arXiv subjects

C. Finn

Publications and source records attributed to C. Finn.

3 recordsLinked to original sources

arXiv2017

Matrix product solution to multi-species ASEP with open boundaries

We study a class of multi-species ASEP with open boundaries. The boundaries are chosen in such a way that all species of particles interact non-trivially with the boundaries and are present in the stationary state. We give the exact expression of the stationary state in a matrix product form and we compute its normalisation. Densities and currents for the different species are then computed in term of this normalisation.

cond-mat.stat-mech↗

arXiv2016

Matrix product construction for Koornwinder polynomials and fluctuations of the current in the open ASEP

Starting from the deformed current-counting transition matrix for the open boundary ASEP, we prove that with a further deformation, the symmetric Koornwinder polynomials for partitions with equal row lengths appear as the normalisation of the twice deformed ground state. We give a matrix product construction for this ground state and the corresponding symmetric Koornwinder polynomials. Based on the form of this construction and numerical evidence, we conjecture a relation between the generating function of the cumulants of the current, and a certain limit of the symmetric Koornwinder polynomials.

math-ph↗

arXiv2016

Integrable boundary conditions for multi-species ASEP

The first result of the present paper is to provide classes of explicit solutions for integrable boundary matrices for the multi-species ASEP with an arbitrary number of species. All the solutions we have obtained can be seen as representations of a new algebra that contains the boundary Hecke algebra. The boundary Hecke algebra is not sufficient to build these solutions. This is the second result of our paper.

math-ph↗