Related papers: Some aspects of functional Bethe ansatz
The Algebraic Bethe Ansatz (ABA) is a highly successful analytical method used to exactly solve several physical models in both statistical mechanics and condensed-matter physics. Here we bring the ABA into unitary form, for its direct…
We prove the orthogonality of the Bethe Ansatz eigenfunctions for the Laplacian on a hyperoctahedral Weyl alcove with repulsive homogeneous Robin boundary conditions at the walls. To this end these eigenfunctions are retrieved as the…
The bound state wave functions for a wide class of exactly solvable potentials are found utilizing the quantum Hamilton-Jacobi formalism. It is shown that, exploiting the singularity structure of the quantum momentum function, until now…
The goal of this paper is to give a geometric construction of the Bethe algebra (of Hamiltonians) of a Gaudin model associated to a simple Lie algebra. More precisely, in this paper a quantum integrable model is assigned to a weighted…
The nested algebraic Bethe ansatz is presented for the anisotropic supersymmetric $U$ model maintaining quantum supersymmetry. The Bethe ansatz equations of the model are obtained on a one-dimensional closed lattice and an expression for…
It is well known that while forward scattering has no effect on the conductance of one-dimensional systems, backscattering off a static impurity suppresses the current. We study the effect of a time-dependent point impurity on the…
We investigate the sub-leading contributions to the free energy of Bethe Ansatz solvable (continuum) models with different boundary conditions. We show that the Thermodynamic Bethe Ansatz approach is capable of providing the O(1) pieces if…
Simple analytical parametrizations for the ground-state energy of the one-dimensional repulsive Hubbard model are developed. The charge-dependence of the energy is parametrized using exact results extracted from the Bethe-Ansatz. The…
It is well known that while forward scattering has no effect on the conductance of one-dimensional systems, backscattering off a static impurity suppresses the current. We study the effect of a time-dependent point impurity on the…
We review the theory for exactly solving quantum Hamiltonian systems through the algebraic Bethe ansatz. We also demonstrate how this theory applies to current studies in Bose-Einstein condensation and metallic grains which are of nanoscale…
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.
From the open boundary t-J model, an impurity model is constructed in which magnetic impurities of arbitrary spins are coupled to the edges of the strongly correlated electron system. The boundary R matrices are given explicitly. The…
The scattering of a wave obeying Helmholtz equation by an elliptic obstacle can be described exactly using series of Mathieu functions. This situation is relevant in optics, quantum mechanics and fluid dynamics. We focus on the case when…
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…
Using the Bethe ansatz (BA), we rigorously obtain non-equilibrium dynamics of an impurity with a large initial momentum $Q$ in the one-dimensional (1D) interacting bosonic medium. We show that magnon and exciton-like states obtained from…
The spectral properties of the quantum mechanical system consisting of a quantum dot with a short-range attractive impurity inside the dot are investigated in the zero-range limit. The Green function of the system is obtained in an explicit…
An integrable quantum spin ladder based on the SU(4) symmetry algebra with boundary defects is studied in the framework of boundary integrability. Five nontrivial solutions of the reflection equations lead to different boundary impurities.…
We use the Bethe Ansatz solution for the one dimensional Hubbard model with open boundary conditions and applied boundary fields to study the spectrum of bound states at the boundary. Depending on the strength of the boundary potentials one…
In this work we have developed the essential tools for the algebraic Bethe ansatz solution of integrable vertex models invariant by a unique U(1) charge symmetry. The formulation is valid for arbitrary statistical weights and respective…
The problem of a travelling wave over an arbitrary quasi-flat bathymetry in a semi infinite channel is studied in the shallow-water formulation. It is shown how the streamfunction can be cast, in the vicinity of an elliptic equilibrium for…