CLASSICAL QUASI-PARTICLE DYNAMICS IN TRAPPED BOSE CONDENSATES

The dynamics of quasiparticles in repulsive Bose condensates in a harm onic trap is studied in the classical limit. In isotropic traps the cl assical motion is integrable and separable in spherical coordinates. I n anisotropic traps the classical dynamics is found, in general, to be nonintegrable. For quasiparticle energies E much smaller than the che mical potential mu, besides the conserved quasiparticle energy, we ide ntify two additional nearly conserved phase-space functions. These ren der the dynamics inside the condensate (collective dynamics) integrabl e asymptotically for E/mu-->0. However, there coexists at the same ene rgy a dynamics confined to the surface of the condensate, which is gov erned by a classical Hartree-Fock Hamiltonian. We iind that also this dynamics becomes integrable for E/mu-->0 because of the appearance of an adiabatic invariant. For E/mu of order 1 a large portion of the pha se-space supports chaotic motion, both for the Bogoliubov Hamiltonian and its Hartree-Fock approximant. To exemplify this we exhibit Poincar e surface of sections for harmonic traps with the cylindrical symmetry and anisotropy found in TOP traps. For E/mu much greater than 1 the d ynamics is again governed by the Hartree Fock Hamiltonian. In the case with cylindrical symmetry it becomes quasiintegrable because the rema ining small chaotic components in phase space are tightly confined by tori. [S1050-2947(97)06912-6].