Integrable Limits of Dynamics in Trapped Bose-Condensates

The dynamics of quasiparticles in Bose condensates at zero temperature, confined in harmonic potentials, are studied using the Bogoliubov-theory. The Hamiltonian of the Bogoliubov-theory, appearing in the semiclassical limit is investigated in detail. The classical motion given by this Hamiltonian is generally chaotic already for axially symmetric traps. But, in certain parameter regions the motion becomes quasi-integrable. Integrable regions are studied classically, and the experimentally accessible low-energy region quantum mechanically.