17/03/2021, 17:00 — 18:00 — Room P3.10, Mathematics Building Online
Cristian Giardinà, Università degli Studi di Modena e Reggio Emilia
Exact solution of an integrable particle system
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).
See also
giardina-lisbon-17march-2021.pdf
Please note change of day and time. Joint session with Seminario Brasileiro de Probabilidade: https://sbp.impa.br
