Related papers: Infinite dimension reflection matrices in the sine…
We describe an integrable system consisting of the sine-Gordon field, restricted to the half line, and coupled to a non-linear oscillator at the boundary. By extension of the coupling constant to imaginary values we also outline the…
We study the inverse resonance problem for conformally compact manifolds which are hyperbolic outside a compact set. Our results include compactness of isoresonant metrics in dimension two and of isophasal negatively curved metrics in…
Ideas from the theory of multisymplectic systems, introduced recently in integrable systems by the author and Kundu to discuss Liouville integrability in classical field theories with a defect, are applied to the sine-Gordon model. The key…
We explore the S-matrices of gapped, unitary, Lorentz invariant quantum field theories with a global O($N$) symmetry in 1+1 dimensions. We extremize various cubic and quartic couplings in the two-to-two scattering amplitudes of vector…
In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…
We show that the the generalized Calogero-Moser model with boundary potential of the P\"oschl-Teller type describes the non-relativistic limit of the quantum sine-Gordon model on a half-line with Dirichlet boundary condition.
Random matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous…
We consider boundary conditions compatible with discrete holomorphicity for the dilute O(n) and C_2^(1) loop models. In each model, for a general set of boundary plaquettes, multiple types of loops can appear. A generalisation of Smirnov's…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
Symmetric Space Sine-Gordon theories are two-dimensional massive integrable field theories, generalising the Sine-Gordon and Complex Sine-Gordon theories. To study their integrability properties on the real line, it is necessary to…
We introduce the concept of boundary degeneracy of topologically ordered states on a compact orientable spatial manifold with boundaries, and emphasize that the boundary degeneracy provides richer information than the bulk degeneracy.…
Relativistic integrable field theories like the sine-Gordon equation have an infinite set of conserved charges. In a light-front formalism these conserved charges are closely related to the integrable modified KdV hierarchy at the classical…
The surface states of intrinsic higher order topological phases are protected by the spatial symmetries of a finite sample. This property makes the existing scattering theory of topological invariants inapplicable because the scattering…
The purpose of this paper is to extend the store of models able to support integrable defects by investigating the two-dimensional Boussinesq nonlinear wave equation. As has been previously noted in many examples, insisting that a defect…
We establish a 3-parameter family of integral identities to be used on a class of theories possessing solitons with spherical symmetry in $d$ spatial dimensions. The construction provides five boundary charges that are related to certain…
We show that for any finite-dimensional algebra $\Lambda$ of infinite representation type, over a perfect field, there is a bounded principal ideal domain $\Gamma$ and a representation embedding from $\Gamma -$mod into $\Lambda -$mod. As an…
We address the scattering problem in two-dimensional integrable models, focusing on the sine-Gordon theory. We use the S-matrix bootstrap approach based on analytical properties of the S-matrix to compute scattering amplitudes of the…
We investigate a mechanical system consisting of infinite number of harmonically coupled pendulums which can impact on two rigid rods. Because of gravitational force the system has two degenerate ground states. The related topological kink…
In this work we present analytical and numerical evidences that classical integrable models possessing infinitely many degrees of freedom unexpectedly exhibit some features that are typical of chaotic systems. By studying how the conserved…
An exact method that analytically provides transfer matrices in finite networks of quasicrystalline approximants of any dimensionality is discussed. We use these matrices in two ways: a) to exactly determine the band structure of an…