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A q-boson representation of Zamolodchikov-Faddeev algebra for stochastic R matrix of U_q(A_n^(1))

Atsuo Kuniba, Masato Okado

Jun 1, 20173 citations

Matrix product formula for U q ( A 2 ( 1 ) ) -zero range process

Atsuo Kuniba, Masato Okado

Abstract The U q ( A n ( 1 ) ) -zero range processes introduced recently by Mangazeev, Maruyama and the authors are integrable discrete and continuous time Markov processes associated with the stochastic R matrix derived from the well-known U q ( A n ( 1 ) ) quantum R matrix. By constructing a representation of the relevant Zamolodchikov–Faddeev algebra, we present, for n = 2, a matrix product formula for the steady state probabilities in terms of q -boson operators.

arXiv:1608.02779Journal of Physics A Mathematical and TheoreticalDec 23, 20167 citations

Boson fock representations of stochastic processes

Luigi Accardi, T. Hida, Win Win Htay

Mathematical NotesJan 1, 20003 citations

The Feynman-Kac Formula for Boson Wiener Processes

R. L. Hudson, Patrick Ion, Kalyanapuram Rangachari Parthasarathy

Springer eBooksJan 1, 19815 citations

Integrable Structure of Multispecies Zero Range Process

Atsuo Kuniba, Masato Okado, Satoshi W. Watanabe

We present a brief review on integrability of multispecies zero range process in one dimension introduced recently.The topics range over stochastic R matrices of quantum affine algebra U q A (1) n , matrix product construction of stationary states for periodic systems, q-boson representation of Zamolodchikov-Faddeev algebra, etc.We also introduce new commuting Markov transfer matrices having a mixed boundary condition and prove the factorization of a family of R matrices associated with the tetrahedron equation and generalized quantum groups at a special point of the spectral parameter.We present a brief review on integrability of multispecies zero range process in one dimension introduced recently.The topics range over stochastic R matrices of quantum affine algebra U q A (1) n , matrix product construction of stationary states for periodic systems, q-boson representation of Zamolodchikov-Faddeev algebra, etc.We also introduce new commuting Markov transfer matrices having a mixed boundary condition and prove the factorization of a family of R matrices associated with the tetrahedron equation and generalized quantum groups at a special point of the spectral parameter.

arXiv:1701.07279Symmetry Integrability and Geometry Methods and ApplicationsJun 17, 20174 citations

On the relationship between a quantum Markov semigroup and its representation via linear stochastic Schrödinger equations

Franco Fagnola, Carlos Mora

arXiv:1405.6374Indian Journal of Pure and Applied MathematicsAug 1, 20158 citations

A q-boson representation of Zamolodchikov-Faddeev algebra for stochastic R matrix of $$\varvec{U_q(A^{(1)}_n)}$$ U q ( A n ( 1 ) )

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A q-boson representation of Zamolodchikov-Faddeev algebra for stochastic R matrix of $$\varvec{U_q(A^{(1)}_n)}$$ U q ( A n ( 1 ) )

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