We study the stability of the paired fermionic p-wave superfluid made out of identical atoms all in the same hyperfine state close to a p-wave Feshbach resonance. First we reproduce known results concerning the lifetime of a 3D superfluid, in particu
lar, we show that it decays at the same rate as its interaction energy, thus precluding its equilibration before it decays. Then we proceed to study its stability in case when the superfluid is confined to 2D by means of an optical harmonic potential. We find that the relative stability is somewhat improved in 2D in the BCS regime, such that the decay rate is now slower than the appropriate interaction energy scale. The improvement in stability, however, is not dramatic and one probably needs to look for other mechanisms to suppress decay to create a long lived 2D p-wave fermionic superfluid.
We examine bosons hopping on a one-dimensional lattice in the presence of a random potential at zero temperature. Bogoliubov excitations of the Bose-Einstein condensate formed under such conditions are localized, with the localization length divergin
g at low frequency as $ell(omega)sim 1/omega^alpha$. We show that the well known result $alpha=2$ applies only for sufficiently weak random potential. As the random potential is increased beyond a certain strength, $alpha$ starts decreasing. At a critical strength of the potential, when the system of bosons is at the transition from a superfluid to an insulator, $alpha=1$. This result is relevant for understanding the behavior of the atomic Bose-Einstein condensates in the presence of random potential, and of the disordered Josephson junction arrays.
