Ground-state energy of a low-density Bose gas: A second-order upper bound

L. Erdös, B. Schlein, H. Yau, Physical Review A - Atomic, Molecular, and Optical Physics 78 (2008).

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Abstract
Consider N bosons in a finite box Λ= [0,L]3⊂ R3 interacting via a two-body non-negative soft potential V=λ V with V fixed and λ>0 small. We will take the limit L,N→∞ by keeping the density =N/L3 fixed and small. We construct a variational state, which gives an upper bound on the ground-state energy per particle ε, ε≤4πa [1+ (128/15π) (a3) 1/2 Sλ] +O (2 ln ), as →0, with a constant satisfying 1≤ Sλ ≤1+Cλ. Here a is the scattering length of V and thus depends on λ. In comparison, the prediction by Lee and Yang [Phys. Rev. 105, 1119 (1957)] and Lee, Huang, and Yang [Phys. Rev. 106, 1135 (1957)] asserts that Sλ =1 independent of λ.
Publishing Year
Date Published
2008-01-01
Journal Title
Physical Review A - Atomic, Molecular, and Optical Physics
Volume
78
Issue
5
IST-REx-ID

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Erdös L, Schlein B, Yau H. Ground-state energy of a low-density Bose gas: A second-order upper bound. Physical Review A - Atomic, Molecular, and Optical Physics. 2008;78(5). doi:10.1103/PhysRevA.78.053627
Erdös, L., Schlein, B., & Yau, H. (2008). Ground-state energy of a low-density Bose gas: A second-order upper bound. Physical Review A - Atomic, Molecular, and Optical Physics, 78(5). https://doi.org/10.1103/PhysRevA.78.053627
Erdös, László, Benjamin Schlein, and Horng Yau. “Ground-State Energy of a Low-Density Bose Gas: A Second-Order Upper Bound.” Physical Review A - Atomic, Molecular, and Optical Physics 78, no. 5 (2008). https://doi.org/10.1103/PhysRevA.78.053627.
L. Erdös, B. Schlein, and H. Yau, “Ground-state energy of a low-density Bose gas: A second-order upper bound,” Physical Review A - Atomic, Molecular, and Optical Physics, vol. 78, no. 5, 2008.
Erdös L, Schlein B, Yau H. 2008. Ground-state energy of a low-density Bose gas: A second-order upper bound. Physical Review A - Atomic, Molecular, and Optical Physics. 78(5).
Erdös, László, et al. “Ground-State Energy of a Low-Density Bose Gas: A Second-Order Upper Bound.” Physical Review A - Atomic, Molecular, and Optical Physics, vol. 78, no. 5, American Physical Society, 2008, doi:10.1103/PhysRevA.78.053627.

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