Related papers: Determinant representation for a quantum correlati…
We consider the quantum sinh-Gordon model in this paper. Using known formulae for form factors we sum up all their contributions and obtain a closed expression for a correlation function. This expression is a determinant of an integral…
We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance dependent correlation functions of…
The foundation for the theory of correlation functions of exactly solvable models is determinant representation. Determinant representation permit to describe correlation functions by classical completely integrable differential equations…
We consider the local field dynamical temperature correlation function of the Quantum Nonlinear Schrodinger equation with the finite coupling constant. This correlation function admits a Fredholm determinant representation. The related…
We consider the dynamical correlation functions of the quantum Nonlinear Schrodinger equation. In a previous paper we found that the dynamical correlation functions can be described by the vacuum expectation value of an operator-valued…
We show how the Riemann-Hilbert problem can be used to compute correlation kernels for determinantal point processes arising in different models of asymptotic combinatorics and representation theory. The Whittaker kernel and the discrete…
We investigate the asymptotic behavior of a generalized sine kernel acting on a finite size interval [-q,q]. We determine its asymptotic resolvent as well as the first terms in the asymptotic expansion of its Fredholm determinant. Further,…
This work investigates the long-time asymptotic behaviors of solutions to the initial value problem of the two-component nonlinear Klein-Gordon equation by inverse scattering transform and Riemann-Hilbert formulism. Two reflection…
The hamiltonian formalism is developed for the sine-Gordon model on the space-time light-like lattice, first introduced by Hirota. The evolution operator is explicitely constructed in the quantum variant of the model, the integrability of…
We consider the one-dimensional delta-interacting electron gas in the case of infinite repulsion. We use determinant representations to study the long time, large distance asymptotics of correlation functions of local fields in the gas…
We study the local lattice integrable regularization of the Sine-Gordon model written down in terms of the lattice Bose-operators. We show that the local spin Hamiltonian obtained from the six-vertex model with alternating inhomogeneities…
In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Klein-Gordon equations in one space dimension. We classify the systems by studying the quotient set of a suitable subset of systems…
Using the determinant representation for the field-field correlation functions of impenetrable anyons at finite temperature obtained in a previous paper, we derive a system of nonlinear partial differential equations completely…
We prove that general correlation functions of both ratios and products of characteristic polynomials of Hermitian random matrices are governed by integrable kernels of three different types: a) those constructed from orthogonal…
We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schr\"odinger model. We derive long-distance/long-time…
We study the asymptotics of singular values and singular functions of a Finite Hilbert transform (FHT), which is defined on several intervals. Transforms of this kind arise in the study of the interior problem of tomography. We suggest a…
Astymptotics of temperature correlations is the most dificult problem of stat. mech. Recently it was solved for the impenetrable Bose Gas. The idea is to represent correlation function as $\tau$ function of calssical completely integrable…
We consider the determinantal point process with the confluent hypergeometric kernel. This process is a universal point process in random matrix theory and describes the distribution of eigenvalues of large random Hermitian matrices near…
We define and study certain integrable lattice models with non-compact quantum group symmetry (the modular double of U_q(sl_2)) including an integrable lattice regularization of the sinh-Gordon model and a non-compact version of the XXZ…
The correlation functions of the quantum nonlinear Schrodinger equation can be presented in terms of a Fredholm determinant. The explicit expression for this determinant is found for the large time and long distance.