Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 4204-4212 |
| Number of pages | 9 |
| Journal | Physical Review A - Atomic, Molecular, and Optical Physics |
| Volume | 54 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 1996 Jan 1 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
Cite this
Quantized hydrodynamic model and the dynamic structure factor for a trapped Bose gas. / Wu, Wen-Chin; Griffin, A.
In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 54, No. 5, 01.01.1996, p. 4204-4212.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Quantized hydrodynamic model and the dynamic structure factor for a trapped Bose gas
AU - Wu, Wen-Chin
AU - Griffin, A.
PY - 1996/1/1
Y1 - 1996/1/1
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
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 -