LESZCZYSZYN, A.M. ... et al., 2009. Transcritical flow of a Bose-Einstein condensate through a penetrable barrier. Physical Review (A), 79 (6), 063608.
The problem of the transcritical flow of a Bose-Einstein condensate through a wide repulsive
penetrable barrier is studied analytically using the combination of the local “hydraulic” solution of
the 1D Gross-Pitaevskii equation and the solutions of the Whitham modulation equations describing
the resolution of the upstream and downstream discontinuities through dispersive shocks. It is
shown that within the physically reasonable range of parameters the downstream dispersive shock
is attached to the barrier and effectively represents the train of very slow dark solitons, which can
be observed in experiments. The rate of the soliton emission, the amplitudes of the solitons in
the train and the drag force are determined in terms of the BEC oncoming flow velocity and the
strength of the potential barrier. A good agreement with direct numerical solutions is demonstrated.
Connection with recent experiments is discussed.
A.M.K. thanks the Royal Society for the financial support
of his visit to Loughborough University. Y.G.G. and
A.M.K. also thank RFBR Grant No. 09-02-00499 for partial