Li Jheng-Wei
le 13 mars 2025
Publié le 11 décembre 2025– Mis à jour le 11 décembre 2025
Francesco Casini
The multi-species stirring process with open boundaries: duality, integrability and scaling limits
Jeudi 13 Mars 2025, 14h00, salle E4.13b
LPENS, École Normale Supérieure
The multi-species stirring process with open boundaries: duality,
integrability and scaling limits
To develop a model for non-equilibrium statistical mechanics, the system is typically brought into contact with two thermodynamic reservoirs, known as boundary reservoirs. These reservoirs impose their own particle density at the system's boundary, thereby inducing a current. Over time, a non-equilibrium steady state emerges, characterized by a stationary current value. Recently, there has been increasing interest in multi-component systems, where various particle species (some times referred to as colors) coexist. In such setups, interactions between di erent species are possible alongside the occupation of available sites.
This work focuses on the boundary-driven multi-species stirring process on a one-dimensional lattice. This process extends naturally from the symmetric exclusion process (SEP) when multiple particle species are considered. Its dynamics involve particles exchanging positions with holes or with particles of di erent colors, each occurring at a rate of 1.
Additionally, the system interacts with boundary reservoirs that inject, remove, and exchange types of particles. After de ning the process's generator using an appropriate representation of the gl(N) Lie algebra, we establish the existence of an absorbing dual process de ned on an extended chain, where the two boundary reservoir are replaced by absorbing extra sites. This dual process shares bulk dynamics with the original but includes extra sites that absorb particles over extended time periods. This multi-species stirring process can be mapped onto a higher rank open XXX-Heisenberg spin chain, therefore we employ absorbing duality and the matrix product ansatz to derive closed-form expressions for the non-equilibrium steady-state multi-point correlations of the process. This result is reported in [1].
Next, scaling limits of the process are examined, particularly the behavior of the properly scaled empirical density of the process. First, hydrodynamic equations are derived, illustrating typical system behavior (in the spirit of the law of large numbers). Second, uctuations from this hydrodynamic limit are investigated, revealing a set of Gaussian processes coupled through noise, resembling aspects of the central limit theorem. Finally, large deviation results are reported, describing the probability of rare trajectories deviating from typical behaviors. An additional outcome of this analysis is the identi cation of a system of hydrodynamic equations featuring a drift due to interaction with an external eld. These scaling limit results are reported in [2] and [3]