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Strong Kac's chaos in the mean-field Bose-Einstein Condensation
- Publication Year :
- 2019
-
Abstract
- A stochastic approach to the (generic) mean-field limit in Bose-Einstein Condensation is described and the convergence of the ground state energy as well as of its components are established. For the one-particle process on the path space a total variation convergence result is proved. A strong form of Kac's chaos on path-space for the $k$-particles probability measures are derived from the previous energy convergence by purely probabilistic techniques notably using a simple chain-rule of the relative entropy. The Fisher's information chaos of the fixed-time marginal probability density under the generic mean-field scaling limit and the related entropy chaos result are also deduced.
- Subjects :
- Mathematics - Probability
Mathematical Physics
60J60, 60K35, 81S20, 94A17
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1903.07128
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1142/S0219493720500318