Andrea Trombettoni — SISSA Trieste #
Suppression of Landau instability for supersonic superfluid flow #

After a general introduction on ultra-cold atoms, I present a discussion on the possible suppression of 
the Landau instability for supersonic flows. For the 1D linear Schrödinger equation in presence of a 
square well/barrier potential the transmission coefficient can be exactly one for specific values of the 
incident momentum. In this talk I will consider the dynamical transmission properties for the 
Gross-Pitaveskii equation in presence of the quartic non-linearity with the same potential and show that 
there are supersonic velocities for which the Landau instability is dramatically reduced: these 
"Landau-free'' momenta are shifted with respect to the corresponding resonant values for the linear case. 
The shift in momentum is seen to be positive (negative) for repulsive (attractive) interaction. We checked 
that the production of excitations at the supersonic Landau-free points is bounded in time, that the flow 
is stable both to small perturbations and for time larger than the typical experimental time scales of 
ultra-cold atoms experiments with 1D Bose condensates, and that the numerically obtained findings do not 
crucially depend on the ramping time of the well/barrier. A comparison with multiple-scale analysis for 
small non-linearities is presented as well.