The Shock Tube and Piston Shock Wave Problems in a Superfluid

The one-dimensional shock tube and piston shock problems are classical results of shock wave theory and are discussed in many textbooks. The analogous problems for a Bose-Einstein condensate (BEC) are considered. In contrast to the well known theory of classical shock waves in a compressible fluid where dissipation plays the dominant role in regularizing the shock solution, the superfluid BEC requires a dispersive regularization, the so-called semi-classical limit. Asymptotic solutions are calculated using Whitham averaging theory for a jump in the superfluid density and velocity (the shock tube problem) and for a "piston" (dipole laser potential) moving with uniform speed into a BEC at rest. It is shown that the behavior of the asymptotic solutions is quite different from their classical counterparts.
 

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