{"id":"openai-math/Quantum-Depletion-for-Fixed-Bounded-Repulsive-Potentials","pdf":"https://github.com/openai/math/blob/main/preprints/Quantum-Depletion-for-Fixed-Bounded-Repulsive-Potentials-October-5-2026/fixed-repulsion-quantum-depletion.pdf","url":"https://github.com/openai/math/tree/main/preprints/Quantum-Depletion-for-Fixed-Bounded-Repulsive-Potentials-October-5-2026","tags":["mathematical-physics","bose-gas","quantum-depletion","many-body"],"score":0,"title":"Quantum Depletion for Fixed Bounded Repulsive Potentials","domain":"Mathematical physics","family":"267","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Positive-temperature Bose–Einstein condensation and exact quantum depletion"}