Ayyer, A and Nadeau, P (2022) Combinatorics of a disordered two-species ASEP on a torus. In: European Journal of Combinatorics, 103 .
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Abstract
We define a new disordered asymmetric simple exclusion process (ASEP) with two species of particles, first-class particles labelled • and second-class particles labelled □, on a two-dimensional toroidal lattice. The dynamics is controlled by particles labelled •, which only move horizontally, with forward and backward hopping rates pi and qi respectively if the • is on row i. The motion of particles labelled □ depends on the relative position of these with respect to •’s, and can be both horizontal and vertical. We show that the stationary weight of any configuration is proportional to a monomial in the pi’s and qi’s. Our process projects to the disordered ASEP on a ring, and so explains combinatorially the stationary distribution of the latter first derived by Evans (Europhysics Letters, 1996). We compute the partition function, as well as densities and currents of •’s and □’s in the stationary state. We observe a novel mechanism we call the Scott Russell phenomenon: the current of □’s in the vertical direction is the same as that of •’s in the horizontal direction.
| Item Type: | Journal Article |
|---|---|
| Publication: | European Journal of Combinatorics |
| Publisher: | Academic Press |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 22 Jun 2022 06:39 |
| Last Modified: | 22 Jun 2022 06:39 |
| URI: | https://eprints.iisc.ac.in/id/eprint/73621 |
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