The activities of our faculty members in Theoretical Condensed-Matter Physics are quite varied, covering a full range of frontier issues.
Professor Joseph Birman carries out research in condensed matter theory on several topics. A major direction relates to symmetry and symmetry breaking in condensed matter. Both "geometrical" and "dynamical" symmetry play important roles. Geometrical symmetry gives rise to "go/no-go" selection rules for allowed/forbidden processes, phase transitions, and response functions. Dynamical symmetry is a powerful tool for the classification of the Hamiltonian of a many-body system. Techniques from Lie Algebras, supersymmetry, and more general algebraic structures are used to classify ground and excited states, transitions, and stability for interacting many-body systems. A continuing interest in Professor Birman's group is the prediction and analysis of optical properties of material systems. Examples include probing optical excitations in Bose-Einstein condensates, and "squeezing" of excitations in solids, analogous to quantum optics. Additional recent topics under active study include: magneto-acoustic transport theory for "composite fermions" in Quantum Hall Systems; nature of the excitations and their propagation in newly found atomic Bose-Einstein condensed systems; optical response of "quantum dot" systems. A recent experimental report on possible coexistence of competing effects such as superconductivity and ferroelectricity led us to the formulation of a new model based on "dynamical-symmetry" incorporating both effects, and our predictions of new effects when magnetic field and external pressure are applied.
Professor Harold Falk's research field is statistical mechanics. His work often uses spin-system techniques and focuses on mathematically exact results. Recently he has been studying the evolution of discrete-time, nonlinear and stochastic models.
Professor Joel Gersten. Condensed Matter Theory. Materials Sicence. Surface Science. Sonoluminescence. Interaction of light with matter.
Professor David Schmeltzer's research in condensed matter physics is devoted to studies of strongly correlated systems in low dimensions. Such systems include the Luttinger liquid in one dimension (quantum wires, spin ladders, edge states in the fractional hall effect) and (due to competing interactions) the Fermi-liquid--non-Fermi-liquid transition (high Tc), the superfluid-insulator transition and probably the metal-insulator transition in two dimensions. All these phenomena can be understood within a "quantum critical theory." Such a theory always emerges in the presence of competing interactions, giving rise to diverging correlation lengths.