Exact solution of an integrable particle system

Abstract: We consider the family of boundary-driven models introduced in [FGK] and show they can be solved exactly, i.e. the correlations functions and the non-equilibrium steady-state have a closed-form expression.

The solution relies on probabilistic arguments and techniques inspired by integrable systems. As in the context of bulk-driven systems (scaling to KPZ), it is obtained in two steps: i) the introduction of a dual process; ii) the solution of the dual dynamics by Bethe ansatz.

For boundary-driven systems, a general by-product of duality is the existence of a direct mapping (a conjugation) between the generator of the non-equilibrium process and the generator of the associated reversible equilibrium process. Macroscopically, this mapping was observed years ago by Tailleur, Kurchan and Lecomte in the context of the Macroscopic Fluctuation Theory.

[FGK] R. Frassek, C. Giardinà, J. Kurchan, Non-compact quantum spin chains as integrable stochastic particle processes, Journal of Statistical Physics 180, 366-397 (2020).

analysis of PDEscombinatoricsprobability

Audience: researchers in the topic

Comments: Zoom password: 958 0581 3232

---

Probability and Stochastic Analysis at Tecnico Lisboa

Series comments: To receive the series announcements, please register in math.tecnico.ulisboa.pt/seminars/ps/index.php?action=subscribe#subscribe

---