One- and two-dimensional reductions of the mean-field description of degenerate Fermi gases

Pablo Díaz*, David Laroze, Iván Schmidt, Boris A. Malomed

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study collective behaviour of Fermi gases trapped in various external potentials, including optical lattices (OLs), in the framework of the mean-field (hydrodynamic) description. Using the variational method, we derive effective dynamical equations for the one- and two-dimensional (1D and 2D) settings from the general 3D mean-field equation. The respective confinement is provided by trapping potentials with the cylindrical and planar symmetries, respectively. The resulting equations are nonpolynomial Schrödinger equations coupled to equations for the local transverse size of the trapped states. Numerical simulations demonstrate close agreement of results produced by the underlying 3D equation and the effective low-dimensional ones. We consider the ground state in these settings. In particular, analytical solutions are obtained for the effectively 2D non-interacting Fermi gas. Differences between the 1D and 2D configurations are highlighted. Finally, we analyse the dependence of the 1D and 2D density patterns of the trapped gas, in the presence of the OL, on the strengths of the confining and OL potentials, and on the scattering length which determines the strength of interactions between non-identical fermions.

Original languageEnglish
Article number145304
JournalJournal of Physics B: Atomic, Molecular and Optical Physics
Issue number14
StatePublished - 28 Jul 2012


Dive into the research topics of 'One- and two-dimensional reductions of the mean-field description of degenerate Fermi gases'. Together they form a unique fingerprint.

Cite this