Related papers: Hidden Symmetries of Stochastic Models
We study Poisson and operator algebras with the ''quasi-linear property'' from the Heisenberg picture point of view. This means that there exists a set of one-parameter groups yielding an explicit expression of dynamical variables…
A novel generalization of the Askey-Wilson algebra is presented and shown to be associated with coproducts in the quantum algebra $U_q(su(1,1))$. This algebra has 15 non-commuting generators given by $Q^{(A)}$, with $A\subset \{1,2,3,4\}$…
The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22], are slightly modified so as to make it transparent that these functions satisfy a…
We investigate a balance network of the asymmetric simple exclusion process (ASEP). Subsystems consisting of ASEPs are connected by bidirectional links with each other, which results in balance between every pair of subsystems. The network…
We define the notion of "diffusion algebras". They are quadratic Poincare-Birkhoff-Witt (PBW) algebras which are useful in order to find exact expressions for the probability distributions of stationary states appearing in one-dimensional…
The Askey-Wilson algebra $AW(3)$ with three generators is shown to serve as a hidden symmetry algebra underlying the Racah and (new) generalized Clebsch-Gordan problems for the quantum algebra $sl_q(2)$. On the base of this hidden symmetry…
We consider a two-component asymmetric simple exclusion process (ASEP) on a finite lattice with reflecting boundary conditions. For this process, which is equivalent to the ASEP with second-class particles, we construct the representation…
Nonlinear SUSY approach to preparation of quantum systems with pre-planned spectral properties is reviewed. Possible multidimensional extensions of Nonlinear SUSY are described. The full classification of ladder-reducible and irreducible…
We apply the bi-moment determinant method to compute a representation of the matrix product algebra -- a quadratic algebra satisfied by the operators $\mathbf{d}$ and $\mathbf{e}$ -- for the five parameter ($\alpha$, $\beta$, $\gamma$,…
This article deals with non-adiabatic processes (i.e. processes excluded by the adiabatic theorem) from the geometrical (group-theoretical) point of view. An approximated formula for the probabilities of the non-adiabatic transitions is…
In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product formulation and the queueing theory picture of…
We study the combinatorics of the change of basis of three representations of the stationary state algebra of the two parameter simple asymmetric exclusion process. Each of the representations considered correspond to a different set of…
Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…
Using the matrix product formalism we formulate a natural p-species generalization of the asymmetric simple exclusion process. In this model particles hop with their own specific rate and fast particles can overtake slow ones with a rate…
As an extension of the theory of Dyson's Brownian motion models for the standard Gaussian random-matrix ensembles, we report a systematic study of hermitian matrix-valued processes and their eigenvalue processes associated with the chiral…
We study the Nonlinear (Polynomial, N-fold,...) Supersymmetry algebra in one-dimensional QM. Its structure is determined by the type of conjugation operation (Hermitian conjugation or transposition) and described with the help of the…
We study a two-species partially asymmetric exclusion process where the left boundary is permeable for the `slower' species but the right boundary is not. We find a matrix product solution for the stationary state, and the exact stationary…
We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix…
In this paper it is shown that the steady-state weights of the asymmetric simple exclusion process (ASEP) with open boundaries and parallel update can be written as a product of a scalar pair-factorized and a matrix-product state. This type…
In a previous Letter (J. Phys. A v.47 (2014) 212003) we have presented numerical evidence that a Hamiltonian expressed in terms of the generators of the periodic Temperley-Lieb algebra has, in the finite-size scaling limit, a spectrum given…