My research focuses on exact solutions in statistical mechanics, effects of random impurities on phase transitions, renormalization group theories of Fermi systems, and the Fractional Quantum Hall Effect.

In statistical mechanics and in the quantum field theory of solids, my graduate student Ganpathy Murthy and I worked on random systems in which the interaction between the microscopic degrees of freedom varies from point to point. We worked out several exact solutions. These are particularly useful in systems with competing interactions where intuition is not a very reliable guide, e.g., a random magnet in which each spin receives conflicting signals from its neighbors on which direction to align.

Together with Prof. Subir Sachdev, Physics and Applied Physics, we have worked on the metal-insulator transition and on the properties of holes in quantum antiferromagnets.
Recently, I have developed a renormalization group approach to the problem of interacting fermions. The presence of a fermi-surface necessitates a modification of the standard RG procedure which integrates out all high momenta. Using the new approach, I was able to recover the results of Landau's Fermi Liquid Theory, a notoriously mysterious and difficult subject. The new approach makes Fermi Liquid Theory simpler and more straightforward and provides information about its instabilities.

Presently, and sometimes in collaboration with Ganpathy Murthy, I am developing a hamiltonian description of the Fractional Quantum Hall Effect. The description has now reached a point where it allows us to compute gaps for all observed fractions, finite temperature properties like polarization, and the relaxation rate. Our description is also able to map the electronic variables in terms of which the problem is originally posed to the Composite Fermion that are the ultimate quasiparticles.

For information on the nature of the problems under research by the Yale theoretical condensed matter physics group, please visit the condensed matter theory group.

For more, visit http://pantheon.yale.edu/~rshankar/

Selected Publications

"Hamiltonian Description of Composite Fermions: Aftermath," R.Shankar, Phys. Rev. Lett., 83, 2382 (1999).

"Effective Field Theory in Condensed Matter Physics," R. Shankar (invited lecture) at Conceptual Foundations of Quantum Field Theory, T.Y.Tao, ed., (Cambridge University Press, Cambridge, UK, 1998). http://xxx.lanl.gov/abs/cond-mat/9703210

Basic Training in Mathematics, R. Shankar (Kluwer-Plenum, New York, 1995).

Principles of Quantum Mechanics, R. Shankar (Kluwer-Plenum, New York, 1994). Second Edition.

Updated: 11/03/99