We study a dilute gas of interacting fermions at temperature $T=0$ and chemical potential $μ\in \mathbb{R}$ . The particles are trapped by an external potential, and they interact via a microscopic attractive two-body potential with a two-body bound state. We prove the emergence of the macroscopic Gross-Pitaevskii theory as first-order contribution to the BCS energy functional in the regime of vanishing micro-to-macro scale parameter.We study a dilute gas of interacting fermions at temperature $T=0$ and chemical potential $μ\in \mathbb{R}$. The particles are trapped by an external potential, and they interact via a microscopic attractive two-body potential with a two-body bound state. We prove the emergence of the macroscopic Gross-Pitaevskii theory as first-order contribution to the BCS energy functional in the regime of vanishing micro-to-macro scale parameter.

arXiv:2208.04584Aug 9, 20220 citations

A renormalized Gross–Pitaevskii theory and vortices in a strongly interacting Bose gas

Ch. Moseley, K. Ziegler

We consider a strongly interacting Bose-Einstein condensate in a spherical harmonic trap. The system is treated by applying a slave-boson representation for hard-core bosons. A renormalized Gross-Pitaevskii theory is derived for the condensate wave function that describes the dilute regime (like the conventional Gross-Pitaevskii theory) as well as the dense regime. We calculate the condensate density of a rotating condensate for both the vortex-free condensate and the condensate with a single vortex and determine the critical angular velocity for the formation of a stable vortex in a rotating trap.We consider a strongly interacting Bose-Einstein condensate in a spherical harmonic trap. The system is treated by applying a slave-boson representation for hard-core bosons. A renormalized Gross-Pitaevskii theory is derived for the condensate wave function that describes the dilute regime (like the conventional Gross-Pitaevskii theory) as well as the dense regime. We calculate the condensate density of a rotating condensate for both the vortex-free condensate and the condensate with a single vortex and determine the critical angular velocity for the formation of a stable vortex in a rotating trap.

arXiv:cond-mat/0505598Journal of Physics B Atomic Molecular and Optical PhysicsJan 24, 20076 citations

Derivation of the Gross-Pitaevskii Equation for Condensed Bosons from the Bogoliubov–de Gennes Equations for Superfluid Fermions

P. Pieri, Giancarlo Calvanese Strinati

We derive the time-independent Gross-Pitaevskii equation at zero temperature for condensed bosons, which form as bound-fermion pairs when the mutual fermionic attractive interaction is sufficiently strong, from the strong-coupling limit of the Bogoliubov-de Gennes equations that describe superfluid fermions in the presence of an external potential. Three-body corrections to the Gross-Pitaevskii equation are also obtained by our approach. Our results are relevant to the recent advances with ultracold fermionic atoms in a trap.We derive the time-independent Gross-Pitaevskii equation at zero temperature for condensed bosons, which form as bound-fermion pairs when the mutual fermionic attractive interaction is sufficiently strong, from the strong-coupling limit of the Bogoliubov-de Gennes equations that describe superfluid fermions in the presence of an external potential. Three-body corrections to the Gross-Pitaevskii equation are also obtained by our approach. Our results are relevant to the recent advances with ultracold fermionic atoms in a trap.

arXiv:cond-mat/0301023Physical Review LettersJul 15, 2003123 citations

We study a dilute gas of interacting fermions at temperature

T=0

and chemical potential

μ\in \mathbb{R}

. The particles are trapped by an external potential, and they interact via a microscopic attractive two-body potential with a two-body bound state. We prove the emergence of the macroscopic Gross-Pitaevskii theory as first-order contribution to the BCS energy functional in the regime of vanishing micro-to-macro scale parameter.