Related papers: Differential equations and the Bethe ansatz
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
With the aim of exploring a massive model corresponding to the perturbation of the conformal model [hep-th/0211094] the nonlinear integral equation for a quantum system consisting of left and right KdV equations coupled on the cylinder is…
This paper proposes a general framework for nonperturbatively defining continuum quantum field theories. Unlike most such frameworks, the one offered here is finitary: continuum theories are defined by reducing large but finite quantum…
The quantum integrability is established for the one-dimensional supersymmetric $U$ model with boundary terms by means of the quantum inverse scattering method. The boundary supersymmetric $U$ chain is solved by using the coordinate space…
We construct integrable generalised models in a systematic way exploring different representations of the gl(N) algebra. The models are then interpreted in the context of atomic and molecular physics, most of them related to different types…
Complex numbers enter fundamental physics in at least two rather distinct ways. They are needed in quantum theories to make linear differential operators into Hermitian observables. Complex structures appear also, through Hodge duality, in…
Models for what may lie behind the Standard Model often require non-perturbative calculations in strongly coupled field theory. This creates opportunities for lattice methods, to obtain quantities of phenomenological interest as well as to…
We study a system of functional relations among a commuting family of row-to-row transfer matrices in solvable lattice models. The role of exact sequences of the finite dimensional quantum group modules is clarified. We find a curious…
Many of the exciting features of the Standard Model of the elementary particles are inherently non-perturbative. A theoretical understanding of many physics aspects beyond the Standard Model of elementary particles also requires a…
The Bethe equation is a nonlinear differential equation that plays an important role in nuclear physics and a variety of applications related to it, such as the description of the behavior of an energetic particle when it penetrates into…
It is shown that the Lattice Boltzmann equation for hydrodynamics can be extended in such a way as to describe non-relativistic quantum mechanics.
The symmetry study of main differential equations of mechanics and electrodynamics has shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered…
We work towards the classification of all one-dimensional exclusion processes with two species of particles that can be solved by a nested coordinate Bethe Ansatz. Using the Yang-Baxter equations, we obtain conditions on the model…
A quantum integrable spin chain model associated with the $G_2$ exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to…
The general theory of (nonlinear) partial differential equations originated by S. Lie had a significant development in the past 30-40 years. Now this theory has solid foundations, a proper language, proper techniques and problems, and a…
The status of lattice calculations in Quantum Field Theory is reviewed. A major part is devoted to recent progress in formulating exact chiral symmetry on the lattice. Another topic which has received a lot of attention is the influence of…
In this work we propose a mechanism for converting the spectral problem of vertex models transfer matrices into the solution of certain linear partial differential equations. This mechanism is illustrated for the…
In this short review the role of the Hirota equation and the tau-function in the theory of classical and quantum integrable systems is outlined.
The main achievements of Pseudo-Hermitian Quantum Mechanics and its distinction with the indefinite-metric quantum theories are reviewed. The issue of the non-uniqueness of the metric operator and its consequences for defining the…
In this chapter we review results on the lattice Schwinger model. In par-ticular, we show how the effect of the anomaly is reproduced on the lattice. We connect these results to recent developments in the field of quantum simulation of…