Extend dilute Bose gas results to interaction potentials with negative parts

Generalize dilute-limit ground state energy density results for Bose gases to two-body interaction potentials v that may take negative values: determine rigorous upper and lower bounds for e(ρ, v) in dimensions two and three under conditions excluding any finite-k bound states and ensuring positive scattering length, thereby removing the current nonnegativity assumption on v.

Background

Most rigorous results reviewed in the paper, including the two-term asymptotic expansions such as the Lee–Huang–Yang formula in three dimensions, assume repulsive interactions v ≥ 0. The authors note that removing this assumption is challenging and that only limited progress exists for potentials with small negative parts and positive scattering length.

The paper highlights that allowing negative components in v risks introducing k-body bound states and metastability, complicating the analysis of the ground state. A comprehensive extension of dilute-gas energy asymptotics to such potentials remains an outstanding task.