05/11/2025, 16:00 — 17:00 — Online
Anastasiia Trofimova, Gran Sasso Science Institute
Scaling properties of current fluctuations in periodic TASEP
The Totally Asymmetric Simple Exclusion Process (TASEP) on a ring of size $ N $ with $ p $ particles is a key model in non-equilibrium statistical physics. While its stationary state is well understood, the relaxation dynamics and current fluctuations in finite systems are less explored. We introduce a deformation parameter $ \gamma $ defining a tilted operator controlling the time-integrated current statistics. Using the coordinate Bethe ansatz, we obtain implicit formulas for the scaled cumulant generating function (SCGF) and spectral gap, expressed via Bethe roots and characterized asymptotically by the Cassini oval geometry.
In the thermodynamic limit with fixed particle density, a dynamical phase transition emerges between fluctuation regimes: for $ \gamma > 0 $, the SCGF scales ballistically with system size, $ \lambda_1 \sim N $, and the spectral gap closes polynomially, $ \Delta \sim N^{-1} $, indicating rapid relaxation. For $ \gamma < 0 $, the SCGF converges to $-1$, with an exponentially closing gap, $ \Delta \sim \exp(-cN) $, signaling metastability. These non-perturbative results provide new insights into large deviations and relaxation dynamics in driven particle systems.
