Quantum Heisenberg models and their probability representations
Goldschmidt, C. (Christina), Ueltschi, Daniel and Windridge, Peter (2011) Quantum Heisenberg models and their probability representations. In: Sims, Robert and Ueltschi, Daniel, (eds.) Entropy and the quantum II : Arizona School of Analysis with Applications, March 15-19, 2010, University of Arizona. Contemporary mathematics, Vol.552 . Providence, R.I.: American Mathematical Society, pp. 177-224. ISBN 9780821868980Full text not available from this repository.
Official URL: http://www.ams.org/bookstore-getitem/item=CONM-552
These notes give a mathematical introduction to two seemingly unrelated topics: (i) quantum spin systems and their cycle and loop representations, due to Toth and Aizenman-Nachtergaele; (ii) coagulation-fragmentation stochastic processes. These topics are nonetheless related, as we argue that the lengths of cycles and loops satisfy an effective coagulation-fragmentation process. This suggests that their joint distribution is Poisson-Dirichlet. These ideas are far from being proved, but they are backed by several rigorous results, notably of Dyson-Lieb-Simon and Schramm.
|Item Type:||Book Item|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Series Name:||Contemporary mathematics|
|Publisher:||American Mathematical Society|
|Place of Publication:||Providence, R.I.|
|Book Title:||Entropy and the quantum II : Arizona School of Analysis with Applications, March 15-19, 2010, University of Arizona|
|Editor:||Sims, Robert and Ueltschi, Daniel|
|Number of Pages:||224|
|Page Range:||pp. 177-224|
|Access rights to Published version:||Restricted or Subscription Access|
Actions (login required)