Multispecies totally asymmetric zero range process: II. Hat relation and tetrahedron equation

@article{Kuniba2015MultispeciesTA,
title={Multispecies totally asymmetric zero range process: II. Hat relation and tetrahedron equation},
author={Atsuo Kuniba and Shouya Maruyama and Masato Okado},
journal={arXiv: Mathematical Physics},
year={2015}
}
• Published 1 September 2015
• Mathematics
• arXiv: Mathematical Physics
We consider a three-dimensional (3D) lattice model associated with the intertwiner of the quantized coordinate ring $A_q(sl_3)$, and introduce a family of layer to layer transfer matrices on $m\times n$ square lattice. By using the tetrahedron equation we derive their commutativity and bilinear relations mixing various boundary conditions. At $q=0$ and $m=n$, they lead to a new proof of the steady state probability of the $n$-species totally asymmetric zero range process obtained recently by…
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References

SHOWING 1-10 OF 24 REFERENCES

Multispecies TASEP and the tetrahedron equation

• Mathematics
• 2015
We introduce a family of layer to layer transfer matrices in a three-dimensional (3D) lattice model which can be viewed as partition functions of the q-oscillator valued six-vertex model on an m × n

Quantum geometry of 3-dimensional lattices and tetrahedron equation

• Mathematics, Physics
• 2010
We study geometric consistency relations between angles of 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that

Multispecies TASEP and combinatorial R

• Mathematics
• 2015
We identify the algorithm for constructing steady states of the n-species totally asymmetric simple exclusion process (TASEP) on an L site periodic chain by Ferrari and Martin with a composition of

Tetrahedron and 3D reflection equations from quantized algebra of functions

• Mathematics
• 2012
Soibelman’s theory of quantized function algebra Aq(SLn) provides a representation theoretical scheme to construct a solution of the Zamolodchikov tetrahedron equation. We extend this idea originally

Combinatorial Yang–Baxter maps arising from the tetrahedron equation

AbstractWe survey the matrix product solutions of the Yang–Baxter equation recently obtained from the tetrahedron equation. They form a family of quantum R-matrices of generalized quantum groups

Multispecies totally asymmetric zero range process: I. Multiline process and combinatorial $R$

• Mathematics
• 2015
We introduce an $n$-species totally asymmetric zero range process ($n$-TAZRP) on one-dimensional periodic lattice with $L$ sites. It is a continuous time Markov process in which $n$ species of

Tetrahedron equation and generalized quantum groups

• Mathematics
• 2015
We construct 2 n ?> -families of solutions of the Yang–Baxter equation from n-products of three-dimensional R and L operators satisfying the tetrahedron equation. They are identified with the quantum

Zamolodchikov's tetrahedron equation and hidden structure of quantum groups

• Mathematics, Physics
• 2006
The tetrahedron equation is a three-dimensional generalization of the Yang–Baxter equation. Its solutions define integrable three-dimensional lattice models of statistical mechanics and quantum field

Exact solution of a 1d asymmetric exclusion model using a matrix formulation

• Mathematics
• 1993
Several recent works have shown that the one-dimensional fully asymmetric exclusion model, which describes a system of particles hopping in a preferred direction with hard core interactions, can be

Condensation in the Zero Range Process: Stationary and Dynamical Properties

• Physics
• 2003
The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which