TY - JOUR

T1 - Quantized hydrodynamic model and the dynamic structure factor for a trapped Bose gas

AU - Wu, Wen Chin

AU - Griffin, A.

PY - 1996

Y1 - 1996

N2 - We quantize the recent hydrodynamic analysis of Stringari for the low-energy collective modes of a trapped Bose gas at T=0. This is based on the time-dependent Gross-Pitaevskii equation, but omits the kinetic energy of the density fluctuations. We diagonalize the hydrodynamic Hamiltonian in terms of the normal modes associated with the amplitude and phase of the inhomogeneous Bose order parameter. These normal modes provide a convenient basis for calculating observable quantities. As applications, we calculate the depletion of the condensate at T=0 as well as the inelastic light-scattering cross section S(q,ω) from low-energy condensate fluctuations. The latter involves a sum over all normal modes, with a weight proportional to the square of the q Fourier component of the density fluctuation associated with a given mode. Finally, we show how the Thomas-Fermi hydrodynamic description can be derived starting from the coupled Bogoliubov equations.

AB - We quantize the recent hydrodynamic analysis of Stringari for the low-energy collective modes of a trapped Bose gas at T=0. This is based on the time-dependent Gross-Pitaevskii equation, but omits the kinetic energy of the density fluctuations. We diagonalize the hydrodynamic Hamiltonian in terms of the normal modes associated with the amplitude and phase of the inhomogeneous Bose order parameter. These normal modes provide a convenient basis for calculating observable quantities. As applications, we calculate the depletion of the condensate at T=0 as well as the inelastic light-scattering cross section S(q,ω) from low-energy condensate fluctuations. The latter involves a sum over all normal modes, with a weight proportional to the square of the q Fourier component of the density fluctuation associated with a given mode. Finally, we show how the Thomas-Fermi hydrodynamic description can be derived starting from the coupled Bogoliubov equations.

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U2 - 10.1103/PhysRevA.54.4204

DO - 10.1103/PhysRevA.54.4204

M3 - Article

AN - SCOPUS:0001474408

VL - 54

SP - 4204

EP - 4212

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 5

ER -