Elliott H. Lieb, Robert Seiringer, Jakob Yngvason
Superfluidity in Dilute Trapped Bose Gases
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ABSTRACT. A commonly used theoretical definition of superfluidity in the ground
state of a Bose gas is based on the response of the system to an
imposed velocity field or, equivalently, to twisted boundary
conditions in a box. We are able to carry out this program in the
case of a dilute interacting Bose gas in a trap. We prove that a gas
with repulsive interactions is 100% superfluid in the dilute limit in
which the Gross-Pitaevskii equation is exact. This is the first
example in an experimentally realistic continuum model in which
superfluidity is rigorously verified.