10:20-11:20 Thursday, 8 May 2025 Auditorium, Rectorate
Abstract
In this talk, we explore various facets of the so-called symmetric harmonic model [1], i.e. the interacting particle system derived from the integrable XXX spin chain with hyperbolic spins. This model can be regarded as the integrable counterpart of the well-known Kipnis–Marchioro–Presutti (KMP) model: it retains the same symmetries and duality structure as KMP, while also being exactly solvable—much like the exclusion process. These features make it a particularly rich framework for investigating energy transport and heat conduction in stochastic systems. The seminar is divided into two parts. In the first part [2], we leverage the model’s integrability to characterize the non-equilibrium steady state explicitly. This allows us to establish a large deviation principle for the empirical energy profile, with a rate function that coincides with the one predicted by the Macroscopic Fluctuation Theory (MFT). In the second part [3], we consider a different large deviation regime—taking a large-spin limit. This leads to a natural lattice discretization of MFT. Remarkably, for the harmonic model, the corresponding lattice MFT equations can be exactly solved by mapping the problem to a classical integrable lattice system. As a result, we derive an explicit formula for the large deviation function of the time-integrated current.