Limit theorems for empirical measures of interacting quantum systems in Wasserstein space
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915359682985984 |
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| author | Portinale, Lorenzo Rademacher, Simone Virosztek, Dániel |
| author_facet | Portinale, Lorenzo Rademacher, Simone Virosztek, Dániel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00541 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Limit theorems for empirical measures of interacting quantum systems in Wasserstein space Portinale, Lorenzo Rademacher, Simone Virosztek, Dániel Mathematical Physics Probability 60F05 35Q40 81Q99 49Q22 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. |
| title | Limit theorems for empirical measures of interacting quantum systems in Wasserstein space |
| topic | Mathematical Physics Probability 60F05 35Q40 81Q99 49Q22 |
| url | https://arxiv.org/abs/2312.00541 |