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Regular version of the site
Of all publications in the section: 90
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Article
Bershtein M., Shchechkin A. Journal of Physics A: Mathematical and Theoretical. 2017. Vol. 50. No. 11. P. 1-28.

We study the explicit formula (suggested by Gamayun, Iorgov and Lisovyy) for the Painlevé III(D 8) τ function in terms of Virasoro conformal blocks with a central charge of 1. The Painlevé equation has two types of bilinear forms, which we call Toda-like and Okamoto-like. We obtain these equations from the representation theory using an embedding of the direct sum of two Virasoro algebras in a certain superalgebra. These two types of bilinear forms correspond to the Neveu–Schwarz sector and the Ramond sector of this algebra. We also obtain the τ functions of the algebraic solutions of the Painlevé III(D 8) from the special representations of the Virasoro algebra of the highest weight (n  +  1/4)2.

Added: Apr 13, 2017
Article
Takebe T. Journal of Physics A: Mathematical and Theoretical. 1995. Vol. 28. P. 6675-6706.
Added: Apr 7, 2009
Article
Takebe T. Journal of Physics A: Mathematical and Theoretical. 1996. Vol. 29. P. 6961-6966.
Added: Apr 7, 2009
Article
Saponov P. A., Gurevich D. Journal of Physics A: Mathematical and Theoretical. 2009. No. 42.
Added: Oct 3, 2011
Article
van de Leur J., Orlov Aleksandr Yur'evich. Journal of Physics A: Mathematical and Theoretical. 2017. P. 1-27.

We consider expansions of certain multiple integrals and BKP tau functions in characters of orhtogonal and symplectic groups.
 In particular, we consider character expansions of integrals over orthogonal and over symplectic matrices

Added: Oct 23, 2017
Article
Levin A., Olshanetsky M., Smirnov A. et al. Journal of Physics A: Mathematical and Theoretical. 2013. Vol. 46. No. 3. P. 035201-035225.

We discuss quantum dynamical elliptic R-matrices related to arbitrary complex simple Lie group G. They generalize the known vertex and dynamical R-matrices and play an intermediate role between these two types. The R-matrices are defined by the corresponding characteristic classes describing the underlying vector bundles. The latter are related to elements of the center of G. While the known dynamical R-matrices are related to the bundles with trivial characteristic classes, the Baxter-Belavin-Drinfeld-Sklyanin vertex R-matrix corresponds to the generator of the center Z N of SL(N). We construct the R-matrices related to SL(N)-bundles with an arbitrary characteristic class explicitly and discuss the corresponding IRF models.

Added: Mar 29, 2013
Article
Pyatov P. N., Saponov P. A. Journal of Physics A: Mathematical and Theoretical. 1995. Vol. 28. P. 4415-4421.
General algebraic properties of the algebras of vector fields over quantum linear groups GLq(N) and SLq(N) are studied. These quantum algebras appears to be quite similar to the classical matrix algebra. In particular, quantum analogues of the characteristic polynomial and characteristic identity are obtained for them. The q- analogues of the Newton relations connecting two different generating sets of central elements of these algebras (the determinant-like and the trace-like ones) are derived. This allows one to express the q-determinant of quantized vector fields in terms of their q-traces.
Added: Oct 16, 2012
Article
Raitza T., Reinholz H., Roepke G. et al. Journal of Physics A: Mathematical and Theoretical. 2009. Vol. 42. P. 214048.

Laser excited small metallic clusters are simulated using classical pseudo potential molecular dynamics simulations. Time-dependent distribution functions are obtained from the electron and ion trajectories in order to investigate plasma properties. The question of local thermodynamic equilibrium is addressed, and size effects are considered. Results for the electron distribution in phase space are given, which are interpreted within equilibrium statistical physics. Momentum autocorrelation functions were calculated for different cluster sizes and for different expansion states from the expanding system after the laser–cluster interaction. A resonance behaviour of the autocorrelation function in finite systems was observed. First, results concerning collision frequencies in small clusters are given.

Added: Mar 14, 2014
Article
Isaev A. P., Pyatov P. N. Journal of Physics A: Mathematical and Theoretical. 1995. Vol. 28. P. 2227-2246.
Added: Mar 9, 2010
Article
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 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 $q \asymp \exp (-\alpha/\sqrt{N})$ 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.

Added: Oct 19, 2020
Article
Isaev A. P., Pyatov P. N., Rittenberg V. Journal of Physics A: Mathematical and Theoretical. 2001. Vol. 34.
Added: Mar 10, 2010
Article
Akhmedova V., Zabrodin A. Journal of Physics A: Mathematical and Theoretical. 2014. Vol. 47. P. 11 -13.

We show that the dispersionless DKP hierarchy (the dispersionless limit of the Pfaff lattice) admits a suggestive reformulation through elliptic functions. We also consider one-variable reductions of the dispersionless DKP hierarchy and show that they are described by an elliptic version of the L¨owner equation. With a particular choice of the driving function, the latter appears to be closely related to the Painlev´e VI equation with special choice of parameters.

Added: Oct 22, 2015
Article
Tobisch E., Pelinovsky E. Journal of Physics A: Mathematical and Theoretical. 2020. Vol. 53. No. 34. P. 345703.

