What is Condensed Matter Physics?

Research problems currently under investigation at Brown include the quantum mechanical many-body problem; the properties of models relevant to high-temperature superconductors and to heavy fermion systems such as the Anderson and Hubbard models, and quantum antiferromagnets; the study of the elementary excitations and the optical and transport properties of artificially structured materials; the effect of disorder in solids; phase transitions; topological order in two-dimensional systems; Josephson junction arrays in a magnetic field (both classical and quantum aspects); liquid crystals; surface reconstruction; microscopic theory of surface diffusion and vibrational relaxation; stability and growth of strained epitaxial layers; and charge transfer at surfaces.
 

Soft Condensed Matter Physics:

"Soft" condensed matter physics involves the study of systems as diverse as polymers, liquid crystals, emulsions, liquids, quasicrystals and related systems. Many problems of interest in soft condensed matter physics have strong overlap with issues of biological relevance such as the mechanical behavior of DNA, biomembranes and biomolecules.

Important tools in tackling these problems (which are often not accessible to purely analytic approaches) are numerical simulations and visualization. Ever increasing computer power has made the simulation of these complex systems feasible and new visualization algorithms and hardware is proving to be an essential component in analyzing the raw data in a useful way. As computer power continues to increase and  new algorithms continue to be developed, the field of computational soft condensed matter physics will continue to blossom. The field also offers many possibilities for interdisciplinary study as there is significant overlap with computer science (both for algorithm development and visualization techniques), biology and chemical physics.
 

Quantum Many-Body Physics:

Extraordinary things can happen when large numbers of electrons interact at low temperatures, a classic problem of "hard" condensed matter physics.  Confined to two dimensions and placed in a large magnetic field, the electrons organize into strange states of matter.  New types of excitations appear, including ones with fractional charge (the fractional quantum Hall effect.)  Take those same electrons, liberate them into the three dimensions of, say, crystalline copper, and they will re-organize into a Landau Fermi liquid -- a state of matter that can be described exactly using a powerful field-theoretic approach called bosonization. In striking contrast, electrons moving in the copper-oxygen planes of the high-temperature superconductors exhibit many qualitatively different phases: a d-wave superconductor, or an antiferromagnetic insulator, or a form of charge-segregation called stripes.

How to account for this wide range of astonishing behavior?  Every theoretical approach has its strengths and weaknesses.  A combination of analytical and numerical methods appears to be the best way to gain a thoroughgoing understanding of quantum condensed matter.  The renormalization-group, Feynman diagrams, mean-field theories, bosonization, mappings between seemingly unrelated problems including those that arise in particle physics, and systematic truncations of the infinite-dimensional Hilbert-space are just some of the methods employed by the Brown condensed matter theory group to study model systems.
 

A Sampling of Current Research in Condensed Matter Theory at Brown:
 
1. Numerical Simulations of Liquid Crystals
2. Dynamical Theory of Charge Transfer Between Complex Atoms and Surfaces
3. Out of Equilibrium Transport Across a Junction of Two Luttinger Liquids
 
 
• Physics of Condensed Matter: Experiment at Brown
 
Studies of magnetoconductive, optical, and mechanical properties of amorphous metals and semiconductors, magnetic solids and high Tc superconductors; electron-electron interactions in two dimensional electron systems at low temperatures, electronic and magnetic properties of artificial superlattices, quantum wires and dots; the quantum Hall effect; nonlinear optical phenomena and plasma dynamics studies in semiconductors using picosecond and femtosecond laser pulses; studies of ultrasonic and thermal properties of solids using picosecond laser pulses; holographic studies; properties of liquid and solid He4 and He3, including elementary excitations and their interactions cavitation and levitation of superfluid He4; NMR studies of the structure and bonding of crystalline and glassy solids; nuclear quadrupole resonance (NQR) studies of electronic distributions in molecules of biological importance and in inorganic solids; studies of chemisorption phenomena, surface band structure, reconstruction and two-dimensional phase transitions by low-energy electron diffraction, Auger and photoelectron spectroscopy, electron energy loss spectroscopy (EELS) and related techniques.