Wasserstein空间中相互作用量子系统经验测度的极限定理
Limit theorems for empirical measures of interacting quantum systems in Wasserstein space
AI总结：
本文研究了量子N体系统在Gross--Pitaevskii极限下经验测度的性质，证明了以凝聚波函数为极限的大数弱定律并刻画了涨落的中心极限定理。
摘要：
我们证明了量子N体系统测量所诱导的经验测度的基本性质。具体而言，我们考虑在Gross--Pitaevskii极限下，对已知呈现Bose--Einstein凝聚的相互作用囚禁Bose气体的基态进行的测量。对于相应的经验测度，我们证明了以凝聚波函数诱导的极限为大数定律弱定律，并通过适当的中心极限定理刻画了其周围的涨落。
英文摘要：
We prove fundamental properties of empirical measures induced by measurements performed on quantum $N$-body systems. More precisely, we consider measurements performed on the ground state of an interacting, trapped Bose gase in the Gross--Pitaevskii regime, known to exhibit Bose--Einstein condensation. For the corresponding empirical measure, we prove a weak law of large numbers with limit induced by the condensate wave function and characterize the fluctuations around through an appropriate central limit theorem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
