Ref HAL: hal-01480834_v1
Ref Arxiv: 1612.07036
DOI: 10.21468/SciPostPhys.2.1.006
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1 Citation
Résumé:

We show that an inhomogeneous coagulation/decoagulation model can be mapped to a quadratic fermionic model via a Jordan-Wigner transformation. The spectrum for this inhomogeneous model is computed exactly and the spectral gap is described for some examples. We construct our inhomogeneous model from two different homogeneous models joined by one special bond (impurity). The homogeneous models we started with are the coagulation/decoagulation models studied previously using the Jordan-Wigner transformation.

Commentaires: . Réf Journal: SciPost Phys. 2, 006 (2017)

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Ref Arxiv: 1509.07589
DOI: 10.1063/1.4962920
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2 Citations
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Using the nested coordinate Bethe ansatz, we study 33-vertex models, where only one global charge with degenerate eigenvalues exists and each site possesses three internal degrees of freedom. In the context of Markovian processes, they correspond to diffusing particles with two possible internal states which may be exchanged during the diffusion (transmutation). The first step of the nested coordinate Bethe ansatz is performed providing the eigenvalues in terms of rapidities. We give the constraints ensuring the consistency of the computations. These rapidities also satisfy Bethe equations involving $4\times 4$ R-matrices, solutions of the Yang--Baxter equation which implies new constraints on the models. We solve them allowing us to list all the solvable 33-vertex models.

Commentaires: 14 pages; title changed according to referee request; an appendix added to describe explicitely the Hamiltonian

Ref HAL: hal-01419364_v1
Ref Arxiv: 1603.06796
DOI: 10.1103/PhysRevE.94.032102
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13 Citations
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We study a one-parameter generalization of the symmetric simple exclusion process on a one-dimensional lattice. In addition to the usual dynamics (where particles can hop with equal rates to the left or to the right with an exclusion constraint), annihilation and creation of pairs can occur. The system is driven out of equilibrium by two reservoirs at the boundaries. In this setting the model is still integrable: it is related to the open XXZ spin chain through a gauge transformation. This allows us to compute the full spectrum of the Markov matrix using Bethe equations. We also show that the stationary state can be expressed in a matrix product form permitting to compute the multipoints correlation functions as well as the mean value of the lattice and the creation-annihilation currents. Finally, the variance of the lattice current is computed for a finite-size system. In the thermodynamic limit, it matches the value obtained from the associated macroscopic fluctuation theory.

Ref HAL: hal-01341993_v1
Ref Arxiv: 1606.08148
DOI: 10.1088/1751-8113/49/47/475001
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13 Citations
Résumé:

We present an explicit representation for the matrix product ansatz for sometwo-species TASEP with open boundary conditions. The construction relies on theintegrability of the models, a property that constrains the possible rates atthe boundaries. The realisation is built on a tensor product of copies of theDEHP algebras. Using this explicit construction, we are able to calculate thepartition function of the models. The densities and currents in the stationarystate are also computed. It leads to the phase diagram of the models. Dependingon the values of the boundary rates, we obtain for each species shock waves,maximal current, or low/high densities phases.

Ref HAL: hal-01341951_v1
Ref Arxiv: 1606.01018
DOI: 10.1088/1751-8113/49/37/375201
WoS: WOS:000383514700006
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17 Citations
Résumé:

The first result of the present paper is to provide classes of explicitsolutions for integrable boundary matrices for the multi-species ASEP with anarbitrary number of species. All the solutions we have obtained can be seen as representations of a newalgebra that contains the boundary Hecke algebra. The boundary Hecke algebra isnot sufficient to build these solutions. This is the second result of ourpaper.

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Ref Arxiv: 1509.05516
DOI: 10.1007/s00220-016-2780-y
WoS: WOS:000392061000005
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3 Citations
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We introduce a new Baxterisation for R-matrices that depend separately on twospectral parameters. The Baxterisation is based on a new algebra, close to butdifferent from the braid group. This allows us to recover the R-matrix of themulti-species generalization of the totally asymmetric simple exclusion processwith different hopping rates.

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Ref Arxiv: 1506.04874
DOI: 10.1088/1751-8113/48/48/484002
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9 Citations
Résumé:

We study discrete time Markov processes with periodic or open boundaryconditions and with inhomogeneous rates in the bulk. The Markov matrices aregiven by the inhomogeneous transfer matrices introduced previously to prove theintegrability of quantum spin chains. We show that these processes have asimple graphical interpretation and correspond to a sequential update. Wecompute their stationary state using a matrix ansatz and express theirnormalization factors as Schur polynomials. A connection between Bethe rootsand Lee-Yang zeros is also pointed out.