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The integrable quantum models associated to the transfer matrices of spin 1/2 highest weight representations for the 6-vertex reflection algebra are studied in the framework of Sklyanin's quantum sepa...
We study amplitudes of five-wave interactions for evolution Hamiltonian equations differ from the KdV equation by the form of dispersion law. We find that five-wave amplitude is canceled for all three...
Abstract: The paper presents the classification of matrix valued superpotentials corresponding to shape invariant systems of Schr\"odinger equations. All inequivalent irreducible matrix superpotential...
Abstract: We show that any symmetric norm on $\bR^n$ induces a metric on U(n), the group of all $n\times n$ unitary matrices. Using the same technique, we prove an inequality concerning the eigenvalue...
Abstract: The absolute value of matrices is used, to give inequalities for the trace of products. An application gives a very short proof of the tracial matrix Hoelder inequality.
Abstract: We describe an analytic continuation of the Euclidean Grosse-Wulkenhaar and LSZ models which defines a one-parameter family of duality covariant noncommutative field theories interpolating b...
Asymptotic Integral Kernel for Ensembles of Random Normal Matrix with Radial Potentials.
Abstract: We present a new framework for defining fuzzy approximations to geometry in terms of a cutoff on the spectrum of the Dirac operator, and a generalization of it that we call the Dirac-Flux op...
Abstract: We present the expressions for the monodromy matrix elements of the six-vertex model in the F-basis for arbitrary Boltzmann weights. The results rely solely on the property of unitarity and ...
Abstract: We extend the results about the fluctuations of the matrix entries of regular functions of Wigner matrices to the case of sample covariance random matrices.
Abstract: We write the loop equations for the $\beta$ two-matrix model, and we propose a topological recursion algorithm to solve them, order by order in a small parameter. We find that to leading ord...
Abstract: In this paper matrix orthogonal polynomials in the real line are described in terms of a Riemann--Hilbert problem. This approach provides an easy derivation of discrete equations for the cor...
We illustrate the stochastic method for solving the Schwinger-Dyson equations in large-N quantum field theories described in ArXiv:1009.4033 on the example of the Gross-Witten unitary matrix model.
We prove that if the two-body terms in the equation of motion for the one-body reduced density matrix are approximated at each instant of time from ground-state functionals, the eigenvalues of the on...

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