<i>T</i>-<i>Q</i> relations for the integrable two-species asymmetric simple exclusion process with open boundaries

Zhang, Xin; Wen, Fakai; Gier, Jan de

doi:10.1088/1742-5468/aaeb4a

Cited by 8 publications

(8 citation statements)

References 57 publications

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“…More recently the transition probability and limit laws have been discussed in two-species models with a small number of particles of a second type [72,42,48,30,56]. The fluctuation exponent of n-ASEP was addressed in finite size scaling of the gap of its generator [5], and the Bethe ansatz for the 2-ASEP with open boundaries was considered in [75]. To our knowledge, full explicit limiting distributions for multi-species models have only been derived recently for the two-species Arndt-Heinzl-Rittenberg (AHR) model [21,20,22], or in cases where there is a relation to a single species model such as shift colour-position symmetry [9,12] and the coalescing random walk [43].…”

Section: Introductionmentioning

confidence: 99%

Transition probability and total crossing events in the multi-species asymmetric exclusion process

Gier¹,

Mead²,

Wheeler³

2021

Preprint

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We present explicit formulas for total crossing events in the multi-species asymmetric exclusion process (r-ASEP) with underlying Uq( slr+1) symmetry. In the case of the two-species TASEP these can be derived using an explicit expression for the general transition probability on Z in terms of a multiple contour integral derived from a nested Bethe ansatz approach. For the general r-ASEP we employ a vertex model approach within which the probability of total crossing can be derived from partial symmetrization of an explicit high rank rainbow partition function. In the case of r-TASEP, the total crossing probability can be show to reduce to a multiple integral over the product of r determinants. For 2-TASEP we additionally derive convenient formulas for cumulative total crossing probabilities using Bernoulli-step initial conditions for particles of type 2 and type 1 respectively.

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Section: Introductionmentioning

confidence: 99%

Transition probability and total crossing events in the multi-species asymmetric exclusion process

Gier¹,

Mead²,

Wheeler³

2021

Preprint

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“…Much less is known rigorously about dynamic properties for multi-species models. The fluctuation exponent of n-ASEP was addressed in finite size scaling of the gap of its generator [2], and the Bethe ansatz for the 2-ASEP with open boundaries was considered in [92]. Limit distributions for a single second class particle have been studied in [68,69].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Limiting current distribution for a two species asymmetric exclusion process

Chen,

de Gier,

Hiki

et al. 2021

Preprint

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We study current fluctuations of a two-species asymmetric exclusion process, known as the Arndt-Heinzel-Rittenberg model. For a step-Bernoulli initial condition with finite number of particles, we provide an explicit multiple integral expression for a certain joint current probability distribution. By performing an asymptotic analysis we prove that the joint current distribution is given by a product of a Gaussian and a GUE Tracy-Widom distribution in the long time limit, as predicted by non-linear fluctuating hydrodynamics.

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“…Our method can be generalized to other integrable open systems, not necessarily of quantum origin, such as the asymmetric simple exclusion process (ASEP) with open boundaries [26,27], the spin-1 Fateev-Zamolodchikov model [28] and spin-s integrable systems [29]. Potentially, a generalization of our results to the XYZ spin- 1 2 chain [30] might exist, which is a challenging open problem.…”

Section: Discussionmentioning

confidence: 98%

Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ spin-$\frac12$ chain

Zhang,

Kluemper,

Popkov

2021

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We construct the coordinate Bethe ansatz for all eigenstates of the open spin-1 2 XXZ chain that fulfill the phantom roots criterion (PRC). Under the PRC, the Hilbert space splits into two invariant subspaces and there are two sets of homogeneous Bethe ansatz equations (BAE) to characterize the subspaces in each case. We propose two sets of vectors with chiral shocks to span the invariant subspaces and expand the corresponding eigenstates. All the vectors are factorized and have symmetrical and simple structures. Using several simple cases as examples, we present the core elements of our generalized coordinate Bethe ansatz method. The eigenstates are expanded in our generating set and show clear chirality and certain symmetry properties. The bulk scattering matrices, the reflection matrices on the two boundaries and the BAE are obtained, which demonstrates the agreement with other approaches. Some hypotheses are formulated for the generalization of our approach.

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T-Q relations for the integrable two-species asymmetric simple exclusion process with open boundaries

Cited by 8 publications

References 57 publications

Transition probability and total crossing events in the multi-species asymmetric exclusion process

Transition probability and total crossing events in the multi-species asymmetric exclusion process

Limiting current distribution for a two species asymmetric exclusion process

Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ spin-$\frac12$ chain

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