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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
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