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Diagonalizing Bose Gases in the Gross-Pitaevskii Regime and Beyond
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We present a novel approach to the Bogoliubov theory of dilute Bose gases, allowing for an elementary derivation of the celebrated Lee-Huang-Yang formula in the Gross-Pitaevskii regime. Furthermore, we identify the low lying excitation spectrum beyond the Gross-Pitaevskii scaling, extending a recent result [3] to significantly more singular scaling regimes. Finally, we provide an upper bound on the ground state energy in the Gross-Pitaevskii regime that captures the correct expected order of magnitude beyond the Lee-Huang-Yang formula.
Forward citations
Cited by 2 Pith papers
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Third Order Upper Bound for the Ground State Energy of the Dilute Bose Gas
The ground state energy density of a dilute Bose gas is rigorously shown to be at most the Lee-Huang-Yang value plus Wu's logarithmic third-order correction, for potentials with positive scattering length.
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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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