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arXiv:cond-mat/0305624 · Physical Review A

Dynamics of a classical gas including dissipative and mean-field effects

P. Pedri, David Guéry-Odelin, S. Stringari

Published Oct 9, 2003• 71 citations
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Abstract

By means of a scaling ansatz, we investigate an approximated solution of the Boltzmann-Vlasov equation for a classical gas. Within this framework, we derive the frequencies and the damping of the collective oscillations of a harmonically trapped gas and we investigate its expansion after releasing of the trap. The method is well suited to study the collisional effects taking place in the system and in particular to discuss the crossover between the hydrodynamic and the collisionless regimes. An explicit link between the relaxation times relevant for the damping of the collective oscillations and for the expansion is established.

DOI
10.1103/physreva.68.043608

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By means of a scaling ansatz, we investigate an approximated solution of the Boltzmann-Vlasov equation for a classical gas. Within this framework, we derive the frequencies and the damping of the collective oscillations of a harmonically trapped gas and we investigate its expansion after releasing of the trap. The method is well suited to study the collisional effects taking place in the system and in particular to discuss the crossover between the hydrodynamic and the collisionless regimes. An explicit link between the relaxation times relevant for the damping of the collective oscillations and for the expansion is established.
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This article is devoted to the study of two-dimensional Bose gases harmonically confined. We first summarize their equilibrium properties. For such a gas above the critical temperature, we also derive the frequencies and the damping of the collective oscillations and we investigate its expansion after releasing of the trap. The method is well suited to study the collisional effects taking place in the system and in particular to discuss the crossover between the hydrodynamic and the collisionless regimes. We establish the link between the relaxation times relevant for the damping of the collective oscillations and for the time-of-flight expansion. We also evaluate the collision rate and its relationship with the relaxation time.
By means of the Boltzmann-Vlasov kinetic equation we investigate dynamical properties of a trapped one-component Fermi gas at zero temperature, featuring the anisotropic and long-range dipole-dipole interaction. To this end, we determine an approximate solution by rescaling both space and momentum variables of the equilibrium distribution, thereby obtaining coupled ordinary differential equations for the corresponding scaling parameters. Based on previous results on how the Fermi sphere is deformed in the hydrodynamic regime of a dipolar Fermi gas, we are able to implement the relaxation-time approximation for the collision integral. Then, we proceed by linearizing the equations of motion around the equilibrium in order to study both the frequencies and the damping of the low-lying excitation modes all the way from the collisionless to the hydrodynamic regime. Our theoretical results are expected to be relevant for understanding current experiments with trapped dipolar Fermi gases.
We investigate the transition and damping of low-energy collective modes in a trapped unitary Fermi gas by solving the Boltzmann-Vlasov kinetic equation in a scaled form, which is combined with both the T-matrix fluctuation theory in normal phase and the mean-field theory in order phase. In order to connect the microscopic and kinetic descriptions of many-body Feshbach scattering, we adopt a phenomenological two-fluid physical approach, and derive the coupling constants in the order phase. By solving the Boltzmann-Vlasov steady-state equation in a variational form, we calculate two viscous relaxation rates with the collision probabilities of fermion's scattering including fermions in the normal fluid and fermion pairs in the superfluid. Additionally, by considering the pairing and depairing of fermions, we get results of the frequency and damping of collective modes versus temperature and s-wave scattering length. Our theoretical results are in a remarkable agreement with the experimental data, particularly for the sharp transition between collisionless and hydrodynamic behaviour and strong damping between BCS and unitary limits near the phase transition. The sharp transition originates from the maximum of viscous relaxation rate caused by fermion-fermion pair collision at the phase transition point when the fermion depair, while the strong damping due to the fast varying of the frequency of collective modes from BCS limit to unitary limit.
By means of the Boltzmann-Vlasov kinetic equation we investigate dynamical properties of a trapped, one-component Fermi gas at zero temperature, featuring the anisotropic and long-range dipole-dipole interaction. To this end, we determine an approximate solution by rescaling both space and momentum variables of the equilibrium distribution, thereby obtaining coupled ordinary differential equations for the corresponding scaling parameters. Based on previous results on how the Fermi sphere is deformed in the hydrodynamic regime of a dipolar Fermi gas, we are able to implement the relaxation-time approximation for the collision integral. Then, we proceed by linearizing the equations of motion around the equilibrium in order to study both the frequencies and the damping of the low-lying excitation modes all the way from the collisionless to the hydrodynamic regime. Our theoretical results are expected to be relevant for understanding current experiments with trapped dipolar Fermi gases.