B. Derrida et al., EXACT DIFFUSION CONSTANT OF A ONE-DIMENSIONAL ASYMMETRIC EXCLUSION MODEL WITH OPEN BOUNDARIES, Journal of statistical physics, 79(5-6), 1995, pp. 833-874
For the 1D fully asymmetric exclusion model with open boundary conditi
ons, we calculate exactly the fluctuations of the current of particles
. The method used is an extension of a matrix technique developed rece
ntly to describe the equal-time steady-state properties for open bound
ary conditions and the diffusion constant for particles on a ring. We
show how the fluctuations of the current are related to non-equal-time
correlations. In the thermodynamic limit, our results agree with rece
nt results of Ferrari and Fontes obtained by working directly in the i
nfinite system. We also show that the fluctuations of the current beco
me singular when the system undergoes a phase transition with disconti
nuities along the first-order transition line.