Limit theorems for empirical measures of interacting quantum systems in Wasserstein space
Abstract
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.
Fields of Study & Subjects
Quantum Mechanics and Applications
Advanced Mathematical Physics Problems
advanced mathematical theories
Publication details
- Journal / source
- Advances in Mathematics
- Volume
- 495
- Pages
- 110972–110972
- Publication date
- 20 April 2026
- Language
- EN