The current large deviation function of the asymmetric simple exclusion process
by Jan de Gier
Abstract: I will discuss a recent result I obtained in collaboration with Fabian Essler on the integrable one-dimensional asymmetric exclusion process with particle injection and extraction at two boundaries. This model of one-dimensional particle diffusion and exclusion is known to exhibit four distinct phases in its stationary state. It is of particular relevance to understand the current statistics at the first site in the low and high density phases. Thanks to the integrability of the model, we are able to find an exact expression for the current large deviation function in the limit of infinite system size. I will discuss certain mathematical peculiarities of this result, such as the fact that even though the model is integrable, Bethe Ansatz equations only exist at a discrete set of points.
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