- Published 2000

We study a generalised Gross-Pitaevskii equation describing a ddimensional harmonic trapped (with trap frequency ω0) interacting Bose gas with a non-linearity of order (2 k + 1) and scaling exponent n of the interaction potential. We explicitly show that for a particular combination of n, k and d, the generalised Gross-Pitaevskii equation has SO (2,1) symmetry and it shows the universal monopole oscillation frequency 2ω0, using the time-dependent variational analysis. We also find that the time evolution of the width in a time-independent trap as well as a time-dependent trap can be described by the non-linear singular Hill’s equation for that particular combination of n, k and d which is analytically solvable in any dimension. We also obtain the condition for the exact self-similar solutions of the GrossPitaevskii equation using the same method. As an application, we consider quasi-two dimensional trapped Bose condensate state interacting through the Fermi pseudopotential and discuss about the universal monopole frequency,

@inproceedings{Ghosh2000MonopoleMS,
title={Monopole mode, scaling property and time evolution of a d-dimensional trapped interacting Bose gas at zero temperature: A time-dependent variational analysis},
author={Tarun Kanti Ghosh},
year={2000}
}