Research Interests (needs updating - Dec. 2000)

My interests are in the areas of condensed matter physics, statistical mechanics, and computational physics. For details, see preprints and published papers.

+ Condensed Matter Physics / Statistical Mechanics

Statistical mechanics studies the properties of systems with many degrees of freedom. In particular, there are many unsolved and important problems concerning the non-equilibrium dynamics of systems with many degrees of freedom . The techniques of statistical mechanics have been applied to electronic devices, the properties of superconductors, and even traffic flow.

I have worked on the dynamics of condensed matter systems such as charge density waves, where an electronic condensate acts as an extended elastic object, something like a rubber membrane being slid over a rough surface (corresponding to impurities in the material). Some of the outstanding questions in charge-density wave dynamics include the importance of defects or ``tears'' in the elastic medium. [Collaboration principally with Cristina Marchetti.]

In very-small scale electronic devices (< 1 micron linear scale), the charging energies of individual electrons can be relatively large, so that conduction is not continuous, but must be studied as the hopping of individual charges. The collective behavior of arrays of such small elements includes threshold voltages and localized rivers of charge flow. [Current collaboration with Shantenu Jha.]

+ Computation

I use computers extensively in studying the above problems. Many of them use large amounts of computer time, so I study algorithms, in the hope of speeding up the simulations. In many cases, simple tricks, like keeping a dynamic list of "active locations" in a dynamical system and only updating those regions, can make large differences in the results. There can be unexpected relationships between physical problems, such as between charge transport in quantum dot arrays and the directed polymer problem, which result in novel applications of well-known algorithms. There are combinatorial optimization algorithms developed by computer scientists which have often not been used by physicists, but which can be of use, such as the minimum cut algorithm, which can be used to find ground states in interface problems with quenched disorder. The theory of computational complexity can be used to show that some problems are intractable in the sense of being NP-complete; in this case one is restricted (at best) to trying to find heuristic and approximate methods, such as finding the barrier between low-lying states. Recently, I have applied combinatorial optimization algorithms to studying the thermodynamic limit of systems with disorder. This subject has been controversial, as systems with quenched disorder can be quite complex. These simulations indicate that for a number of systems, the thermodynamic limit is well defined, that is, there are only a small number of ground states, rather than many nearly degenerate ones. [Principal collaborators: Daniel Fisher, Chen Zeng, David McNamara.]
Material on these pages is based upon work supported by the National Science Foundation (DMR-9702242, CAREER award) and the Alfred P. Sloan Foundation. (Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.)
See timings for production code on Linux boxes.
Email: aam@syr.edu