Exact soultion of asymmetric diffusion with second-class particles of arbitrary size

Details Exact soultion of asymmetric diffusion with second-class particles of arbitrary size Exact soultion of asymmetric diffusion with second-class particles of arbitrary size

2000-07-25

arxiv.org/abs/cond-mat/0007390v1

Braz. J. Phys., vol. (30) pg. 13-26 (2000)

Physics

Condensed Matter

Statistical Mechanics

21 pages, 7 figures

Scientific paper

The exact solution of the asymmetric exclusion problem with particles of first and second class is presented. In this model the particles (size 1) of both classes are attached on lattice points and diffuse with equal asymmetric rates, but particles in the first class do not distinguish those in the second class from the holes (empty sites). We generalize and solve exactly this model by considering molecules in the first and second class with sizes $s_1$ and $s_2$ ($s_1,s_2 = 0,1,2,...$), in units of lattice spacing, respectively. The solution is derived by a Bethe ansatz of nested type. We give in this paper a pedagogical and simple presentation of the Bethe ansatz solution of the problem which can easily be followed by a non specialized audience in exactly integrable models.

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