Abstract

A unique feature of superfluidity is the frictionless flow below a critical velocity. This was first pointed out by L. D. Landau who argued that only above the speed of sound the excitations of linear or sound waves is energetically favoured [1] leading to a finite drag and to a break down of superfluidity. The superfluid motion of a dilute Bose-Einstein condensate is modelled by the Gross-Pitaveskii or nonlinear Schrödinger equation. Remarkably for the nonlinear Schrödinger flow past an immobile obstacle the critical velocity lies below the one determined from the Landau criteria. However this is not a contradiction to the argument of Landau since it includes the excitations of linear waves, only. The reduction of the critical velocity aries due to excitation of nonlinear waves, that are gray solitons and dispersive shock waves [2, 3]. In these scenarios the obstacle is considered to be immobile and thus modelled as an external potential.

© 2011 IEEE