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Kuniba, Atsuo; Mangazeev, Vladimir V.

doi:10.1016/j.nuclphysb.2017.07.001

Cited by 4 publications

(7 citation statements)

References 25 publications

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“…Also the multi-species version of q-boson model was constructed [59,60]. The stationary measure for the latter was obtained in the matrix product form and used for determining of the current and density profile [61].…”

Section: Introductionmentioning

confidence: 99%

Current statistics in the q-boson zero range process

Trofimova¹,

Povolotsky²

2020

J. Phys. A: Math. Theor.

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We obtain exact formulas of the first two cumulants of particle current in the q-boson zero range process on a ring via exact perturbative solution of the TQequation. The result is represented as an infinite sum of double contour integrals. We perform the asymptotic analysis of the large system size limit N → ∞ of the expressions obtained. For |q| = 1 the leading terms of the second cumulant reproduce the N 3/2 scaling expected for models in the Kardar-Parisi-Zhang universality class. The scaling q exp(−α/ √ N) → 1 corresponds to the crossover between the Kardar-Parisi-Zhang and Edwards-Wilkinson universality classes. Under this scaling the sum converges to an integral, resulting in the crossover scaling function derived previously for the asymmetric simple exclusion process and conjectured to be universal.

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Section: Introductionmentioning

confidence: 99%

Current statistics in the q-boson zero range process

Trofimova¹,

Povolotsky²

2020

J. Phys. A: Math. Theor.

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“…The path followed is not necessarily easier than the one originally followed in [20], but rather provides a different perspective on the derivation. Our aim was to show that the matrix-product ansatz approach may also be valid to determine the steady-state distribution of boundary-driven one-dimensional lattice models with unbounded number of particles on each site (see also, e.g., [21,22,23] for other applications of the matrix ansatz to models with unbounded local number of particles and periodic boundary conditions). It also shows that in some specific cases, the homogeneous matrix product form and the inhomogeneous factorized form (i.e., with local distributions that explicitly depend on the site), may be two sides of the same coin.…”

Section: Discussionmentioning

confidence: 99%

Matrix product representation of the stationary state of the open zero range process

Bertin¹,

Vanicat²

2018

J. Phys. A: Math. Theor.

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Many one-dimensional lattice particle models with open boundaries, like the paradigmatic Asymmetric Simple Exclusion Process (ASEP), have their stationary states represented in the form of a matrix product, with matrices that do not explicitly depend on the lattice site. In contrast, the stationary state of the open one-dimensional Zero-Range Process (ZRP) takes an inhomogeneous factorized form, with site-dependent probability weights. We show that in spite of the absence of correlations, the stationary state of the open ZRP can also be represented in a matrix product form, where the matrices are site-independent, non-commuting and determined from algebraic relations resulting from the master equation. We recover the known distribution of the open ZRP in two different ways: first, using an explicit representation of the matrices and boundary vectors; second, from the sole knowledge of the algebraic relations satisfied by these matrices and vectors. Finally, an interpretation of the relation between the matrix product form and the inhomogeneous factorized form is proposed within the framework of hidden Markov chains.

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“…Also the multi-species version of q-boson model was constructed [50,51]. The stationary measure for the latter was obtained in the matrix product form and used for determining of the current and density profile [52].…”

Section: Introductionmentioning

confidence: 99%

Current statistics in the q-boson zero range process

Trofimova,

Povolotsky

2020

Preprint

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We obtain exact formulas of the first two cumulants of particle current in the q-boson zero range process via exact perturbative solution of the TQ-relation. The result is represented as an infinite sum of double contour integrals. We perform the asymptotic analysis of the large system size limit N → ∞ of the expressions obtained. For |q| = 1 the leading terms of the second cumulant reproduce the N 3/2 scaling expected for models in the Kardar-Parisi-Zhang universality class. The scaling q exp(−α/ √ N ) → 1 corresponds to the the crossover between the Kardar-Parisi-Zhang and Edwards-Wilkinson universality classes. Under this scaling the sum converges to an integral, resulting in the crossover scaling function derived previously for the asymmetric simple exclusion process and conjectured to be universal.

show abstract

Density and current profiles inUq(A2(1))

Cited by 4 publications

References 25 publications

Current statistics in the q-boson zero range process

Current statistics in the q-boson zero range process

Matrix product representation of the stationary state of the open zero range process

Current statistics in the q-boson zero range process

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