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Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime
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abstract
For a translation invariant system of $N$ bosons in the Gross-Pitaevskii regime, we establish a precise bound for the ground state energy $E_N$. While the leading, order $N$, contribution to $E_N$ has been known since [30,28] and the second order corrections (of order one) have been first determined in [5], our estimate also resolves the next term in the asymptotic expansion of $E_N$, which is of the order $(\log N) / N$.
Forward citations
Cited by 3 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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The Gibbs state of the mean-field Bose gas
The Gibbs state of the mean-field Bose gas at critical temperatures is proven to be, in trace norm, a coherent-state weighted average of Bogoliubov states governed by a one-mode Phi^4 condensate distribution.
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A Lee-Huang-Yang type expansion for the thermodynamic energy density of a dilute mixture of Bose gases
For dilute 3D two-species Bose gases with soft repulsive interactions, the energy density equals the mean-field term plus the Lee-Huang-Yang correction, with error smaller than the correction.
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