In this paper we study dispersive enhancement of a wave train in systems described by the fractional Korteweg–de Vries-type equations of the form ut + αn un ux + βm(Dm{u})x = 0,Dm{u} = −|k|m u(k) where the operator Dm{u} is written in the Fourier space, αn, βm are arbitrary constants and n,m being rational numbers (positive or negative). Using both approximate and exact solutions of these wave equations we describe constructively the process of dispersive focusing. It is based on a time-reversing approach with the expected rogue wave chosen as the initial condition for a solution of these equations. We demonstrate the qualitative difference in the shape of the focused wavetrains for various n and m. Our results can be used for prediction of the rogue wave appearance arising in many types of weakly nonlinear and weakly dispersive wave systems in physical context.

Added: Aug 4, 2020
Article
Руднева Д., Zabrodin A. Journal of Physics A: Mathematical and Theoretical. 2020. Vol. 53. No. 7. P. 075202.

We derive equations of motion for poles of elliptic solutions to the B-version of the Kadomtsev–Petviashvili equation (BKP). The basic tool is the auxiliary linear problem for the Baker–Akhiezer function. We also discuss integrals of motion for the pole dynamics which follow from the equation of the spectral curve.

Added: Aug 20, 2020
Article
Rudneva D., Zabrodin A. Journal of Physics A: Mathematical and Theoretical. 2020. Vol. 53.

We derive equations of motion for poles of elliptic solutions to the

B-version of the Kadomtsev-Petviashvili equation (BKP).

The basic tool is the auxiliary linear problem for the Baker-Akhiezer function.

We also discuss integrals of motion for the pole dynamics which follow from the equation

of the spectral curve.

 

Added: Feb 2, 2021
Article
Vassily Gorbounov, Talalaev D. Journal of Physics A: Mathematical and Theoretical. 2020. Vol. 53. No. 45. P. 1-28.

We propose a new approach to studying electrical networks interpreting the Ohm law as the operator which solves certain Local Yang-Baxter equation. Using this operator and the medial graph of the electrical network we define a vertex integrable statistical model and its boundary partition function. This gives an equivalent description of electrical networks. We show that, in the important case of an electrical network on the standard graph introduced in [1], the response matrix of an electrical network, its most important feature, and the boundary partition function of our statistical model can be recovered from each other. Defining the electrical varieties in the usual way we compare them to the theory of the Lusztig varieties developed in [2]. In our picture the former turns out to be a deformation of the later. Our results should be compared to the earlier work started in [3] on the connection between the Lusztig varieties and the electrical varieties. There the authors introduced a one-parameter family of Lie groups which are deformations of the Unipotent group. For the value of the parameter equal to 1 the group in the family acts on the set of responce matrices and is related to the symplectic group. Using the data of electrical networks we construct a representation of the group in this family which corresponds to the value of the parameter −1 in the symplectic group and show that our boundary partition functions belong to it. Remarkably this representation has been studied before in the work on six vertex statistical models and the representations of the Tempeley-Lieb algebra.

Added: Sep 9, 2020
Article
Зотов А., Левин А. М., Ольшанецкий М. Journal of Physics A: Mathematical and Theoretical. 2006. Т. 39. № 39.
Added: Oct 1, 2010
Article
Prokofev V., Zabrodin A. Journal of Physics A: Mathematical and Theoretical. 2021. Vol. 54. No. 30.

We consider solutions of the Kadomtsev-Petviashvili hierarchy which are elliptic functions of x = t (1). It is known that their poles as functions of t (2) move as particles of the elliptic Calogero-Moser model. We extend this correspondence to the level of hierarchies and find the Hamiltonian H ( k ) of the elliptic Calogero-Moser model which governs the dynamics of poles with respect to the kth hierarchical time. The Hamiltonians H ( k ) are obtained as coefficients of the expansion of the spectral curve near the marked point in which the Baker-Akhiezer function has essential singularity.

Added: Sep 7, 2021
Article
Kolokolov I. Journal of Physics A: Mathematical and Theoretical. 2017. Vol. 50. No. 155501. P. 1-12.

The two-point correlation tensor of small-scale fluctuations of magnetic field B in a two-dimensional chaotic flow is studied. The analytic approach is developed in the framework of the Kraichnan–Kazantsev model. It is shown that the growth of the field fluctuations takes place in an essentially resistive regime and stops at large times in accordance with the so-called anti-dynamo theorems. The value of B2 is enhanced in the course of the evolution by the magnetic Prandtl number.

Added: Mar 28, 2017
Article
Dunin-Barkowski P., Smirnov A., Sleptsov A. Journal of Physics A: Mathematical and Theoretical. 2012. Vol. 45. No. 38. P. 533-557.

We solve the regularized Knizhnik-Zamolodchikov equation and find an explicit expression for the Drinfeld associator. We restrict to the case of the fundamental representation of gl(N). Several tests of the results are presented. It can be explicitly seen that components of this solution for the associator coincide with certain components of WZW conformal block for primary fields. We introduce the symmetrized version of the Drinfeld associator by dropping the odd terms. The symmetrized associator gives the same knot invariants, but has a simpler structure and is fully characterized by one symmetric function which we call the Drinfeld prepotential.

 

Added: Nov 5, 2014
Article
Feher L., Marshall I. Journal of Physics A: Mathematical and Theoretical. 1997. No. 30. P. 5815-5824.
Added: Oct 30, 2010