We study relations between the eigenvectors of rational matrix functions on Riemann sphere. Our main result is that for a subclass are products two elementary blocks it possible to represent these in combinatorial–geometric way using diagram cube. In this representation, vertices cube eigenvectors, edges labeled by differences locations zeroes and poles determinant our function, each face corre...

Using a rational R-matrix associated with the 4 × 4 defining matrix representation of c 2 ∼ = sp(4), the Lie algebra of Sp(4), a one-site operator solution of the associated Yang-Baxter algebra acting in the Fock space of two harmonic oscillators is derived. This is used to define N-site integrable systems, which are soluble by a version of the algebraic Bethe ansatz method without nesting. All...

Random matrix theory (RMT) provides a common mathematical formulation of distinct physical questions in three different areas: quantum chaos, the 1-d integrable model with the 1/r2 interaction (the Calogero-Sutherland-Moser system), and 2-d quantum gravity. We review the connection of RMT with these areas. We also discuss the method of loop equations for determining correlation functions in RMT...

Some numerical algorithms are known to be related to discrete-time integrable systems, where it is essential that quantities to be computed (for example, eigenvalues and singular values of a matrix, poles of a continued fraction) are conserved quantities. In this paper, a new application of conserved quantities of integrable systems to numerical algorithms is presented. For an N × N (N ≥ 2) rea...

We propose a general method for constructing boundary integrable Gaudin models associated with (twisted) affine algebras G (k) (k = 1, 2), where G is a simple Lie algebra or superalgebra. Many new integrable Gaudin models with boundaries are constructed using this approach. In [1], Gaudin proposed a quantum integrable model describing N spin 1/2 particles with long-range interactions. Due to it...

We show that there are solitons with fractional fermion number in integrable N=2 supersymmetric models. We obtain the soliton S-matrix for the minimal, N=2 supersymmetric theory perturbed in the least relevant chiral primary field, the Φ(1,3) superfield. The perturbed theory has a nice Landau-Ginzburg description with a Chebyshev polynomial superpotential. We show that the S-matrix is a tensor ...

Abstract Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large self-adjoint random matrices from the generalized unitary ensembles. This paper considers discrete Tracy–Widom operators, and gives sufficient conditions for a discrete integrable operator to be the square of a Hankel matrix. Examples include the discrete Bessel kerne...

We approach the study of non–integrable models of two–dimensional quantum field theory as perturbations of the integrable ones. By exploiting the knowledge of the exact S-matrix and Form Factors of the integrable field theories we obtain the first order corrections to the mass ratios, the vacuum energy density and the S-matrix of the non-integrable theories. As interesting applications of the f...