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The Lowest Landau Level (LLL) equation emerges as an accurate approximation for a class of dynamical regimes of Bose-Einstein Condensates (BEC) in two-dimensional isotropic harmonic traps in the limit of weak interactions.
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For concreteness, we assume that g > 0 g>0 (repulsive interactions); however, in the the weakly nonlinear regime considered here, all our results hold true for g < 0 g<0 (attractive interactions) as well
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For this solution ψ ( t , z ) = e − i λ τ ψ ( 0 , e − i ω τ z ) \psi(t,z)=e^{-i\lambda\tau}\psi(0,e^{-i\omega\tau}z) . Such stationary solutions are sometimes called traveling waves (if ω ≠ 0 \omega\neq 0 ) and standing waves (if ω = 0 \omega=0 )
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