We study the minimizers of a magnetic 2D non-linear Schr\"odinger energy functional in quadratic trapping potential, describing rotating Bose-Einstein condensate. derive an effective Thomas-Fermi-like model rapidly limit where centrifugal force compensates confinement, and available states are restricted to lowest Landau level. The coupling constant Thomas-Fermi is linked emergence vortex latti...

Thomas-Fermi theory is developed to evaluate nuclear matrix elements averaged on the energy shell, on the basis of independent particle Hamiltonians. Oneand two-body matrix elements are compared with the quantal results and it is demonstrated that the semiclassical matrix elements, as function of energy, well pass through the average of the scattered quantum values. For the one-body matrix elem...

We evaluate the thermodynamic critical angular velocity Ωc(T ) for creation of a vortex of lowest quantized angular momentum in a strictly two-dimensional Bose gas at temperature T , using a mean-field two-fluid model for the condensate and the thermal cloud. Our results show that (i) a Thomas-Fermi description of the condensate badly fails in predicting the particle density profiles and the en...

We study non-linear ground states of the Gross–Pitaevskii equation in the space of one, two and three dimensions with a radially symmetric harmonic potential. The Thomas–Fermi approximation of ground states on various spatial scales was recently justified using variational methods. We justify here the Thomas–Fermi approximation on an uniform spatial scale using the Painlevé-II equation. In the ...

An exactly solvable model of two-component interacting Fermi vapour in two dimension within Thomas Fermi approach has been proposed. We assume a realistic off-diagonal s-wave interaction between fermions in the two hyperfine states. The interaction is taken to be given by a screened Coulomb interaction which is both relevant and is analytically tractable. There are two distinct limits in the ca...