## Research

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# Theoretical Condensed Matter Physics

## 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

*History of Science, Theoretical physics, hydrodynamics, statistical physics.*

Leo Kadanoff's homepage

I do research connected with the history and philosophy of science, particularly aimed at describing and interpreting condensed matter theory. I am also interested in the connection between condensed matter and particle physics.

My physics research of my group is aimed at non-linear systems with the aid of techniques coming from 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. My most recent work has aimed at understanding the eigenvalue structure of singular Toeplitz matrices.

In the year 2007, I was President of the American Physical Society.

### Selected Publications:

- More is the Same; Mean Field Theory and Phase Transitions, Journal of Statistical Physics. Volume
**137**, pp 777-797, (December 2009) arXiv:0906.0653. - Theories of Matter: Infinities and Renormalization, to be published in The Oxford Handbook of the Philosophy of Physics editor Robert Batterman, Oxford University Press (2011). arXiv:1002.2985.
- Relating Theories via Renormalization, submitted to studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, (August 2010).
- Expansions for Eigenfunction and Eigenvalues of large-n Toeplitz Matrices, Papers in Physics, vol. 2 art 020003 (2010) arXiv:0906.0760.
- Hip Bone is Connected to... II, Leo P. Kadanoff,
*Physics Today*(March 2009). - 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). - An educational moment, Leo P. Kadanoff, Physics Today, (September 2006).
- Pulled Fronts and the Reproductive Individual, Leo P. Kadanoff,
*Journal of Statistical Physics*, p. 1-4 (April 2006).

### Related Links:

*Updated 2/2011*

## Kathryn Levin

Ph.D., Harvard, 1970.

Prof., Dept. Physics, James Franck Inst., and the College.

*Theoretical physics, solid state physics.*

Since 2003 (with the discovery of the fermionic atomic superfluids), our research has moved to the interface of condensed matter and AMO (atomic, molecular and optical) physics. We have been most interested in what one can learn from these trapped atomic gases about high temperature superconductors. Others in the Physics community are interested in using these systems as prototypes for a very strongly interacting fermionic system such as one finds in nuclear matter, in astrophysics or quark-gluon plasmas. This is an exciting time period where a range of different physics sub-disciplines have come together to address some of their common interests. This seems in many ways all the more novel because the difference in energy scales between, say, the quark-gluon plasmas and the atomic gases represents 21 orders of magnitude!

Superfluidity in fermions is ultimately driven by an attractive interaction, which effectively converts fermions into "bosons" (called Cooper pairs) which can then Bose condense. They will do so into their lowest energy state which corresponds to a situation where the individual fermions are associated with time reversed states. The remarkable aspect of the ultracold gases is that one can with a magnetic field tune the strength of the attractive interaction from weak (Bardeen Cooper Schrieffer or BCS) to strong (Bose Einstein condensation or BEC). That there is a connection between these atomic Fermi superfluids and high temperature superconductors is due, we presume to the fact that the cuprates are mid-way between BCS and BEC. This can be justified by the small size of the Cooper pairs and by the relatively high transition temperatures, both of which suggest the attraction or "glue" is stronger than in conventional superconductors.

Our work is based on many body quantum field theory and is closely tied to experiments. We have, on several occasions collaborated with experimentalists in the cold gas community. Recently we have been exploring the commonalities of these two different systems via spectroscopic, scattering and transport probes. Of particular interest lately has been the question of "perfect fluidity" in the atomic gases, associated with very low shear viscosity. This, we argue, is related to "bad metal" behavior in the cuprates, with very low conductivity. This perfect fluidity is also of great interest to physicists who work on Quantum Chromodynamics (QCD).

