András Csordás

Hydrodynamic excitations of Bose Condensates in anisotropic traps

The collective excitations of Bose condensates in anisotropic axially symmetric harmonic traps are investigated in the hydrodynamic and Thomas-Fermi limit. We identify an additional conserved quantity, besides the axial angular momentum and the total energy, and separate the wave equation in elliptic coordinates. The solution is thereby reduced to the algebraic problem of diagonalizing finite dimensional matrices. The classical quasi-particle dynamics in the local density approximation for energies of the order of the chemical potential is shown to be chaotic.

Shifts and widths of collective excitations in trapped Bose gases determined by the dielectric formalism

We present predictions for temperature-dependent shifts and damping rates. They are obtained by applying the dielectric formalism to set up a self-consistent model of a trapped Bose gas which can be shown to satisfy generalized Ward identities. Within the framework of the model we use lowest-order perturbation theory to determine the first-order correction to the results of Hartree-Fock-Bogoliubov-Popov theory for the complex collective excitation frequencies, and present numerical results for the temperature dependence of the damping rates and the frequency shifts. Good agreement with the experimental values measured by Jin et al. [Phys. Rev. Lett. 77, 420 (1996)] are found for the

Finite-temperature excitations of Bose gases in anisotropic traps

m=2

Collective excitations in Bose-Einstein condensates in triaxially anisotropic parabolic traps

mode, while we find disagreements in the shifts for

Classical quasiparticle dynamics in trapped Bose condensates

m=0.

SEMICLASSICAL WAVE FUNCTIONS AND ENERGY LEVELS OF BOSE-CONDENSED GASES IN SPHERICALLY SYMMETRIC TRAPS

The latter point to the necessity of a nonperturbative treatment for an explanation of the temperature dependence of the

Finite-temperature hydrodynamic modes of trapped quantum gases

m=0

Collective excitations of trapped Fermi or Bose gases

shifts.

Integrable Limits of Dynamics in Trapped Bose-Condensates

The mode frequencies of a weakly interacting Bose gas in a magnetic trap are studied as a function of the anisotropy of the trap. As in earlier works, the generalized Hartree-Fock-Bogoliubov equations within the Popov approximation are used for our calculations. A feature of our work is the combined use of a mode expansion in a finite basis and a semiclassical approximation of the highly excited states. The results are applied to check the accuracy of the recently suggested equivalent zero temperature condensate approximation, which involves a much simpler model.

Singularities in Rényi information as phase transitions in chaotic states

The wave equation of low-frequency density waves in Bose-Einstein condensates at vanishing temperature in arbitrarily anisotropic harmonic traps is separable in elliptic coordinates, provided the condensate can be treated in the Thomas-Fermi approximation. We present a complete solution of the mode functions, which are polynomials of finite order, and their eigenfrequencies, which are characterized by three-integer quantum numbers.