From bosonic canonical ensembles to non-linear Gibbs measures
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917363772817408 |
|---|---|
| author | Dinh, van Duong Rougerie, Nicolas |
| author_facet | Dinh, van Duong Rougerie, Nicolas |
| contents | We study the mean-field limit of the 1D bosonic canonical ensemble in a superharmonic trap. This is the regime with temperature proportional to particle number, both diverging to infinity, and correspondingly scaled interactions. We prove that the limit model is a classical field theory based on a non-linear Schr{ö}dinger-Gibbs measure conditioned on the L2 mass, thereby obtaining a canonical analogue of previous results for the grand-canonical ensemble. We take advantage of this set-up with fixed mass to include focusing/attractive interactions/non-linearities in our study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13597 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From bosonic canonical ensembles to non-linear Gibbs measures Dinh, van Duong Rougerie, Nicolas Analysis of PDEs Mathematical Physics Probability We study the mean-field limit of the 1D bosonic canonical ensemble in a superharmonic trap. This is the regime with temperature proportional to particle number, both diverging to infinity, and correspondingly scaled interactions. We prove that the limit model is a classical field theory based on a non-linear Schr{ö}dinger-Gibbs measure conditioned on the L2 mass, thereby obtaining a canonical analogue of previous results for the grand-canonical ensemble. We take advantage of this set-up with fixed mass to include focusing/attractive interactions/non-linearities in our study. |
| title | From bosonic canonical ensembles to non-linear Gibbs measures |
| topic | Analysis of PDEs Mathematical Physics Probability |
| url | https://arxiv.org/abs/2412.13597 |