Theoretical Condensed Matter Physics

Ilya Ilya A. Gruzberg

Ph.D., Yale University, 1998.
Associate 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.

Selected Publications:

  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 Kadanoff 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.
Leo Kadanoff's homepage

We work on non-linear systems using the techniques of statistical physics. More specifically, we are studying how turbulent, chaotic, and stochastic behavior arises in dynamical systems, particularly hydrodynamical and biological systems. For example, we have been extensively concerned with the development of simplified models for the development of fractal patterns (Loewner evolution), turbulence, and biological systems. We have also studied the nature of mathematical infinities in the flow of fluids. We use both analytical and simulational methods and try to use experimental data whenever possible. Our basic goal is to understand the nature of the complex motion that can arise in even very simple systems. This work has applications to mathematics, astronomy, and chemical engineering.

I also do research and writing about the public presentation of science, particularly in the context of science museums. In the year 2007, I was President of the American Physical Society.

Selected Publications:

  • Exact Solutions for Loewner Evolutions, Wouter Kager, Bernard Nienhuis, and L. P. Kadanoff. Journal of Statistical Physics, 115 3/4, 805-822 (May 2004).
  • Discrete Charges on a Two Dimensional Conductor, M.Kl. Berkenbusch, I. Claus, C. Dunn, L.P. Kadanoff, M. Nicewicz, and S.C. Venkataramani. Journal of Statistical Physics, 116, 5/6, (September 2004).
  • Trace for the Loewner Equation with Singular Forcing, Leo P. Kadanoff and Marko Kleine Berkenbusch. Nonlinearity, 17 4, R41-R54 (2004).
  • Stochastic Loewner evolution driven by Lévy processes, I. Rushkin, P. Oikonomou, L.P. Kadanoff and I.A. Gruzberg. J. Stat. Mech. P01001 (January 2006).
  • The Loewner Equation: Maps and Shapes. Ilya A. Gruzberg and Leo P. Kadanoff. Journal of Statistical Physics, 114 5, 1183-1198 (March 2004).
  • Computational Scenarios. Leo. P. Kadanoff, Physics Today, pp.10-11 (November 2004).
  • Hip Bone is Connected to..., Leo P. Kadanoff, Physics Today (September 2005).
  • Pulled Fronts and the Reproductive Individual, Leo P. Kadanoff, Journal of Statistical Physics, p. 1-4 (April 2006).
  • The value of physics, My election statement for APS, Leo P. Kadanoff, APS News, (May 2006).

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Kathryn Levin 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.

Selected Publications:

  • "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 Mazenko 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 eA/T as temperature T is lowered. Much remains to be worked out for this model.

Selected Publications:

  • 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 Wiegmann Paul B. Wiegmann

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

Condensed Matter Physics: Electronic Physics in Low Dimensions, Quantum Magnetism, Correlated Electronic Systems, Quantum Hall Effects, Topological aspects of Condensed Matter Theories, Superconductivity, Superconductor-Insulator Transition, Quantum Melting.

Mathematical Physics: Integrable Models of Quantum Field Theory and Statistical Mechanics, Quantum Groups and Representation theory, Anomalies in Quantum Field Theory, Topological Field Theory, Conformal Field Theory; Quantum gravity and Stochastic geometry.

Nonlinear Physics: Dynamical systems, Fractal aspects of Pattern Formation, Interface Dynamics, Incommensurate Systems, Integrable aspects of nonlinear physics.

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

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Thomas Witten Thomas A. Witten

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

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.

Selected Publications:

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Wendy Zhang

Wendy Zhang

Ph.D., Harvard, 2001.
Associate Professor, Dept. of Physics, James
Franck Institute, and the College.
Theoretical physics, soft condensed matter.

I am interested in the formation of singularities, e.g. divergences in physical quantities such as pressure, on a fluid surface due to flow and surface tension effects. Two examples are the breakup of a liquid drop and viscous entrainment. In studying how nonlinear interactions give rise to singularities, we hope to understand the kinds of simplification in dynamics that can result when a physical process involves disparate length- and time-scales. We also hope that surface tension effects can be used to create structures which span a few molecules in one dimension but are macroscopic in other dimensions. More generally, thin tendril-like structures which extend over large distances arise in many contexts and can often strongly influence the large-scale dynamics. Examples include thermal and compositional convection, Coulomb fission and the formation of tether structure on a fluid surface due to optical radiation pressure. We use analytical methods, often based on asymptotic analysis, and numerical simulations. Many of the work are inspired by, or happen in parallel with, experimental work.

Selected Publications

  • Balance of actively generated contractile and resistive forces controls cytokinesis dynamics. W. W. Zhang & D. N. Robinson, PNAS 102, 2005.
  • Drop Splashing on a Dry Smooth Surface. L. Xu, W. W. Zhang & S. R. Nagel, Phys. Rev. Lett. 94 2005.
  • Viscous Entrainment from a Nozzle: Singular Liquid Spouts. W. W. Zhang, Phys. Rev. Lett. 93 2004.
  • Persistence of Memory in Drop Breakup: The Breakdown of Universality. P. Doshi, I. Cohen, W. W. Zhang, P. Howell, M. Siegel, O. A. Basaran, & S. R. Nagel, Science, 302 2003.
  • Shake-Gels: Shear-induced gelation of laponite-PEO mixtures. J. Zebrowski, V. Prasad, W. W. Zhang, L. M. Walker & D. A. Weitz, Colloid & Surface Sci. A 213 2003.

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