Fluctuations of the current and optimal profiles in the open Asymmetric Simple Exclusion Process
Alexandre Lazarescu, Institute for Theoretical Physics, KU Leuven
The asymmetric simple exclusion process (ASEP), where particles perform biased random walks with hard core repulsion, is one of the most studied model in non-equilibrium statistical physics. It has the mathematical property of being integrable, which makes it a good candidate for in-depth exact calculations. The quantity of particular interest there is the current of particles that flows through the system due to the bias of the jumps.
In this presentation, we will see how we can obtain information about the distribution of that current, through various techniques: integrability, macroscopic fluctuation theory, and asymptotic direct diagonalisation. This allows us to build the phase diagram for the large deviations of the current, and examine the corresponding density profiles in each of its five phases. We show that two situations arise: in most phases, the system can be described hydrodynamically, but in one phase, where the current is larger than the limit set by hydrodynamics, the system becomes highly correlated. If time allows it, we will also see how these techniques and results could be generalised to some other observables or models.