On the Limit of Superposition States
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916618376839168 |
|---|---|
| author | Accardi, Luigi Souissi, Abdessatar Soueidy, El Gheteb |
| author_facet | Accardi, Luigi Souissi, Abdessatar Soueidy, El Gheteb |
| contents | In this paper, we study the structure of a family of superposition states on tensor algebras. The correlation functions of the considered states are described through a new kind of positive definite kernels valued in the dual of C$^\ast$-algebras, so-called Schur kernels. Mainly, we show the existence of the limiting state of a net of superposition states over an arbitrary locally finite graph. Furthermore, we show that this limiting state enjoys a mixing property and an $α$-mixing property in the case of the multi-dimensional integer lattice $\mathbb{Z}^ν$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_00371 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the Limit of Superposition States Accardi, Luigi Souissi, Abdessatar Soueidy, El Gheteb Mathematical Physics In this paper, we study the structure of a family of superposition states on tensor algebras. The correlation functions of the considered states are described through a new kind of positive definite kernels valued in the dual of C$^\ast$-algebras, so-called Schur kernels. Mainly, we show the existence of the limiting state of a net of superposition states over an arbitrary locally finite graph. Furthermore, we show that this limiting state enjoys a mixing property and an $α$-mixing property in the case of the multi-dimensional integer lattice $\mathbb{Z}^ν$. |
| title | On the Limit of Superposition States |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2011.00371 |