  We consider a gas of fermions with a short-range attractive intercomponent
interaction in a parabolic external potential and derive the conditions of the
local density approximation. The obtained spectrum of quasiparticle (isospin)
excitations shows equidistant low-energy levels, which is equivalent to a
linear momentum dependence and is fundamentally different from the ordinary
Dirac spectrum in the spatially uniform case.

Strongly Correlated Electrons