arXiv:2406.09019 · Letters in Mathematical Physics

Ground state energy of a dilute Bose gas with three-body hard-core interactions

Lukas Junge, François Louis Antoine Visconti

Published Mar 27, 2026• 0 citations

Abstract

We consider a gas of bosons interacting through a three-body hard-core potential in the thermodynamic limit. We derive an upper bound on the ground state energy of the system at the leading order using a Jastrow factor. Our result matches the lower bound proven by Nam-Ricaud-Triay (J Math Phys 63:071903, 2022) and therefore resolves the leading order. Moreover, a straightforward adaptation of our proof can be used for systems interacting via combined two-body and three-body interactions to generalise Theorem 1.2 from (Ann. Henri Poincaré, 2026) to hard-core potentials.

DOI: 10.1007/s11005-026-02067-7

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arXiv:2406.09019 · Letters in Mathematical Physics

Ground state energy of a dilute Bose gas with three-body hard-core interactions

Lukas Junge, François Louis Antoine Visconti

Published Mar 27, 2026• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.1007/s11005-026-02067-7

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Phan Thành Nam, Julien Ricaud, Arnaud Triay

arXiv:2201.13440Journal of Mathematical PhysicsJul 1, 202213 citations

We consider a gas of bosons interacting through a hard-sphere potential with radius

\frak{a}

in the thermodynamic limit. We derive a simple upper bound for the ground state energy per particle at low density. Our bound captures the leading term

4πρ\frak{a}

and shows that corrections are smaller than

C ρ\frak{a} (ρ\frak{a}^3)^{1/2}

, for a sufficiently large constant

C > 0

. In combination with a known lower bound, our result implies that the first sub-leading term to the ground state energy is, in fact, of the order

ρ\frak{a} (ρ\frak{a}^3)^{1/2}

, in agreement with the Lee-Huang-Yang prediction.

Abstract We consider a gas of bosons interacting through a hard-sphere potential with radius

\mathfrak {a}

a in the thermodynamic limit. We derive an upper bound for the ground state energy per particle at low density. Our bound captures the leading term

4\pi \rho \mathfrak {a}

4 π ρ a and shows that corrections are smaller than

C \rho \mathfrak {a} (\rho {{\mathfrak {a}}}^3)^{1/2}

C ρ a ( ρ a 3 ) 1 / 2 , for a sufficiently large constant

C > 0

C > 0 . In combination with a known lower bound, our result implies that the first sub-leading term to the ground state energy of a dilute gas of hard spheres is, in fact, of the order

\rho \mathfrak {a}(\rho {{\mathfrak {a}}}^3)^{1/2}

ρ a ( ρ a 3 ) 1 / 2 , in agreement with the Lee–Huang–Yang prediction.