Rapidly rotating Bose-Einstein condensates∗ Alexander Fetter ...

In a rotating two-dimensional gas, the compressibility
becomes important, as shown by Sonin [23, 24] and Baym [25]
• let the speed of sound in the compressible gas be c s
• coupling between the vortices and the compressible
fluid leads to generalized dispersion relation
ω 2 = c 2 T
c 2 sk 4
4Ω 2 + c 2 sk 2
• if c s k ≫ Ω, recover Tkachenko’s result ω = c T k
(short-wavelength incompressible limit)
• but if c s k ≪ Ω (long wavelength), mode becomes soft
with ω ∝ k 2
• Sonin [24] obtains dynamical equations for waves in a
nonuniform condensate, along with appropriate
boundary conditions at the outer surface
• Baym [25] uses theory for uniform condensate plus
approximate boundary conditions from Anglin and
Crescimanno [26]
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