ON THIS PAGE: Ilya A. Gruzberg | Leo P. Kadanoff | Kathryn Levin | Gene F. Mazenko | Paul B. Wiegmann | Thomas A. Witten

Theoretical Condensed Matter Physics

U of C physics faculty conduct a wide range of theoretical investigations into condensed matter phenomena.   The main site of this research is the interdisciplinary James Franck Institute, or JFI, pictured above.  The faculty of the Institute are physicists, physical chemists, geochemists, and applied mathematicians who combine their strengths to attack phenomena that go beyond the physics discipline.  Physics students studying condensed matter interact closely and regularly with these other disciplines.

Below, each faculty member describes his or her research interests and representative publications.  They update these every year or more.  For more current information, see the Materials Center, a federally funded research center closely connected with the JFI.  The Center studies the fundamental basis for new materials from polymer films to singular flows. The granular physics group site describes collaborative research on granular materials.   The ASCI Flash center conducts research on collective, singular astrophysical events, like explosions.   Related research is described on our condensed matter experiment page, and our main theoretical physics page.

Ilya A. Gruzberg

Ph.D., Yale University, 1998.
Assistant Prof., Dept. Physics, James Franck Inst., and the College
Theoretical physics, condensed matter physics.

I pursue research in two major directions. I briefly list relevant subjects, and then comment on them.

Mathematical physics: stochastic Loewner evolution, stochastic growth phenomena, conformal field theory, statistical mechanics, critical phenomena, random matrix theory, supersymmetry, algebraic and field-theoretical methods in condensed matter physics.

In the last few years, new insights have permitted unexpected progress in the study of fractal shapes in two dimensions. A new approach, called stochastic Loewner evolution (SLE), has arisen through analytic function theory and probability theory, and given a new way of calculating fractal shapes in critical phenomena, and in other problems like diffusion limited aggregation (DLA), the theory of random walks, and of percolation. This new method has close and beautiful connections to a number of older subjects: conformal field theory, random matrices and integrable systems. It has been already applied to such diverse problems as two-dimensional turbulence, spin glasses, and chaotic systems.

Condensed matter physics: disordered systems, mesoscopic physics, localization, quantum Hall effects, superconductivity, interplay of interactions and disorder, strongly correlated systems.

In this more traditional area I am mostly working on the theory of disordered systems, and in particular, on various aspects of localization phenomena: critical behavior at localization transitions, multifractiality of critical wave functions, and the like.

1. Exact exponents for the spin quantum Hall transition, I. A. Gruzberg, A. W. W. Ludwig, and N. Read, Phys. Rev. Lett. 82, 4524 (1999).
   Published version    cond-mat/9902063
2. Localization and delocalization in dirty superconducting wires, P. W. Brouwer, A. Furusaki, I. A. Gruzberg, and C. Mudry, Phys. Rev. Lett. 85, 1064 (2000).
   Published version    cond-mat/0002016
3. Random-bond Ising model in two dimensions, the Nishimori line, and supersymmetry, I. A. Gruzberg, N. Read, and A. W. W. Ludwig, Phys. Rev. B 63, 104422 (2001).
   Published version    cond-mat/0007254
4. The Loewner equation: maps and shapes, I. A. Gruzberg and L. P. Kadanoff, J. Stat. Phys. 114, 1183 (2004).
   Published version    cond-mat/0309292
5. Localization in disordered superconducting wires with broken spin-rotation symmetry, I. A. Gruzberg, N. Read, and S. Vishveshwara, Phys. Rev. B 71, 245124 (2005).
   Published version    cond-mat/0412413
6. Stochastic Loewner evolution for conformal field theories with Lie-group symmetries, E. Bettelheim, I. A. Gruzberg, A. W. W. Ludwig, and P. Wiegmann, Phys. Rev. Lett. 95, 251601 (2005).
   Published version    hep-th/0503013
7. Harmonic measure of critical curves, E. Bettelheim, I. Rushkin, I. A. Gruzberg, and P. Wiegmann, Phys. Rev. Lett. 95, 170602 (2005).
   Published version    hep-th/0507115
8. Stochastic Loewner evolution driven by Lévy processes, I. Rushkin, P. Oikonomou, L. P. Kadanoff, and I. A. Gruzberg, J. Stat. Mech. (2006) P01001
   Published version    cond-mat/0509187
9. Surface criticality and multifractality at localization transitions. A. R. Subramaniam, I. A. Gruzberg, A. W. W. Ludwig, F. Evers, A. Mildenberger, and A. D. Mirlin, Phys. Rev. Lett. 96, 126802 (2006).
   Published version    cond-mat/0512040

