Reorganization of Kohn mode from harmonic to toroidal trap

We report the structural transformation of Kohn mode, from radial to circular one, in Bose-Einstein condensates as the harmonic confining potential is transformed to a toroidal one. A change which translates to modification of a pancake to a toroidal shaped condensate. For this we employ Hartree-Fock-Bogoliubov theory to examine the evolution of low energy quasiparticles. We, then, use Hartree-Fock-Bogoliubov theory with Popov approximation to demonstrate a striking change in the density profile of the non-condensate or thermal atoms accompanying the transformation of the trapping potential at [Math Processing Error]. That is, the condensate and non-condensate density distributions have overlapping maxima in the toroidal condensate, which is in stark contrast to the case of pancake geometry.