Related papers: Quantum Sine(h)-Gordon Model and Classical Integra…
We present a unified method of construction of surfaces associated with Grassmannian sigma models, expressed in terms of an orthogonal projector. This description leads to compact formulae for structural equations of two-dimensional…
We unveil a remarkable connection between the sine-Gordon quantum field theory and the Kardar-Parisi-Zhang (KPZ) growth equation. We find that the non-relativistic limit of the two point correlation function of the sine-Gordon theory is…
We review our recent results on the on-shell description of sine-Gordon model with integrable boundary conditions. We determined the spectrum of boundary states together with their reflection factors by closing the boundary bootstrap and…
The Sine-Gordon model is obtained by tilting the law of a log-correlated Gaussian field $X$ defined on a subset of $\mathbb{R}^d$ by the exponential of its cosine, namely $\exp(\alpha \smallint \cos (\beta X))$. It is an important model in…
We present an integrable Hamiltonian which describes the sinh-Gordon model on the half line coupled to a non-linear oscillator at the boundary. We explain how we apply Sklyanin's formalism to a dynamical reflection matrix to obtain this…
We describe a procedure naturally associating relativistic Klein-Gordon equations in static curved spacetimes to non-relativistic quantum motion on curved spaces in the presence of a potential. Our procedure is particularly attractive in…
In this paper, we examine the complex sine-Gordon model in the presence of a boundary, and derive boundary conditions that preserve integrability. We present soliton and breather solutions, investigate the scattering of particles and…
A comprehensive symmetry analysis of the N=1 supersymmetric sine-Gordon equation is performed. Two different forms of the supersymmetric system are considered. We begin by studying a system of partial differential equations corresponding to…
We consider a parabolic sine-Gordon model with periodic boundary conditions. We prove a fundamental maximum principle which gives a priori uniform control of the solution. In the one-dimensional case we classify all bounded steady states…
Using the results of previous investigations on sine-Gordon form factors exact expressions of all breather matrix elements are obtained for several operators: all powers of the fundamental bose field, general exponentials of it, the energy…
We present here an explicit classical solution of the type of perturbiner in Sin(h)-Gordon model. This solution is a generating function for form-factors in the tree approximation.
Investigation of strongly interacting, nonlinear quantum field theories (QFT-s) remains one of the outstanding challenges of modern physics. Here, we describe analog quantum simulators for nonlinear QFT-s using mesoscopic superconducting…
We consider a modified Klein-Gordon equation that arises at ultra high energies. In a suitable approximation it is shown that for the linear potential which is of interest in quark interactions, their confinement for example,we get…
We present an exact field theoretical representation of the statistical mechanics of classical hard-core Coulomb systems. This approach generalizes the usual sine-Gordon theory valid for point-like charges or lattice systems to continuous…
In this paper, we propose fully discrete analogues of a generalized sine-Gordon (gsG) equation $u_{t x}=\left(1+\nu \partial_x^2\right) \sin u$. The bilinear equations of the discrete KP hierarchy and the proper definition of discrete…
We discuss certain integrable quantum field theories in (1+1)-dimensions consisting of coupled sine/sinh-Gordon theories with N=1 supersymmetry, positive kinetic energy, and bosonic potentials which are bounded from below. We show that…
The discrete quantum Sine-Gordon model at roots of unity remarkably combines a classical integrable system with an integrable quantum spin system, whose parameters obey classical equations of motion. We show that the fundamental R-matrix of…
We study the 2D coupled wave-Klein-Gordon systems with semi-linear null nonlinearities $Q_0$ and $Q_{\alpha\beta}$. The main result states that the solution to the 2D coupled systems exists globally provided that the initial data are small…
We propose a system of sine-Gordon equations, with the $\mathcal{PT}$ symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling stems from…
We construct defects in the XXZ and sine-Gordon models by making use of the representation theory of quantum affine sl_2. The representations involved are generalisations of the infinite-dimensional, q-oscillator representations used in the…