RESEARCH INTERESTS
My research interests were diverse and can be summarized as:
- Bose-Einstein Condensation: The
study of the following aspects of
codensates using the numerical solution of the mean-field time-dependent
Gross-Pitaevskii equation is the principal area of my research.
Stationary and time-evolution problems of
single and coupled condensates under the action of trap; Thermodynamics of
condensates; Vortices and superfluidity; Phase coherence; Classical
dynamical superfluid-insulator transition;
Interference of
matter wave; Collapse and explosion of strongly attractive condensates;
Josephson oscillation in condensates; Dynamics of condensates in
double-well and periodic
optical lattice potentials.
- Degenerate Fermi gas of atoms: Formation of solitons and Collapse of fermions in coupled
degenerate boson-fermion and
fermion-fermion mixtures
- Positron and positronium scattering:
Positronium
formation in positron scattering; Model-exchange potential for positronium
scattering; variational and coupled-channel methods
- High-temperature Superconductivity: Bardeen-Cooper-Schrieffer
equation; Cooper pair problem; mixed-angular momentum states for the order
parameter; thermodynamical properties
- Renormalization in Quantum Mechanics:
Renormalization of quantum
few-body problems; renormalization group equation.
- Quantum Mechanical Few-Particle Problem:
- Fractal, fragmentation and complex system:
- Numerical Analysis: Numerical
solution of
integral and differential equations of scattering applied to
atomic and nuclear problems; Numerical solution of nonlinear
partial differential Gross-Pitaevskii equation