RUI: Roughened Manifolds in Ill-Condensed Matter

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This is a Research at Undergraduate Institution grant to conduct theoretical research concerning the static and dynamic scaling properties of a variety of surfaces which exhibit entropic roughening due to thermal fluctuations, but in the presence of quenched disorder (in the form of randomly distributed pinning impurities) can lead to wandering that is enhanced many-fold. There are a number of fundamental theoretical issues of great practical importance which arise from the delicate interplay between thermal and disorder-induced roughening. This follows naturally from the fact that most experimental systems are to some degree forms of ill-condensed matter; the smallest modicum of randomness having potentially drastic effects upon not merely the critical properties, but the entire global structure of the phase diagram. Among the various manifolds to be discussed are individual vortex lines in ceramic superconductors, directed polymers in random media, and domain walls in impurity-stricken magnets. A mapping via Burgers equation permits us to connect the directed polymer problem to stochastic growth models such as ballistic deposition and Eden clusters. Also considered are interfacial delocalization due to quenched disorder and impurity controlled distortions of Abrikosov flux line lattices. %%% Analytical and computational research will be conducted at Barnard College on the effects of disorder on the general properties of surfaces and their manifestations in particular physical systems such as polymers, superconductors and magnets. The work will utilize undergraduates.