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Exponential bounds of the condensation for dilute Bose gases
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abstract
We consider N bosons on the unit torus $\Lambda = [0,1]^3$ in the Gross-Pitaevski regime where the interaction potential scales as $N^2 V (N(x -y))$. We prove that the thermal equilibrium at low temperatures exhibits the Bose-Einstein condensation in a strong sense, namely the probability of having $n$ particles outside of the condensation decays exponentially in $n$.
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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.
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