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 Leo P. Kadanoff

Ph.D., Harvard, 1960.
John D. MacArthur Distinguished Srvc. Prof. Emeritus, Depts. Physics and Math., James Franck Inst., Enrico Fermi Inst., and the College
Theoretical physics, hydrodynamics, statistical physics.
Home Page: http://jfi.uchicago.edu/~leop/

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 Kathryn Levin

Ph.D., Harvard, 1970.
Prof., Dept. Physics, James Franck Inst., and the College
Theoretical physics, solid state physics.

Our interest is primarily in theoretical studies of exotic superconducting and magnetic systems. We ask questions such as what makes different materials magnetic or superconducting? What is the nature of their superconductivity? The co-operative effects associated with magnetism and superconductivity lead to some of the most exciting and mysterious phenomena within the sub-field of condensed matter physics. Our experimental colleagues continue to discover and create new materials with fascinating properties, such as the heavy fermion and oxide superconductors. What distinguishes our sub-field of physics is the close and timely interaction between theory and experiment, as well as the long range possibility for making technological impact. This close theory/experiment interaction is at the heart of our research agenda.

While we have, over many years, been interested in the high temperature superconductors, we have now turned our attention to a new class of ultracold fermionic superfluids which are made by atomic physicists in atomic traps. We believe these "materials" may be prototypes of the cuprate superconductors and are particularly excited about the interesting problems which arise in these systems. How does one measure temperature? How does one prove superfluidity? The properties of this strange class of superfluids are intermediate between conventional (BCS) theory and Bose Einstein condensation. Most importantly, with the application of a magnetic field the system can be tuned from one behavior to another.

• "Heat Capacity of a Strongly-Interacting Fermi Gas." J. Kinast, A. Turlapov, J.E. Thomas, Qijin Chen, Jelena Stajic, Science 307, 1296 (2005).
• "Density Profiles of Strongly Interacting Trapped Fermi Gases." Jelena Stajic, Qijin Chen and K. Levin, Physical Review Letters 94, 060401 (2005).
• "BCS-BEC Crossover: From High Temperature Superconductors to Ultracold Superfluids." Qijin Chen, Jelena Stajic and K. Levin, Physics Reports 412, 1 (2005).
• "Superfluid Phase Diagram in Trapped Fermi Gases", Qijin Chen, C.A. Regal, M. Greiner, D. S. Jin and K. Levin, Phys Rev. A 73, 041601(R), 2006.
• "Thermodynamics of Interacting Fermions in Atomic Traps." Qijin Chen, Jelena Stajic and K. Levin, Phys. Rev. Letters 95, 260405 (2005).
• "Population of closed-channel molecules in trapped Fermi gases with broad Feshbach resonances", Qijin Chen and K. Levin, Phys. Rev. Lett. 95, 260406 (2005).
• "Intermediate Temperature Superfluidity in an Atomic Fermi Gas with Population Imbalance", Chin-Chun Chien, Yan He, Qijin Chen and K. Levin, cond-mat/0605039.
• "Finite Temperature Momentum Distribution of a Trapped Fermi Gas", Qijin Chen, C. A. Regal, D. S. Jin and K. Levin, cond-mat/0604469.

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 Gene F. Mazenko

Ph.D., Massachusetts Institute of Technology, 1971.
Prof., Dept. Physics, James Franck Inst., and the College
Theoretical physics, statistical physics.

Various materials, for example magnets, superconductors, liquid crystals, diblock copolymers and conventional solids, when temperature quenched from a high to a low temperature grow over time into ordered structures. In quenching a material from a temperature where it is a liquid down to a temperature corresponding to a solid we go from a material which is a uniform fluid to a final state where we have a crystalline solid. In the kinetic process taking us from the fluid to the crystal one finds intermediate states where the order is broken up by defects. Examples are dislocations in solids and vortices in magnets. We are interested in the appearance, motion and annihilation of these defects.

