Abstract:
This thesis is devoted to theoretical study of various aspects of low energy collective excitations in a trapped interacting alkali-metal atomic gases (Bose and Fermi) and of fractional quantum hall systems. An equation of motion for velocity fluctuations of a two-dimensional deformed trapped Bose gas just above the critical temperature in the hydrodynamical regime is derived. From this equation, the eigenfrequencies and corresponding density fluctuations for a few lo-lying excitation modes are calculated. The method of averages are used to derive a dispersion relation in a deformed trap at very high temperature that interpolates between the collisionless and hydrodynamic regimes. The frequencies and the damping rates for monopole and quadrupole modes in both the regimes, are calculated using this dispersion relation. It is shown that the time evolution of the wave packet width of a Bose gas in a time-independent as well as time-dependent trap can be obtained from the method of averages. A general dispersion relation of monopole and two quadrupole excitations of a two dimensional deformed trapped interacting quantum gas. Also analytical expressions for monopole and two quadrupole mode frequencies of a two-dimensional unpolarized Fermi gas in an anisotropic trap, derived using this general dispersion relation.
