## Exact results for one-dimensional totally asymmetric diffusion models.(English)Zbl 1085.83501

Summary: Several types of totally asymmetric diffusion models with and without exclusion are considered. For some models, conditional probabilities of finding $$N$$ particles on lattice sites $$x_1,\cdots,x_N$$ at time $$t$$ with initial occupation $$y_1,\cdots,y_N$$ at time $$t=0$$ are expressed in a determinant form. On the other hand, the $$q$$-boson totally asymmetric diffusion model is introduced which interpolates the free boson model and the model with exclusion-like interaction. The effects of the interaction are compared for the case of two-particle diffusion.

### MSC:

 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems) 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
Full Text: