My Research

This page relates in brief, the problems that I currently work on or have worked in the past. Most of these are related to theoretical physics and in exceptional cases to fluid mechanics, nonlinear dynamics etc. This is not a complete listing since I do not remember some of the more transient ones and I don’t intend to put down some of the more spectacular failures . The list is ordered in reverse chronological order and is still under construction.

• Quantum opto-mechanics: dynamics and entanglement dynamics

• Phase problem is quantum mechanics: Wigner phase distributions and their liftings

• Control of finite level Rydberg atoms using radiation fields via ultra-short interactions – use of these techniques for quantum information processing etc

• Quantization of electrodynamics in nonlinear material media and its application to the study of optical solitons (part of my undergraduate thesis)

• Characterisation of quantised multi-mode radiation fields using its phase measurements.

• Cavity quantum electrodynamics under the Jaynes-Cummings and related hamiltonians; effects of quantum noise on the dynamics of these states; study of the Pegg-Bernett phase dynamics for various states of a quantised radiation field.

• Analysis of particle-atom interactions (in particular, scattering and photo-ionization) in confined geometries (specifically matter-wave guides).

• Study of elastic delta scattering as a model for analyzing general potential scattering scenarios.

• Investigation of solitons in electromagnetic media due to positive feedback mechanisms and medium-field coupling.

• Study of 2-RDM (Reduced Density Matrix) formulation of multi-electron quantum systems (along the lines of David A. Mazziotti).

• Application of supersymmetric quantum mechanical methods to Wigner-Brillouin perturbation theory.

• Existence of quasi-bound states in the scattering of electrons by nanotubes.

• Search for solitons in the (1+1)-d incompressible Navier-Stokes equation for the case of particular forms of pressure gradients and body forces.

• Quaternionic reformulation of the free particle Dirac equation using quaternionic representation of observables.

• Modeling a deuteron as a two-particle system under the Yukawa potential; solution for the wavefunction and search for the energy eigenvalues using a variational method for the radial part.

• Analysis of a drop falling on a liquid surface (initially at rest) using non-numerical techniques and a study of ripples thus formed on the surface.

• Existence of period-doubling chaos in a forced pendulum with two degrees of freedom, oscillating in a viscous medium.