Remarks on BEC on graphs
Abstract
We consider Bose-Einstein condensation (BEC) on graphs with transient adjacency matrix. We prove the equivalence of BEC and non-factoriality of the quasi-free state. Moreover, quasi-free states exhibiting BEC decompose into generalized coherent states. We review necessary and sufficient conditions that a quasi-free state is faithful, factor, and pure and quasi-free states are quasi-equivalent, including the papers of Araki and Shiraishi [1], Araki [2], and Araki and Yamagami [3]. Using their formats and results, we prove necessary and sufficient conditions that a generalized coherent state is faithful, factor, and pure and generalized coherent states are quasi-equivalent as well.
- Publication:
-
Reviews in Mathematical Physics
- Pub Date:
- 2017
- DOI:
- 10.1142/S0129055X17500246
- arXiv:
- arXiv:1705.00820
- Bibcode:
- 2017RvMaP..2950024K
- Keywords:
-
- CCR algebra;
- generalized coherent state;
- quasi-equivalence;
- Bose–Einstein condensation;
- Mathematical Physics;
- Mathematics - Operator Algebras
- E-Print:
- 18 pages, Revised version, to appear in Reviews in Mathematical Physics