On Reduction of Critical Velocity in a Model of Superfluid Bose-gas with Boundary Interactions

The existence of superfluidity in a 3D Bose-gas can depend on boundary interactions with channel walls. We study a simple model where the dilute moving Bose-gas interacts with the walls via hard-core repulsion. Special boundary excitations are introduced, and their excitation spectrum is calculated within a semiclassical approximation. It turns out that the state of the moving Bose-gas is unstable with respect to the creation of these boundary excitations in the system gas + walls, i.e. the critical velocity vanishes in the semiclassical (Bogoliubov) approximation. We discuss how a condensate wave function, the boundary excitation spectrum and, hence, the value of the critical velocity can change in more realistic models, in which ``smooth'' attractive interaction between the gas and walls is taken into account. Such a surface mode could exist in ``soft matter'' containers with flexible walls.