Séminaire de groupe
|Analytical methods for extreme fluctuations in generalised exclusion processes|
|Equipe 106, Institut Jean Lamour|
|jeudi 29 juin 2017 , 10h25|
|Salle de séminaire du groupe de Physique Statistique|
The simple exclusion process is a model from classical non-equilibrium statistical physics where particles hop from site to site on a 1D lattice without crossing each-other (which is to say that they interact through hard-core repulsion, or "exclusion"). It is a well loved and well studied model for various reasons, one of them being that it is exactly solvable, and even sometimes exactly solved (depending on the physical objects of interest). In particular, the large deviation function (i.e. rescaled logarithm of the probability distribution) of the current of particles flowing through the system can be obtained exactly from integrability techniques, and shows a few interesting phase transitions, including one from a hydrodynamic phase to a highly correlated one. Unfortunately, the methods used to analyse that phase transition are specific and limited to integrable models, and adding any extra feature to the simple exclusion process (such as a nearest-neighbour interaction, or site-dependent rates) breaks its integrability. After a broad introduction to the topic, the model, and standard techniques to analyse large deviations, I will show how one can still obtain analytical expressions of the large deviations of the current in those generalised exclusion processes, in the limits of very large deviations (i.e. a current going to 0 or infinity), and how those expressions indicate the existence of a phase transition similar to the one mentioned before.