Calculus of Variations and Geometric Measure Theory

L. Portinale - S. Rademacher - D. Virosztek

Limit theorems for empirical measures of interacting quantum systems in Wasserstein space

created by portinale on 05 Dec 2023



Inserted: 5 dec 2023

Year: 2023

ArXiv: 2312.00541 PDF


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.