### 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 |
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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.

Research output: Contribution to journal › Article

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 54, no. 5, pp. 4204-4212. https://doi.org/10.1103/PhysRevA.54.4204

}

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 -