I will first formulate a problem in the theory of group representations and show how to solve it; then I will discuss the relation of this problem to the theory of automorphic forms. Since there is no point in striving for maximum generality, I start with a connected semisimple group G with finite center. An irreducible unitary representaiton π of G on the Hilbert space H is said to be square-i...

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F -matrices (or the so-called F -basis) play an important role in the construction. In the F -basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely ...

The enhancement of tunneling probability in the nearly integrable system is closely examined, focusing on tunneling splittings plotted as a function of the inverse of the Planck's constant. On the basis of the analysis using the absorber which efficiently suppresses the coupling, creating spikes in the plot, we found that the splitting curve should be viewed as the staircase-shaped skeleton acc...

We study level statistics in ensembles of integrable N×N matrices linear in a real parameter x. The matrix H(x) is considered integrable if it has a prescribed number n>1 of linearly independent commuting partners H^{i}(x) (integrals of motion) [H(x),H^{i}(x)]=0, [H^{i}(x),H^{j}(x)]=0, for all x. In a recent work [Phys. Rev. E 93, 052114 (2016)2470-004510.1103/PhysRevE.93.052114], we developed ...

We deal with a perturbation of a hyperbolic integrable Hamiltonian system with n + 1 degrees of freedom. The integrable system is assumed to have n-dimensional hyperbolic invariant tori with coincident whiskers (separatrices). Following Eliasson, we use a geometric approach that takes advantage of the Lagrangian properties of the whiskers, to show that the splitting distance between the perturb...

Renormalization of twist-three operators and integrable lattice models. Abstract We address the problem of solution of the QCD three-particle evolution equations which govern the Q 2-dependence of the chiral-even quark-gluon-quark and three-gluon correlators contributing to a number of asymmetries at leading order and the transversely polarized structure function g 2 (x Bj). The quark-gluon-qua...

We present an inverse scattering approach to defects in classical integrable field theories. Integrability is proved systematically by constructing the generating function of the infinite set of modified integrals of motion. The contribution of the defect to all orders is explicitely identified in terms of a defect matrix. The underlying geometric picture is that those defects correspond to Bäc...

Integrability in string/field theories is known to emerge when considering dynamics in the moduli space of physical theories. This implies that one has to look at the dynamics with respect to unusual time variables like coupling constants or other quantities parameterizing configuration space of physical theories. The dynamics given by variations of coupling constants can be considered as a can...

The one dimensional $\delta$-function interacting Bose gas (the Lieb-Liniger model) is an integrable system, which can model experiments with ultra cold atoms in traps. Even though the integrable, integrability breaking effects are always present real world experiments. In this work we consider due to atomic loss, most relevant effect We set up a framework for exact computation of losses canoni...