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The master T-operator for vertex models with trigonometric R-matrices as classical tau-function
ИТЭФ
,
2012.
No. 17.
The construction of the master T-operator recently suggested is applied to integrable vertex models and associated quantum spin chains with trigonometric R-matrices. The master T-operator is a generating function for commuting transfer matrices of integrable vertex models depending on infinitely many parameters. At the same time it turns out to be the tau-function of an integrable hierarchy of classical soliton equations in the sense that it satisfies the the same bilinear Hirota equations. The class of solutions of the Hirota equations that correspond to eigenvalues of the master T-operator is characterized and its relation to the classical Ruijsenaars-Schneider system of particles is discussed.
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
Zabrodin A., Теоретическая и математическая физика 2013 Т. 174 № 1 С. 59-76
Недавно предложенная конструкция управляющего Т-оператора применяется к интегрируемым вершинным моделям и связанным с ними квантовым спиновым цепочкам с тригонометрическими R-матрицами. Управляющий Т-оператор - это производящая функция коммутирующих трансфер-матриц интегрируемых вершинных моделей, зависящая от бесконечного набора параметров.
В тоже время он оказывается тау-функцией интегрируемой иерархии классических солитонных уравнений в том смысле, что удовлетворяет тем же билинейным уравнения ...
Added: February 13, 2013
Zabrodin A., Alexandrov A., Kazakov V. et al., Journal of High Energy Physics 2013 Vol. 09 P. 064
For an arbitrary generalized quantum integrable spin chain we introduce a “master T-operator” which represents a generating function for commuting quantum transfer matrices constructed by means of the fusion procedure in the auxiliary space. We show that the functional relations for the transfer matrices are equivalent to an infinite set of model-independent bilinear equations of ...
Added: November 14, 2013
Zabrodin A., Proceedings of Physics and Mathematics of Nonlinear Phenomena 2014 Vol. 482 No. 012047 P. 10
This short note is a review of the intriguing connection between the quantum Gaudin model and the classical KP hierarchy recently established in [A.Alexandrov, S.Leurent, Z.Tsuboi, A.Zabrodin, The master T-operator for the Gaudin model and KP hierarchy, Nuclear Physics B 883 (2014) 173-223]. We construct the generating function of integrals of motion for the quantum ...
Added: July 15, 2014
Zabrodin A., Alexandrov A., Leurent S. et al., Nuclear Physics B 2014 Vol. 883 No. P. 173-223
Following the approach of [Alexandrov A., Kazakov V., Leurent S., Tsuboi Z., Zabrodin A., J. High Energy Phys. 2013 (2013), no. 9, 064, 65 pages, arXiv:1112.3310], we construct the master T-operator for the quantum Gaudin model with twisted boundary conditions and show that it satisfies the bilinear identity and Hirota equations for the classical KP ...
Added: July 15, 2014
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
Zabrodin A., Journal of Physics A: Mathematical and Theoretical 2013 Vol. 46 No. 18 P. 185203
We study the integrable structure of the 2D Laplacian growth problem with zero surface tension in an infinite channel with periodic boundary conditions in a transverse direction. Similarly to the Laplacian growth in radial geometry, this problem can be embedded into the 2D Toda lattice hierarchy in the zero dispersion limit. However, the relevant solution ...
Added: April 29, 2013
Zabrodin A., Alexandrov A., Journal of Geometry and Physics 2013 Vol. 67 P. 37-80
We review the formalism of free fermions used for construction of tau-functions of classical integrable hierarchies and give a detailed derivation of group-like properties of the normally ordered exponents, transformations between different normal orderings, the bilinear relations, the generalized Wick theorem and the bosonization rules. We also consider various examples of tau-functions and give their ...
Added: February 16, 2013
Pyatov P. N., Ogievetsky O., / Cornell University. Series math "arxiv.org". 2020.
We establish the analogue of the Cayley--Hamilton theorem for the quantum matrix algebras of the symplectic type. ...
Added: January 26, 2021
Ogievetsky O., Pyatov P. N., Journal of Geometry and Physics 2021 Vol. 165 Article 104211
We establish the analogue of the Cayley–Hamilton theorem for the quantum matrix algebras of the symplectic type. We construct the algebra in which the quantum characteristic polynomial acquires a factorized form. The low-dimensional examples and the classical limit are discussed. ...
Added: March 18, 2021
Baibikova T., Domoratsky E., Вестник Московского финансово-юридического университета 2017 № 1 С. 200-206
Some questions of scientific visualization are under consideration in this paper. This article also discusses the peculiarities of application of cognitive computer graphics, singles out a range of tasks of scientific visualization. The paper gives a brief overview of modern support tools for program visualization, tendencies of their development and their main characteristics. A module ...
Added: June 10, 2017
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
Kiselyova N. N., Dudarev V.A., Korzhuev M. A., Inorganic Materials: Applied Research 2016 Vol. 7 No. 1 P. 34-39
A database (DB) on the bandgap of inorganic substances available via the Internet (http://bg.imetdb.ru) was developed for the information service of specialists in the sphere of inorganic chemistry and materials science. The DB is integrated with other information systems on the properties of inorganic substances and materials, which provides the search of a wide range ...
Added: February 23, 2016
Toldova S., Azerkovich I., Гришина Ю. et al., / НИУ ВШЭ. Series WP BRP "Linguistics". 2015.
Building benchmark corpora in the domain of coreference and anaphora resolution is an important task for developing and evaluating NLP systems and models. Our study is aimed at assessing the feasibility of enhancing corpora with information about coreference relations. The annotation procedure includes identification of text segments that are subjects to annotation (markables), marking their ...
Added: December 15, 2015
Vishnekov A., Erokhin V., Ivanova E., Датчики и системы 2018 Т. 221 № 1 С. 18-24
The article discusses the recovery of distributed control systems of technical objects. The options for the design of subsystems recovery after hardware or software fault of the sensor system are investigated. The development of an integrated subsystems recovery is proposed on the basis of decision-making system to develop the most rational control actions by ...
Added: January 27, 2018
М. : National Instruments Russia, 2017
Содержание сборника составляют доклады с результатами оригинальных исследований и технических решений, ранее не публиковавшиеся. Мы надеемся, что предлагаемый сборник окажется полезным для специалистов, работающих в различных областях науки и техники, для широкого круга преподавателей, аспирантов и студентов ВУЗов, а также для преподавателей средних школ и технических колледжей. ...
Added: May 10, 2017
Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253
Added: December 22, 2016
ООО Фирма "Элист", 2014
В книге представлены тезисы докладов I тура XV Всероссийской научно-технической конференции и школы молодых ученых, аспирантов и студентов. ...
Added: October 17, 2014
Barcelona : International Association of Technology, Education and Development , 2012
Added: September 11, 2012
Shuranov E., / Cornell University. Series Computer Science "arxiv.org". 2021.
Text encodings from automatic speech recognition (ASR) transcripts and audio representations have shown promise in speech emotion recognition (SER) ever since. Yet, it is challenging to explain the effect of each information stream on the SER systems. Further, more clarification is required for analysing the impact of ASR's word error rate (WER) on linguistic emotion ...
Added: February 14, 2023
Decrouez G. G., Hall P., Bernoulli: a journal of mathematical statistics and probability 2013 Vol. 19 No. 4 P. 1268-1293
Motivated by a problem arising when analysing data from quarantine searches, we explore properties of distributions of sums of independent means of independent lattice-valued random variables. The aim is to determine the extent to which approximations to those sums require continuity corrections. We show that, in cases where there are only two different means, the ...
Added: September 29, 2014
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Karpov V. E., Karpova I. P., Procedia Engineering 2015 Vol. 100 P. 1459-1468
Work solutions are proposed for problems of leader definition and role distribution in homogeneous groups of robots. It is shown that transition from a swarm to a collective of robots with hierarchical organization is possible using exclusively local interaction. The local revoting algorithm is central to the procedure for choice of leader while redistribution of roles can ...
Added: March 14, 2015
Каз. : Издательство «Фэн» Академии наук Республики Татарстан, 2013
Материалы и доклады Шестой Всероссийской научно-практической конференции по имитацонному моделированию и его применению в науке и промышленности. ...
Added: December 14, 2013