Webinar

I will discuss the relation between non-compact spin chains studied first in the context of high energy physics following ideas of Lipatov, Faddeev and Korchemsky, and Beisert and the zero-range processes introduced by Sasamoto-Wadati, Povolotsky and Barraquand-Corwin. The main difference compared to the prime examples of integrable particle processes, namely the symmetric simple exclusion process (SSEP) and the asymmetric simple exclusion process (ASEP), is that for the models discussed in this talk several particles can occupy one and the same site. For the models with symmetric hopping rates, I will introduce integrable boundary conditions that are obtained from new solution to the boundary Yang-Baxter equation (K-matrix) that allows to define analogues of the open SSEP with boundary reservoirs. Finally, I will present an explicit mapping of these boundary driven models to equilibrium. This mapping allows us to obtain closed-form solutions of the probabilities in steady state and of k-point correlations functions. The talk is based on collaborations with C. Giardinà and J. Kurchan.