Symmetric Matrix Ensemble and Integrable Hydrodynamic Chains

Autor:	Benassi, Costanza, Dell'Atti, Marta, Moro, Antonio
Rok vydání:	2021
Předmět:	Mathematical Physics Nonlinear Sciences - Exactly Solvable and Integrable Systems
Druh dokumentu:	Working Paper
DOI:	10.1007/s11005-021-01416-y
Popis:	The partition function of the Symmetric Matrix Ensemble is identified with the $\tau-$function of a particular solution of the Pfaff Lattice. We show that in the case of even power interactions, in the thermodynamic limit, the $\tau-$function corresponds to the solution of an integrable chain of hydrodynamic type. We prove that the hydrodynamic chain so obtained is diagonalisable and admits hydrodynamic reductions in Riemann invariants in an arbitrary number of components. Comment: 22 pages. Some typos have been corrected. The introduction has been revised. Appendix A has been added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2101.10232 Zobrazit plný text záznamu View this record from Arxiv