Numerical solution of the Boltzmann equation for the collective modes of trapped Fermi gases

Details Numerical solution of the Boltzmann equation for the collective modes of trapped Fermi gases Numerical solution of the Boltzmann equation for the collective modes of trapped Fermi gases

2010-04-29

arxiv.org/abs/1004.5241v2

Phys. Rev. A 82, 023609 (2010)

Physics

Condensed Matter

Quantum Gases

13 pages, 8 figures, accepted for publication in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.82.023609

We numerically solve the Boltzmann equation for trapped fermions in the normal phase using the test-particle method. After discussing a couple of tests in order to estimate the reliability of the method, we apply it to the description of collective modes in a spherical harmonic trap. The numerical results are compared with those obtained previously by taking moments of the Boltzmann equation. We find that the general shape of the response function is very similar in both methods, but the relaxation time obtained from the simulation is significantly longer than that predicted by the method of moments. It is shown that the result of the method of moments can be corrected by including fourth-order moments in addition to the usual second-order ones and that this method agrees very well with our numerical simulations.

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