Next: Attractive one-dimensional two-component gas
Up: 1Dfermions
Previous: 1Dfermions
We consider one-dimensional two-component fermi gas at zero
temperature. Pauli principle applies to fermions of same spin (and
spin orientation). We model interactions between fermions of
different spins by pseudopotential of strength
with being the one-dimensional
scattering length. We consider both negative (attraction)
and positive (repulsion).
The Hamiltonian of a homogeneous system is given by
|
|
|
(1) |
where
is total number of
fermions of mass . In following we consider same number of
fermions of one spin state and the other spin state
. Properties of a homogeneous system is
defined by the one-dimensional gas parameter with
being density of the system.
In presence of external harmonic confinement the one-dimensional
Hamiltonian is given by
|
|
|
(2) |
In this system an important parameter is
with
being oscillator length.