(1975-)
Optics: Starting with some remarks by Radhakrishnan on polarised
aperture
synthesis, I tried to construct a global phase convention for polarised
light without discontinuities anywhere on the Poincare sphere and found to
my surprise that it was impossible (Ref.2). It needed a firm suggestion
years later from Ramaseshan to see and work out explicitly the connection
of Pancharatnam's phase convention to Berry's geometric phase. (Ref.6)
Another simple but useful optical venture, with Blandford and Narayan, was
the application of wavefronts and Fermat's principle to gravitational
lenses, which were, till then, (and sometimes still are) analysed in
terms of rays (Ref.7). A fully general relativistic formulation was
developed with Samuel (Ref.8).
Statistical physics: Measurements of the resistivity of binary mixtures were made very near their critical point. The simple mixture formula was used and gave a reasonable account of the observed exponent (Ref.1) especially after Surjit Singh's remark that the variance of the local concentration behaves like the energy (its derivative like the specific heat). With G.S.Ranganath, anisotropic defect interaction forces in a nematic were studied exploiting the scale invariance of the free energy outside a core. The result could be expressed purely in terms of single defect properties. With hindsight, this is a simple example of an anomaly - a calculable consequence of a cutoff breaking scale invariance (Ref.3).
The approach to a steady state of collisionless dark matter in a galaxy is an interesting case of ``dissipation without dissipation" (Ref.10), there can relaxation but to a variety of final states which retain some but not full memory of the initial conditions. In fact, Sridhar, (who got me into this area) even produced examples of oscillating steady states. Another astrophysically inspired problem in non-equilibrium statistical physics which I think is wide open is the non-linear clustering of dark matter in an expanding universe. One guess at a scaling law with Padmanabhan (Ref.9) has proved useful but efforts (at least mine) aimed at a deeper dynamical understanding have not yet borne fruit.
Ill-posed inversion problems such as deconvolution, synthesis imaging and crystal structure determination were a major concern in the early eighties. In work with Narayan (Ref.5). maximum ``entropy" methods were studied and a viewpoint attributing their success to a priori information rather than their ``maximally non-committal" nature was developed. In astronomical image processing, this helped in understanding the behaviour of various variational algorithms, while in the case of crystallography, intriguing connections to direct methods such as the maximum determinant method emerged (Ref.4). All this is not strictly statistical physics, perhaps physical statistics would be closer, but is certainly a live and useful area of research.
Selected Publications: