?
Многоточечные пространственно-временные переходы в простом полностью асимметричном процессе с исключающим взаимодействием
Теоретическая и математическая физика. 2011. Т. 169. № 1. С. 167-175.
Povolotsky A. M., Приезжев В. Д.
Priority areas:
mathematics
Language:
Russian
Zabrodin A., (Mathematical Sciences 2013 No. 596 P. 7-12
We review the role of the Hirota equation and the tau-function in the theory of classical and quantum integrable systems. ...
Added: February 16, 2013
A A Trofimova, A M Povolotsky, Journal of Physics A: Mathematical and Theoretical 2022 Vol. 55 No. 2 Article 025202
We consider the particle current in the asymmetric avalanche process on a ring. It is known to exhibit a transition from the intermittent to continuous flow at the critical density of particles. The exact expressions for the first two scaled cumulants of the particle current are obtained in the large time limit t → ∞ ...
Added: August 15, 2022
А. М. Поволоцкий, Физика элементарных частиц и атомного ядра 2021 Т. 52 № 2 С. 459-529
This review gives a survey of some results about systems of interacting particles and
the laws characterizing their behavior on large scales, which are common for a number of
phenomena uniˇed under the notion of the KardarÄParisiÄZhang universality class. ...
Added: August 15, 2022
Pavel Pyatov, Povolotsky A. M., Rittenberg V., Journal of Statistical Mechanics: Theory and Experiment 2018 Vol. 2018 No. 053107 P. 1-26
We study the large deviation functions for two quantities characterizing the avalanche dynamics in the Raise and Peel model: the number of tiles removed by avalanches and the number of global avalanches extending through the whole system. To this end, we exploit their connection to the groundstate eigenvalue of the XXZ model with twisted boundary ...
Added: July 17, 2018
Hutsalyuk A., Liashyk A, Pakuliak S. Z. et al., Nuclear Physics B 2017 Vol. 923 P. 277-311
We study scalar products of Bethe vectors in the models solvable by the nested algebraic Bethe ansatz and described by superalgebra. Using coproduct properties of the Bethe vectors we obtain a sum formula for their scalar products. This formula describes the scalar product in terms of a sum over partitions of Bethe parameters. We also obtain recursions for ...
Added: October 26, 2017
Hutsalyuk A., Liashyk A., Pakuliak S. Z. et al., SciPost Physic (Нидерланды) 2018 Vol. 4 No. 006 P. 1-30
We obtain recursion formulas for the Bethe vectors of models with periodic boundary conditions solvable by the nested algebraic Bethe ansatz and based on the quantum affine algebra U_q(gl_n). We also present a sum formula for their scalar products. This formula describes the scalar product in terms of a sum over partitions of the Bethe parameters, ...
Added: September 13, 2018
Liashyk A., Slavnov N. A., Journal of High Energy Physics 2018 Vol. 06 No. 018 P. 1-31
We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing gl_3-invariant R-matrix. We study a new recently proposed approach to construct on-shell Bethe vectors of these models. We prove that the vectors constructed by this method are semi-on-shell Bethe vectors for arbitrary values of Bethe parameters. They thus do become on-shell vectors provided ...
Added: September 13, 2018
Feigin B. L., Jimbo M., Mukhin E., Journal of Physics A: Mathematical and Theoretical 2017 Vol. 50 No. 46 Article 464001
We identify the Taylor coefficients of the transfer matrices corresponding to quantum toroidal algebras with the elliptic local and non-local integrals of motion introduced by Kojima, Shiraishi, Watanabe, and one of the authors.
That allows us to prove the Litvinov conjectures on the Intermediate Long Wave model.
We also discuss the (gl(m),gl(n)) duality of XXZ models in ...
Added: November 5, 2020
Tamm M., Nechaev S., Majumdar S., Journal of Physics A: Mathematical and Theoretical 2011 Vol. 44 P. 012002
A novel discrete growth model in 2+1 dimensions is presented in three equivalent formulations: (i) directed motion of zigzags on a cylinder, (ii) interacting interlaced TASEP layers and (iii) growing heap over 2Dsubstrate with a restrictedminimal local height gradient. We demonstrate that the coarsegrained behavior of this model is described by the two-dimensional Kardar– Parisi–Zhang ...
Added: November 19, 2013
Khoroshkin S. M., Пакуляк С. З., Ragoucy E. et al., Annales Henri Poincare. A Journal of Theoretical and Mathematical Physics 2009 Vol. 10 No. 3 P. 513-548
We consider universal off-shell Bethe vectors given in terms of Drinfeld
realization of the algebra Uq(glN). We investigate ordering properties
of the product of the transfer matrix and these vectors. We derive that
these vectors are eigenvectors of the transfer matrix if their Bethe parameters
satisfy the universal Bethe equations. ...
Added: October 15, 2012
Povolotsky A. M., Journal of Statistical Mechanics: Theory and Experiment 2023 Article 033103
This work continues the study started in [1], where the exact densities of loops in the
O(1) dense loop model on an infinite strip of the square lattice with periodic boundary conditions
were obtained. These densities are also equal to the densities of critical percolation clusters on the
forty five degree rotated square lattice rolled into a cylinder. ...
Added: February 1, 2024
Hutsalyuk A., Liashyk A., Pakuliak S. Z. et al., Nuclear Physics B 2018 Vol. 926 P. 256-278
We study quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing gl(m|n)-invariant R-matrix. We compute the norm of the Hamiltonian eigenstates. Using the notion of a generalized model we show that the square of the norm obeys a number of properties that uniquely fix it. We also show that a Jacobian of the system ...
Added: September 13, 2018
Gorsky A., Zabrodin A., Zotov A., Journal of High Energy Physics 2014 No. 01 P. 070,28
In this paper we clarify the relationship between inhomogeneous quantum spin chains and classical integrable many-body systems. It provides an alternative (to the nested Bethe ansatz) method for computation of spectra of the spin chains. Namely, the spectrum of the quantum transfer matrix for the inhomogeneous glninvariant XXX spin chain on N sites with twisted ...
Added: July 15, 2014
Rybnikov L. G., Chervov A., Falqui G., Letters in Mathematical Physics 2010 Vol. 91 No. 1 P. 129-150
Gaudin algebras form a family of maximal commutative subalgebras in the tensor product of n copies of the universal enveloping algebra U(g) of a semisimple Lie algebra g. This family is parameterized by collections of pairwise distinct complex numbers z1; : : : ; zn . We obtain some new commutative subalgebras in U(g)n as ...
Added: October 12, 2012
Povolotsky A. M., Journal of Statistical Mechanics: Theory and Experiment 2019 No. 074003 P. 1-22
We establish the exact laws of large numbers for two time additive quantities in the raise and peel model, the number of tiles removed by avalanches and the number of global avalanches happened by given time. The validity of conjectures for the related stationary state correlation functions then follow. The proof is based on the ...
Added: October 8, 2019
Hutsalyuk A., Liashyk A., Pakuliak S. Z. et al., Russian Mathematical Surveys 2017 Vol. 72 No. 1 P. 33-99
Bethe vectors are found for quantum integrable models associated with the supersymmetric Yangians in terms of the current generators of the Yangian double . The method of projections onto intersections of different types of Borel subalgebras of this infinite-dimensional algebra is used to construct the Bethe vectors. Calculation of these projections makes it possible to express the ...
Added: October 26, 2017
Trofimova A., Povolotsky A. M., Journal of Physics A: Mathematical and Theoretical 2020 Vol. 53 No. 36 P. 365203
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 TQ-equation. 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 ...
Added: October 19, 2020
A.V.Zabrodin, Zotov A. V., Liashyk A. et al., Theoretical and Mathematical Physics 2017 Vol. 192 No. 2 P. 1141-1153
We discuss the correspondence between models solved by the Bethe ansatz and classical integrable systems of the Calogero type. We illustrate the correspondence by the simplest example of the inhomogeneous asymmetric six-vertex model parameterized by trigonometric(hyperbolic) functions. ...
Added: October 26, 2017
Hutsalyuk A., Liashyk A., Pakuliak S. et al., Journal of Physics A: Mathematical and Theoretical 2016 Vol. 49 P. 1-28
We study scalar products of Bethe vectors in integrable models solvable by nested algebraic Bethe ansatz and possessing gl(2|1) symmetry. Using explicit formulas of the monodromy matrix entries multiple actions onto Bethe vectors we obtain a representation for the scalar product in the most general case. This explicit representation appears to be a sum over partitions ...
Added: December 1, 2016
Derbyshev A. E., Povolotsky A. M., Priezzhev V. B., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2015 Vol. 91 P. 022125
The generalized totally asymmetric exclusion process (TASEP) [J. Stat. Mech. (2012) P05014] is an integrable generalization of the TASEP equipped with an interaction, which enhances the clustering of particles. The process interpolates between two extremal cases: the TASEP with parallel update and the process with all particles irreversibly merging into a single cluster moving as ...
Added: February 19, 2015
191574970, Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90
It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...
Added: September 23, 2016
Losev A. S., Slizovskiy S., JETP Letters 2010 Vol. 91 P. 620-624
Added: February 27, 2013
Ilyashenko Y., Яковенко С. Ю., М. : МЦНМО, 2013
Предлагаемая книга—первый том двухтомной монографии, посвящённой аналитической теории дифференциальных уравнений.
В первой части этого тома излагается формальная и аналитическая теория нормальных форм и теорема о разрешении особенностей для векторных полей на плоскости.
Вторая часть посвящена алгебраически разрешимым локальным задачам теории аналитических дифференциальных уравнений , квадратичным векторным полям и проблеме локальной классификации ростков векторных полей в комплексной области ...
Added: February 5, 2014
Kalyagin V.A., Koldanov A.P., Koldanov P.A. et al., Physica A: Statistical Mechanics and its Applications 2014 Vol. 413 No. 1 P. 59-70
A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...
Added: July 19, 2014