Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 267-03. Quantum Depletion for Fixed Bounded Repulsive Potentials
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OpenAI@2026-10-07#rem:oai-p-267-03
Authors: OpenAI. Family 267.
Title: Quantum Depletion for Fixed Bounded Repulsive Potentials.
Abstract: We prove the Bogoliubov quantum-depletion asymptotic for the ground state of a three-dimensional Bose gas with a fixed bounded, nonnegative, radial interaction of finite range and positive scattering length a. The thermodynamic limit is taken at each fixed density ρ before the dilute limit. Every thermodynamic accumulation value of the fraction outside the constant mode is ${}frac{8}{3{}sqrt{}pi}{}sqrt{{}rho a{}3}+o({}sqrt{{}rho a{}3})$ as ${}rho{}downarrow0$. The assertion is uniform over ground-state density matrices and does not require the occupation to have a unique thermodynamic limit.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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