相关论文: The Quantum Inverse Scattering Method for Hubbard-…

The Algebraic Bethe ansatz for a supersymmetric nineteen vertex-model constructed from a three-dimensional representation of the twisted quantum affine Lie superalgebra $\mathcal{U}_{q}[\mathrm{osp}(2|2)^{(2)}]$ is presented in detail. The…

Supersymmetric quantum mechanics is well known to provide, together with the so-called shape invariance condition, an elegant method to solve the eigenvalue problem of some one-dimensional potentials by simple algebraic manipulations. In…

In this paper we consider an inverse problem for the $n$-dimensional random Schr\"{o}dinger equation $(\Delta-q+k^2)u = 0$. We study the scattering of plane waves in the presence of a potential $q$ which is assumed to be a Gaussian random…

We investigate the quantum Jaynes-Cummings model - a particular case of the Gaudin model with one of the spins being infinite. Starting from the Bethe equations we derive Baxter's equation and from it a closed set of equations for the…

In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it…

Calculating the ground state properties of a Hamiltonian can be mapped to the problem of finding the ground state of a smaller Hamiltonian through the use of embedding methods. These embedding techniques have the ability to drastically…

The semiclassical limit of the algebraic quantum inverse scattering method is used to solve the theory of the Gaudin model. Via Off-shell Bethe ansatz equations of an integrable representation of the graded osp(1|2) vertex model we find the…

This paper introduces a novel deep neural network architecture for solving the inverse scattering problem in frequency domain with wide-band data, by directly approximating the inverse map, thus avoiding the expensive optimization loop of…

We investigate the inverse scattering problem for the massive Thirring model, focusing particularly on cases where the transmission coefficient exhibits $N$ pairs of higher-order poles. Our methodology involves transforming initial data…

The transfer matrix of a possibly complex and energy-dependent scattering potential can be identified with the $S$-matrix of a two-level time-dependent non-Hermitian Hamiltonian H(t). We show that the application of the adiabatic…

In an innovative inverse-problem construction the measured, experimental energies $E_1$, $E_2$, ...$E_N$ of a quantum bound-state system are assumed fitted by an N-plet of zeros of a classical orthogonal polynomial $f_N(E)$. We reconstruct…

Extensions of standard one-dimensional supersymmetric quantum mechanics are discussed. Supercharges involving higher order derivatives are introduced leading to an algebra which incorporates a higher order polynomial in the Hamiltonian. We…

A new exactly solvable one-dimensional spin-3/2 Heisenberg model with SO(5)-invariance is proposed. The eigenvalues and Bethe ansatz equations of the model are obtained by using the nested algebraic Bethe ansatz approach. Several exotic…

We solve the Cauchy problem of the Ward model in light-cone coordinates using the inverse spectral (scattering) method. In particular we show that the solution can be constructed by solving a $2\times 2$ local matrix Riemann-Hilbert problem…

We study the spectral theory and inverse problem on asymptotically hyperbolic manifolds. The main subjects are as follows: (1)Location of the essential spectrum. (2)Absence of eigenvalues embedded in the continuous spectrum. (3)Limiting…

We discuss classical and quantum symmetries of extended Hubbard models. The quantum symmetries are shown to be related to the known superconducting SU(2) symmetry of the original Hubbard model at half filling via generalized Lang-Firsov…

A self-consistent spin-fluctuation theory is developed to obtain T_N vs. U for the half-filled Hubbard antiferromagnet in the whole U/t range. Good agreement is obtained in the strong coupling limit with the high-temperature…

The recent progress in revealing classical integrable structures in quantum models solved by Bethe ansatz is reviewed. Fusion relations for eigenvalues of quantum transfer matrices can be written in the form of classical Hirota's bilinear…

We consider a generalisation of the p+ip pairing Hamiltonian with external interaction terms. These terms allow for the exchange of particles between the system and its environment. As a result the u(1) symmetry associated with conservation…

The initial-value problem for cylindrical gravitational waves is studied through the development of the inverse scattering method scheme. The inverse scattering transform in this case can be viewed as a transformation of the Cauchy data to…