### 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). - "Theory of Radio Frequency Spectroscopy Experiments in Ultracold Fermi Gases and Their Relation to Photoemission Experiments in the Cuprates", Qijin Chen, Yan He, Chih-Chun Chien and K. Levin,
*Rep. Prog. Phys.***72**(2009) 122501. - "Comparison of Different Pairing Fluctuation Approaches to BCS-BEC Crossover", K. Levin, Qijin Chen, Chih-Chun Chien and Yan He.
*Annals of Physics*,**325**, 233-264 (2010). - "Establishing the Presence of Coherence in Atomic Fermi Superfluids: Spin Flip and Spin-Preserving Bragg Scattering at Finite Temperatures", Hao Guo, Chih-Chun Chien and K. Levin,
*Phys. Rev. Lett***105**, 120401 (2010) - "Microscopic Approach to Viscosities in Superfluid Fermi Gases: From BCS to BEC" H. Guo, D. Wulin, Chih-Chun Chien, K. Levin, ArXiv 1008.0423
- "Perfect fluids and Bad Metals: Transport Analogies Between Ultracold Fermi gases and High T_c superconductors". Guo, D. Wulin, Chih-Chun Chien and K. Levin, ArXiv 1009.4678
- "Conductivity in Pseudogapped Superconductors: The Role of the Fermi Arcs" Dan Wulin, Benjamin M. Fregoso, Hao Guo, Chih-Chun Chien and K. Levin, ArXiv 1012.4498
- "Spin Transport in Cold Fermi Gases: A Pseudogap Interpretation of Spin Diffusion Experiments at Unitarity" Dan Wulin, Hao Guo, Chih-Chun Chien and K. Levin, ArXiv 1102.0997
- "Nucleation of Spontaneous Vortices in Trapped Fermi Gases Undergoing a BCS-BEC Crossover" A. Glatz, H. Roberts, I.S. Aronson, K. Levin, ArXiv 1102.1792

### Related Links:

- Papers from x-arXiv/cond-mat
- Honors
- Contact information

*Updated 2/2011*

## Michael Levin

PH.D., Massachusetts Institute of Technology, 2006.

Assistant Prof., Dept. Physics, James Franck Inst., and the College*Theoretical physics, condensed matter physics*

Recently, my research has focused on two areas of quantum condensed matter physics. The first area is the study of "topological phases" of matter, such as quantum Hall liquids and topological insulators. These phases have a rich internal structure, but unlike conventional phases like magnets or superconductors, this structure has nothing to do with symmetry breaking or order parameters. Instead, the defining features of these phases have a topological character. As a result, entirely new concepts and tools need to be constructed to understand these systems. Much of my research is devoted to developing these new methods and approaches.

My second area of focus is at the intersection of quantum information theory and condensed matter physics. Here the fundamental problems are (1) to determine which quantum many-body systems can be efficiently simulated on a classical computer and (2) to develop methods to accomplish this task. In addition to its potential practical implications, this problem is closely related to many basic conceptual questions such as the nature of entanglement in many-body ground states and the classification of gapped quantum phases of matter.

**Selected publications:**

- M. Levin. Protected edge modes without symmetry. Phys. Rev. X 3, 021009 (2013).
- M. Levin and Z.-C. Gu. Braiding statistics approach to symmetry-protected topological phases. Phys. Rev. B 86, 115109 (2012).
- M. Levin and A. Stern. Fractional topological insulators. Phys. Rev. Lett. 103, 196803 (2009).
- M. Levin and C. P. Nave. Tensor renormalization group approach to 2D classical lattice models. Phys. Rev. Lett. 99, 120601 (2007).
- M. Levin and X.-G. Wen. Detecting topological order in a ground state wave function. Phys. Rev. Lett. 96, 110405 (2006).

### Related Links:

- Honors
- Contact Information

*Updated 10/2013*

## Peter B. Littlewood

Ph.D., Cambridge, 1980.

Prof., Dept. Physics, James Franck Inst., and the College; Associate Director - Physical Sciences & Engineering, Argonne Natl. Lab.

