For trapped Bose-Einstein condensates in the Gross-Pitaevskii regime, the exponential moment <ψ_N, exp(κ N_⊥)ψ_N> is uniformly bounded in N for small κ>0, giving exponential decay of the excitation probability.
Generating function for quantum depletion of Bose-Einstein condensates
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We consider a Bose gas on the unit torus at zero temperature in the Gross-Pitaevskii regime, known to perform Bose-Einstein condensation: a macroscopic fraction of the bosons occupy the same quantum state, called condensate. We study the Bose gas' quantum depletion, that is the number of bosons outside the condensate, and derive an explicit asymptotic formula of its generating function. Moreover, we prove an upper bound for the tails of the quantum depletion.
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Exponential Control of Excitations for Trapped BEC in the Gross-Pitaevskii Regime
For trapped Bose-Einstein condensates in the Gross-Pitaevskii regime, the exponential moment <ψ_N, exp(κ N_⊥)ψ_N> is uniformly bounded in N for small κ>0, giving exponential decay of the excitation probability.