Condensed Matter Theory Home Pages
Condensed Matter Theory
Condensed matter physics is the study of systems with a large number of interacting degrees of freedom, such as a collection of electrons, atoms or molecules. Key questions in Condensed Matter Theory include: Can we understand emergent properties of matter such as the existence of metallic and insulating states, superconductivity, and magnetic long-range order from the relatively simple interaction laws at the microscopic level? Is there universal behavior at large length and time scales which is insensitive to the details of the microscopic interaction?
Condensed
matter research is at present in a truly exciting period.
Recent advances in materials science and fabrication techniques
leading to such systems as high Tc cuprate superconductors
and artificial structured nanoscale materials continue to
generate more fundamental questions to be answered. For example,
in the effort to try to understand the integer and fractional
quantum Hall effects, new collective phases of interacting
electrons have been discovered, and the whole field of strongly
correlated electrons is more active than ever. Other areas
of the condensed matter theory, such as material far from
equilibrium and disordered systems, continue to challenge
our understanding; and new concepts and approaches are continuously
being developed. Soft condensed matter physics, which deals
with colloids, emulsions, foams and complex fluids, is also
receiving increasing attention. The formidable inventory of
analytic and numerical techniques developed in studying condensed
matter has also found application in subjects beyond the boundary
of the field such as DNA sequence matching and protein folding.
Below we give a brief description of some projects of Brown's
condensed matter theory group:
Liquid crystals are fascinating materials with properties
intermediate between those of solids and liquids. An outstanding
question in liquid crystal research is how molecular structure
influences observed macroscopic behavior. Bob Pelcovits is
engaged in carrying out large-scale numerical simulations
of a variety of models of liquid crystals. The physical phenomena
studied include: flexo-electricity (the electrical response
of a liquid crystal to an orientational deformation), the
formation of chiral liquid crystal phases from achiral molecules,
the mechanism underlying molecular tilt in smectic phases,
topological defects in nematics, and the properties of confined
nematics.
The basic laws of quantum and statistical physics were discovered many decades ago, yet we continue to be amazed by the rich variety of behaviors and phases that emerge from these laws. Experiments on several classes of layered materials, on transport through nanostructures, and on nanoscale aqueous actinide complexes call for a deeper theoretical understanding of strongly correlated electronic systems. The statistics of dynamical systems such as turbulent flows also require the accurate treatment of strong many-body correlations. Brad Marston works with systematic analytical and numerical methods to establish phase diagrams, to study charge-transfer at surfaces and in aqueous environments, and to describe statistically nonlinear systems driven out of equilibrium. Attaining a better understanding of this physics is of both fundamental and practical importance.
Modern technology provides the means to construct semiconductors at
nanometer scales that confine electrons in one or two dimensions.
The states of matter formed by electrons in such confined systems cannot be described as simple one- and two-dimensional versions of the electronic matter found in conventional three-dimensional
semiconductors. Understanding these novel states and the
transitions between them is one of the key problems in condensed matter physics. The fractional quantum Hall effect is a particularly striking example. In quantum Hall systems electrons split into several pieces that are neither conventional fermions nor bosons, with a charge that is a fraction of the electron charge. One of the directions of Dima Feldman's research is an attempt to understand how the fractionally charged particles propagate and what happens at the phase transitions between quantum Hall phases with different fractional charges. A very interesting question concerns quantum Hall systems with filling factors 5/2 and 12/5. These might exhibit non-Abelian statistics and open a road to the practical implementation of quantum computing.
Macroscopic
quantum tunneling of particles coupled to a dissipative background
is a central problem in such diverse areas as Josephson junction
arrays, electronic transport in nanostructures and surface
diffusion of Hydrogen adatoms. See-Chen Ying is studying the classical and quantum aspect of surface diffusion and friction., as well as the dynamics of systems with complex energy landscapes. A novel approach to macroscopic tunneling has been developed by formulating a Stochastic Schrodinger equation. This allows one to study the limit of long coherent tunneling over many lattice sites in addition to the conventional nearest neighbor tunneling model . The dynamics of complex systems includes systems such as bioplymers translocating through nanopores, self organized growth of nano-islands and breakdown of epitaxial film through spontaneous generation of misfit dislocations. For the activated dynamics in these systems, a new numerical method is being developed that allows the determination of multiple saddle point regions around a local minimum. The actual transition rate can then be obtained through an ensemble average of all the transition paths going through different saddle point regions.
Mike Kosterlitz studies the properties of condensed matter systems in the presence of quenched disorder. Numerical simulations are performed for well defined models of spin and vortex glasses . It is necessary to define an excitation relative to an unknown ground state and to compute its energy to high precision to determine whether these systems have distinct thermodynamic phases at low temperatures. These studies can lead to an understanding of memory effects and the very slow dynamics in the ordered phase of vortex and spin glasses.
Selected Recent PhD Dissertations
Nobuhiko Akino, "Numerical Study of XY Spin Glass and Gauge Glass Models"
S. Badescu,"Dynamics of Hydrogen Atoms Adsorbed on Surfaces"
Andrew Callan-Jones, "Topological Defects in Liquid Crystalline Matter: Strain Transitions, Simulations, and Visualization of Core Structure and Fluctuations"
Chung-Hou Chung, "Systematic Approaches to Layered Materials with Strong Electron Correlations"
Antonella Cucchetti, "Microscopic Models for Adatom Dynamics"
Shan-Wen Tsai, "Systematic Analytical and Numerical Studies of Highly Correlated Electron Systems"
Ilya Vekhter, "Quasiclassical Approach to Transport in the Vortex State of Type II Superconductors and the Hall Effect"
