the tools of statistical physics.

Research in Professor Scarola's group spans several subfields of theoretical quantum physics with the aim of fostering quantum state engineering in the laboratory. The pristine environments we study typically allow for close connection with experiment in, e.g., two dimensional materials as well as atomic, molecular, and optical systems. Recent research directions include algorithms for quantum simulation, modelling of quantum computing hardware, quantum analogue simulation, and topological states of matter.

Research interests in Professor Tuber's group are in soft condensed matter and non-equilibrium systems. Specific research interests include: structural phase transitions; dynamic critical behavior near equilibrium phase transitions; phase transitions and scaling in systems far from equilibrium; statistical mechanics of flux lines in superconductors; and applications of statistical physics to biological problems. The group employs Monte Carlo and Langevin molecular dynamics simulations to solve stochastic equations of motion, as well as field theory representations to construct perturbational treatments and renormalization group approaches that improve on mean-field approximations.

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