Related papers: Bethe ansatz solution of discrete time stochastic …
We study a stochastic PDE limit of the height function of the dynamic asymmetric simple exclusion process (dynamic ASEP). A degeneration of the stochastic Interaction Round-a-Face (IRF) model of arXiv:1701.05239, dynamic ASEP has a jump…
We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…
The probability distribution of the current in the asymmetric simple exclusion process is expected to undergo a phase transition in the regime of weak asymmetry of the jumping rates. This transition was first predicted by Bodineau and…
We define one-dimensional particles as non-abelian representations of the symmetric group $S_N$. The exact solution of an $XXZ$ type Hamiltonian built up with such particles is achieved using the coordinate Bethe Ansatz. The Bethe equations…
We solve the gl(1|2) generalized model by means of the algebraic Bethe ansatz. The resulting eigenvalue of the transfer matrix and the Bethe ansatz equations depend on three complex functions, called the parameters of the generalized model.…
We consider two versions of discrete time totally asymmetric simple exclusion processes (TASEPs) with geometric and Bernoulli random hopping probabilities. For the process mixed with these and continuous time dynamics, we obtain a single…
The graded off-diagonal Bethe ansatz method is proposed to study supersymmetric quantum integrable models (i.e., quantum integrable models associated with superalgebras). As an example, the exact solutions of the $SU(2|2)$ vertex model with…
We obtain the Bethe Ansatz equations for the broken ${\bf Z}_{N}$-symmetric model by constructing a functional relation of the transfer matrix of $L$-operators. This model is an elliptic off-critical extension of the Fateev-Zamolodchikov…
This paper studies a class of non$-$Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a $Z-$constrained…
An ASEP with two species of particles and different hopping rates is considered on a ring. Its integrability is proved and the Nested Algebraic Bethe Ansatz is used to derive the Bethe Equations for states with arbitrary numbers of…
New classes of integrable boundary conditions for the q-deformed (or two-parameter) supersymmetric U model are presented. The boundary systems are solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are…
We propose a set of conventional Bethe Ansatz equations and a corresponding expression for the eigenvalues of the transfer matrix for the open spin-1/2 XXZ quantum spin chain with nondiagonal boundary terms, provided that the boundary…
We have recently constructed a large class of open quantum spin chains which have quantum-algebra symmetry and which are integrable. We show here that these models can be exactly solved using a generalization of the analytical Bethe Ansatz…
The problem of diagonalization of the quantum mechanical Hamiltonian, governing dynamics of an electron on a two-dimensional triangular or square lattice in external uniform magnetic field, applied perpendicularly to the lattice plane, the…
We study discrete time Markov processes with periodic or open boundary conditions and with inhomogeneous rates in the bulk. The Markov matrices are given by the inhomogeneous transfer matrices introduced previously to prove the…
The off-diagonal Bethe Ansatz method [1] is used to revisit the periodic XXX Heisenberg spin-1/2 chain. It is found that the spectrum of the transfer matrix can be characterized by an inhomogeneous T-Q relation, a natural but nontrivial…
The zero-range process is a stochastic interacting particle system that exhibits a condensation transition under certain conditions on the dynamics. It has recently been found that a small perturbation of a generic class of jump rates leads…
It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is…
We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes…
We study the long time asymptotics of the relaxation dynamics of the totally asymmetric simple exclusion process on a ring. Evaluating the asymptotic amplitudes of the local currents by the algebraic Bethe ansatz method, we find the…