Institute of Condensed Matter Theory at the U of I
Professor Eduardo Fradkin is a Donald Biggar Willett Professor of Physics and a Center for Advanced Study Professor at the University of Illinois. He is the current Director of the Institute for Condensed matter Theory. He received his Licenciado (Master's) degree in physics from Universidad de Buenos Aires (Argentina) and his PhD in physics from Stanford University in 1979. He came to the University of Illinois in 1979 as a postdoctoral research associate, and became an assistant professor of physics at Illinois in 1981. He was promoted to associate professor in 1984, and became a full professor in 1989. Professor Fradkin is an internationally recognized leader in theoretical physics, who has contributed to many problems at the interface between quantum field theory (QFT) and condensed matter physics (CMP). Eduardo is a fellow of the American Physical Society, a fellow of the American Academy of Arts and Sciences and member of the National Academy of Sciences.
In his early work, he pioneered the use of concepts from CMP and statistical physics, such as order parameters and phase diagrams, to problems of QFT and high energy physics, in particular to the non-perturbative behavior of gauge theories. Perhaps his most important result in this area was the proof that when matter fields carry the fundamental unit of charge, the Higgs and confinement phases of gauge theories are smoothly connected to each other and are as different as a liquid is from a gas. This result remains one of the cornerstones of our understanding of the phases of gauge theories and represents a lasting contribution to elementary particle physics.
Professor Fradkin's unique perspective has allowed him to invoke and apply results from QFT to CMP. He was one of the first theorists to use gauge theory concepts in the theory of spin glasses and to use concepts of chaos and non-linear systems in equilibrium statistical mechanics of frustrated systems. Professor Fradkin has pioneered the application of QFT methods to the physics of correlated disordered electronic systems and the quantum stability of the spontaneously dimerized state of polyacetylene.
Professor Fradkin also pioneered the use of Dirac fermions for CMP problems, particularly in two space dimensions. A prime example is his work on Dirac fermions on random fields (which he began with former graduate student Dr. Matthew Fisher), which is now regarded as the universality class of the transition between quantum Hall plateaus in the integer Hall effect. This work is also important for the description of quasiparticles in disordered d-wave superconductors. He also applied, quite early on, these ideas to the physics of what nowadays are known as topological insulators, showing that in the presence of lattice topological defects, these systems exhibit a non-trivial electronic spectrum with a parity anomaly.
A major achievement of Professor Fradkin's recent research has been the development, in collaboration with former graduate student Dr. Ana López, of the fermion Chern-Simons field theory of the fractional quantum Hall effect. This theory has played a central role in the current research effort in this exciting problem in CMP. Professor Fradkin and his collaborators have extended this theory to the more challenging problem of the non-Abelian quantum Hall states and developed a theory of a non-Abelian interferometer to study the unusual properties of the vortices of these quantum fluids. This approach is one of the possible directions for the development of a topological qubit.
More recently Professor Fradkin and his collaborators introduced the notion of electronic liquid crystal states, which are phases of quantum fermionic strongly correlated systems exhibiting properties akin to those of classical complex fluids. These ideas play a crucial role in the current understanding of the pseudogap regime of high temperature superconductors. More recently, this approach led to Fradkin and coworkers to develop the concept of Intertwined Orders and to the proposal of a novel superconducting state, the Pair density Wave, may be the prime competitor of d-wave superconductivity.
Fradkin and his graduate student Hart Goldman developed a loop model approach which provides a heuristic derivation of the web of dualities that relate multiple theories of interest in condensed matter and high energy physics.
Research Interests: quantum and statistical mechanics, condensed matter, and machine learning.
Here's a general description of some of my results and aims. Specifically, I'm interested in:
Read more about Kay at https://faculty.math.illinois.edu/~kkirkpat/
Macromolecular, Colloidal, and Complex Fluid Theory
Our overarching goal is the development and application of novel molecular-scale statistical mechanical theories of the equilibrium and dynamic properties of polymers, colloids, nanoparticles, liquid crystals, elastomers, nanocomposites and other complex fluids and soft materials. A common theme is to both understand existing systems at a fundamental level and develop predictive methods for guiding the experimental design of new materials. Five broad areas are of present interest.
The uniquely slow dynamics and elasticity of entangled polymer liquids is a fascinating scientific problem of high engineering and processing importance. Existing theoretical approaches are phenomenological. We are developing first principles statistical mechanical theories that explicitly capture the dynamical consequences of polymer connectivity and uncrossability for diverse macromolecular architectures (rigid rods, flexible chains, star-branched objects) in solution, melts, thin films and liquid crystalline states. Molecular level theories of the rheology of these systems under both constant constant stress and strain rate conditions are also being developed. The work is relevant not only to synthetic polymeric materials, but also dense collections of stiff biopolymers commonly found in cell biology and crucial for the mechanical function of the cytoskeleton.
"Particle-polymer" mixtures, in solution and melt states, are ubiquitous in diverse areas of science and technology. We have developed predictive theories of the equilibrium structure, properties and phase behavior of such polymer nanocomposites based on integral equation methods. Present work is focused on dense nanocomposites involving functional particles such as buckeyballs, or fillers that are soft and fluctuating such as crosslinked nanogels. We are building on our advances in predicting equilibrium structure to tackle the complex problem of the dynamics and mechanical response of these hybrid materials. Questions such as how fast do nanoparticles diffuse and hop in a polymer liquid or network, can nanoparticles gel or jam in the polymer matrix, how do particles modify polymer entanglements, elasticity (reinforcement) and viscosity, and the role of particle size, shape, interactions with the polymer, and nanocomposite statistical microstructure are being investigated.
A broad area of enduring interest is the slow dynamics of glass-forming fluids. We are developing molecular-level theories of relaxation, diffusion, viscoelasticity and vitrification of deeply supercooled liquids including molecular, polymer, metallic and colloidal and nanoparticle systems. New ideas about the origin of dynamic cooperativity and rare collective activated events have been conceived and are being quantitatively applied to experimental materials. This advance provides a foundation for treating polymer thin films which are of high engineering importance. A major aim is to understand the remarkably large speed up of dynamics observed when polymer films are thinner than 30-50 nanometers and have at least one surface exposed to air.
The development of functional colloidal assemblies in solution is of high interest. We are developing microscopic statistical mechanical theories of the self-assembly of patchy Janus colloids, the coupled translation-rotation dynamics, vitrification, and gelation of dense suspensions of nonspherical particles, electron conductivity in metallic nanoparticle gels, and how colloids organize and move in large mesh polymer networks. These topics connect with our efforts in the interdisciplinary area of basic energy sciences.
A new direction is to understand gas and molecule permeability in polymeric materials in the molten, crosslinked rubber, and glass states. This requires treating the effect of penetrant size, shape and interactions with the polymer on solubility, and the role of length scale dependent polymer dynamics and free volume on penetrant diffusion. A major goal is to establish molecular-level design rules for both optimizing permeability for membrane-based separation applications, and minimizing permeability to fabricate new barrier materials that protect polymers from degradation processes. In addition, the effect of nonequilibrium physical aging and external stress on these phenomena is of interest. This research also underpins the development of high performance self-healing materials where controlling the transport of small molecules and oligomers in polymeric microcapsules is essential.