*Theoretical physics, condensed matter physics.*

Professor Littlewood's research has focused on the dynamics of collective transport; phenomenology and microscopic theory of high-temperature superconductors, transition metal oxides and other correlated electronic systems; and optical properties of highly excited semiconductors. He has applied his methods to engineering, including holographic storage, optical fibers and devices.

### Selected Publications (TBD):

- Band Structure of SnTe studies by Photoemission Spectroscopy, P.B. Littlewood, B. Mihaila, R.K. Schulze, D.J. Safarik, J.E. Gubernatis, A. Bostwick, E. Rotenberg, C.P. Opeil, T. Durakiewicz, J.L. Smith, and J.C. Lashley,
*Physical Review Letters*,**105**, 086404 (2010). - Polariton Condensates, D. Snoke and P.B. Littlewood,
*Physics Today*,**63**, 42 (August 2010).

### Related Links:

- Papers from x-arXiv/cond-mat
- Honors
- Contact information

*Updated 8/2012*

## 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.

### 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).

### Related Links:

- Papers from x-arXiv/cond-mat
- Honors
- Contact information

*Updated 8/2006*

## Dam T. Son

Ph.D., Institute for Nuclear Research - Moscow, 1995.

University Prof., Dept. Physics, Enrico Fermi Institute, James Franck Inst., and the College.

*Theoretical physics*

I have a broad research program encompassing several areas of theoretical physics.

*String Theory*: applications of gauge-gravity duality in the physics of the quark-gluon plasma and other strongly interacting systems.

*Nuclear Physics*: properties of the hot and dense states of matter, e.g., the quark gluon plasma and dense quark matter (color superconductors).

*Condensed matter physics*: physics of the quantum Hall system, graphene; applications of quantum field theory.

*Atomic physics*: many-body physics of cold trapped atoms, BCS-BEC crossover, applications of quantum field theoretical techniques.

### Selected Publications:

- R. Baier, A.H. Mueller, D. Schiff, and D.T. Son, "Bottom-up" thermalization in heavy ion collisions,
*Phys. Lett. B***502**, 51 (2001). - P. Kovtun, D.T. Son, and A.O. Starinets, Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics,
*Phys. Rev. Lett*.**94**, 111601 (2005). - Y. Nishida and D.T. Son, Epsilon Expansion for a Fermi Gas at Infinite Scattering Length,
*Phys. Rev. Lett*.**97**, 050403 (2006). - C. Hoyos and D.T. Son, Hall Viscosity and Electromagnetic Response,
*Phys. Rev. Lett*.**108**, 066805 (2012).

### Related Links:

- Papers from arXiv.org
- Honors
- Contact information

*Updated 10/2012*

## Paul B. Wiegmann

Ph.D., Landau Inst., Moscow, 1978.

Robert W. Reneker Distinguished Service 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, Electronic systems far from equilibrium.

*Statistical Mechanics*: Non-equilibrium Statistical Mechanics, Critical phenomena governed by Conformal Symmetry, Conformal stochastic processes, Stochastic geometry, Random Matrix Theory.

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

*Nonlinear Physics*: Driven non-equilibrium systems, Turbulence, Fractal aspects of Pattern Formation, Interface Dynamics, Incommensurate Systems, Integrable aspects of nonlinear physics, Quantum Non-linear Phenomena.

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

### Related Links:

- Papers from x-arXiv/cond-mat
- Contact information

*Updated 2/2011*

## Thomas A. Witten

Ph.D., San Diego, 1971.

Prof. Emeritus, 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:

- Robust fadeout profile of an evaporation stain T. A. Witten,
*EPL***86**64002 (2009) - Chiral sedimentation of extended objects in viscous media Nathan W. Krapf, Thomas A. Witten, and Nathan C. Keim,
*Physical Review E***79**056307 (2009) - Stress focusing in elastic sheets T. A. Witten,
*Reviews of Modern of Physics*,**79** *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)

### Related Links:

- Papers from x-arXiv/cond-mat
- Honors
- Contact information

*Updated 2/2011*

## 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.

### Related Links:

*Updated 6/2008 *