固定有界排斥势的量子损耗
Quantum Depletion for Fixed Bounded Repulsive Potentials
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具体内容
该稿件研究三维玻色气体基态的 Bogoliubov 量子损耗渐近，相互作用为固定、有界、非负、有限程且散射长度为正的径向势。作者先在固定密度下取热力学极限，再取稀薄极限，声称非凝聚态占比的每个热力学累积值均为 (8/(3√π))√(ρa^3)+o(√(ρa^3))。摘要强调该断言对基态密度矩阵一致成立，不要求占据数具有唯一热力学极限。
- 针对固定有界非负径向势的三维玻色气体基态证明量子损耗渐近。
- 非凝聚占比的累积值趋于 (8/(3√π))√(ρa^3) 量级。
- 结论对基态密度矩阵一致，不要求占据数唯一热力学极限。
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英文原始摘要
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.
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