Related papers: Norm of Bethe Wave Function as a Determinant
The paper studies the initial boundary value problem related to the dynamic evolution of an elastic beam interacting with a substrate through an elastic-breakable forcing term. This discontinuous interaction is aimed to model the phenomenon…
The algebraic Bethe ansatz can be performed rather abstractly for whole classes of models sharing the same $R$-matrix, the only prerequisite being the existence of an appropriate pseudo vacuum state. Here we perform the algebraic Bethe…
We propose time-domain boundary integral and coupled boundary integral and variational formulations for acoustic scattering by linearly elastic obstacles. Well posedness along with stability and error bounds with explicit time dependence…
Solvable via Bethe Ansatz (BA) anisotropic statistical model on cubic lattice consisting of locally interacting 6-vertex planes, is studied. Symmetries of BA lead to infinite hierarchy of possible phases, which is further restricted by…
The partition function of the six-vertex model on a square lattice with domain wall boundary conditions (DWBC) is rewritten as a hermitean one-matrix model or a discretized version of it (similar to sums over Young diagrams), depending on…
For a spinless quantum particle in a one-dimensional box or an electromagnetic wave in a one-dimensional cavity, the respective Dirichlet and Neumann boundary conditions both lead to non-degenerate wave functions. However, in two spatial…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the sixth paper, exact analysis of the wave propagation in a beam with rectangular…
A methodology for determining the scattered Electromagnetic (EM) fields present for interconnected regions with common metasurface boundaries is presented. The method uses a Boundary Element Method (BEM) formulation of the frequency domain…
In this paper we revisit the derivation of boundary conditions for the Boltzmann Equation. The interaction between the wall atoms and the gas molecules within a thin surface layer is described by a kinetic equation introduced in [9] and…
The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex model with fixed open boundary conditions and the corresponding $SU_{q}(n)$ invariant…
In the course of devising a simple method for extraction of the S-matrix poles from the data, an additional fundamental resonance property emerged. It is a reaction invariant quantity, and since it is directly related to the Breit-Wigner…
The eigenfunctions and eigenvalues of the master-equation for zero range process with totally asymmetric dynamics on a ring are found exactly using the Bethe ansatz weighted with the stationary weights of particle configurations. The Bethe…
In this paper and upcoming ones, we initiate a systematic study of Bethe ansatz equations for integrable models by modern computational algebraic geometry. We show that algebraic geometry provides a natural mathematical language and…
We expand the Bethe/Gauge dictionary between the XXX Heisenberg spin chain and 2d N = (2,2) supersymmetric gauge theories to include aspects of the algebraic Bethe ansatz. We construct the wave functions of off-shell Bethe states as…
We solve the XXZ Gaudin model with generic boundary using the modified algebraic Bethe ansatz. The diagonal and triangular cases have been recovered in this general framework. We show that the model for odd or even lengths has two different…
The recently proposed exact quantum solution for two $\delta$-function-interacting particles with a mass-ratio $3\!:\!1$ in a hard-wall box [Y. Liu, F. Qi, Y. Zhang and S. Chen, iScience 22, 181 (2019)] violates the conventional necessary…
The Bethe Ansatz is a method that is used in quantum integrable models in order to solve them explicitly. This method is explained here in a general framework, which applies to 1D quantum spin chains, 2D statistical lattice models (vertex…
We use the Bethe Ansatz to derive analytical expressions for the current statistics in the asymmetric exclusion process with both forward and backward jumps. The Bethe equations are highly coupled and this fact has impeded their use to…
We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes…
Bethe strings are bound states of constituent particles in a variety of interacting many-body one-dimensional (1D) integrable quantum models relevant to magnetism, nanophysics, cold atoms and beyond. As emergent fundamental excitations,…