In the case of magnets and superfluids, where the final ordered state is uniform, the theory has been been developed to the state where we have been able to answer questions like: What is the velocity distribution for these evolving defects.

We are currently interested in the fundamental question of the nature of defect structures in pattern forming systems. Our interest is in those structures which form naturally under experimental circumstances. Our guide is to try and understand recent experiments on microphase separating diblock copolymer systems. Such systems grow a layered or striped phase. These systems are fundamentally important as prototypical two dimensional ordering systems but also as building blocks on the nano scale. Previously we have developed numerical techniques for looking at the nature of kinetic models proposed to describe systems of this type.

We are also working on the theoretical description of the kinetics of the liquid-glass transition. We have developed a new field theoretical model, called the hindered diffusion model, which leads naturally, to characteristic times which are activated, grow as e^A/T as temperature T is lowered. Much remains to be worked out for this model.

• G.F. Mazenko, Vortex Velocities in the O(n) Symmetric TDGL Model. Phys. Rev. Lett 78, 401, 1997.
• H. Qian and G. F. Mazenko, Vortex Dynamics in a Coarsening Two Dimensional XY Model, Phys. Rev. E 68, 021109/4 (2003).
• H. Qian and G. F. Mazenko, Defect Structures in the Growth Kinetics of the Swift-Hohenberg Model, Phys. Rev. E 67, 036102/12 (2003).

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 Paul B. Wiegmann

Ph.D., Landau Inst., Moscow, 1978.
Prof., Dept. Physics, James Franck Inst., Enrico Fermi Inst., and the College
Theoretical physics, condensed matter physics.

My research focuses on the non-perturbative aspects of quantum field theory, primarily electronic systems, where interaction controls the properties of the system. This includes electronic physics in low dimensions, quantum Hall effect, and strongly correlated electronic systems. In recent works on condensed matter physics, I have concentrated on topological aspects of quantum interference.

In the area of mathematical physics, my interests include completely integrable models of quantum field theory and statistical mechanics, quantum groups, and anomalies in quantum field theory.

In recent years I have also become interested in singular behavior developing in dynamical systems.

Papers I've published since 1993 are available in x-arXiv/cond-mat and x-arXiv/hep-th.

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 Thomas A. Witten

Ph.D., San Diego, 1971.
Prof., Dept. Physics, James Franck Inst., and the College
Theoretical condensed matter physics, weakly-connected matter.

Prof. Witten has a home page.

My research concerns collective mechanisms for creating spontaneous structure in forms of conventional condensed matter such as polymer liquids, evaporating liquid drops, layer-forming surfactant micelles and thin elastic sheets. All these materials when subjected to structureless external forces develop new forms of spontaneous structure at a fine length scale, such as the sharp folds of a crumpled sheet or the thin ring stain left when a drop of dirty fluid has evaporated. These new forms of force-induced structure often arise from fundamental mechanical properties such as the competition between bending and stretching energy in an elastic sheet or between evaporative flows and capillary forces in an evaporating drop. They may arise from fundamental statistical properties such as the randomness of a chain polymer molecule or the random, tenuous structure of a colloidal aggregate. In either case the fundamental origins of the resulting structures mean that they can be used and manipulated in a wide range of material realizations independent of the specific properties of the materials.

• Stress focusing in elastic sheets T. A. Witten, Reviews of Modern of Physics, submitted April 2006
• Structured fluids: polymers, colloids, surfactants (Oxford University Press: 2003)
• Geometric origin of excess low-frequency vibrational modes in amorphous solids Matthieu Wyart, Sidney R. Nagel, T.A. Witten Europhysics Letters 71 1-7(2005)
• Confined Multilamellae Prefer Cylindrical Morphology Jung-Ren Huang, Ling-Nan Zou, Thomas A. Witten, European Physics Journal E 18 279-285(2005)
• Spontaneous curvature cancellation in forced thin sheets, Tao Liang, Thomas A. Witten, Phys. Rev. E 73 046604 (2006)
• Insights from Soft Condensed Matter. T.A. Witten. In More Things in Heaven and Earth: A Celebration of Physics at the Millennium, ed., B. Bederson, Springer, 1999.

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