Theoretical Problems in Condensed Matter and Statistical Physics

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9416910 Halperin Research will focus on a range of theoretical problems in the field of condensed matter and statistical physics. Long-range goals are to improve the basic understanding of strongly interacting many- body systems and highly disordered materials, to develop new theoretical and computational techniques, and to explain outstanding experimental puzzles. A major concern will be properties of quasi-two-dimensional electron systems at low temperatures, in very strong magnetic fields. Research will concentrate on Landau-level filling fractions where the quantised Hall effect is not observed. Theoretical analysis will be based on a mathematical transformation where the electrons become a set of fermions that interact through a fictitous electric and magnetic field of the Chern-Simons type. Topics to be studied include finite temperature transport experiments, as well as fundamental limits to the applicability of the fermion Chern-Simons theory. Another major concern will be low-temperature properties of spin systems where quantum mechanical fluctuations are very important. One focus will be properties of materials such as high temperature superconductors which contain quasi-one-dimensional spin-one spin chains with antiferromagnetic interactions. Other work will explore higher dimensional spin systems with frustrated interactions. Other research will include properties of disordered systems, especially nuclear magnetic resonance studies of water in porous media such as rocks. The focus here will be the analysis of the effects of the diffusion of water molecules on nuclear magnetic resonance signals obtained using various pulse sequences in complex geometries. %%% Research will focus on a range of theoretical problems in the field of condensed matter and statistical physics. A major concern will be properties at low temperatures, in very strong magnetic fields of quasi-two-dimensional electron layers, which occur in various semiconductor devices such as the field-effect transistor. The research also has implications for other materials such as high- temperature superconductors. Other research will include properties of disordered systems, especially nuclear magnetic resonance studies of water in porous media such as rocks. This work may have application to oil recovery.