U. Physics Lab.- PHY 170, PHY 175

Research Interests: My research interests are mainly in the application of the methods of statistical physics. There are two general directions in my research, one more mathematical and one more directly related to physical systems. One general problem is the study of the connections between spectral analysis and phase transitions. A good example of such a connection is provided by a one-dimensional model defined on Farey fractions (see publications below). These models are of interest to both physicists and number theorists. The interactions between the "spins" are long-range, which leads to an unusual phase transition. Here we can find an associated transfer operator and analyze its spectrum to understand the character of the phase transition. The phase transition is continuous, but there are logarithmic corrections due to the presence of a marginal field when analyzed by renormalization group methods. The study of these models leads to connections with the Riemann Zeta function, modular theory, Maas cusp forms, the Lewis three term equation, and classical and quantum motion on the hyperbolic upper half plane. Further research on extensions of these models by including an external field may lead to more rigorous results.

The second direction is the study of the dynamics of first-order phase transitions, including phenomena such as nucleation, spinodal decomposition, and late stage growth and coarsening. In a typical situation, a system is rapidly quenched from a one-phase, thermal equilibrium state to a metastable or unstable state. Such a quenched system then gradually evolves to an equilibrium state.

Here is example of my simulations of the Ising model with a long range interaction. I study the early time morphology of the ordering with nonconserved order parameter (i.e. continuous ordering - model A) and with conserved order parameter (i.e.spinodal decomposition).

Other courses: Classical Dynamics, Atomic and Nuclear Physics, Computational Physics, Conceptual Physics, Electricity and Magnetism

"Science is built upon facts, as a house is built of stones; but an accumulation of facts is no more a science that a heap of stones is a house."

"Mathematics is the art of giving the same name to different things. [As opposed to the quotation: Poetry is the art of giving different names to the same thing]."

"It is through science that we prove, but through intuition that we discover."                                   Henri Poincaré

Curriculum Vitae (pdf file)

Dissertation (pdf file)