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

Sasamoto, Tomohiro; Wadati, Miki

J. Phys. A, Math. Gen. 31, No. 28, 6057-6071 (1998).

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