Related papers: Quantum inverse scattering method and generalizati…
L\"uscher's formula relates the elastic scattering phase shifts to the two-particle energy levels in a finite cubic box. The original formula was obtained for elastic scattering of two massive spinless particles in the center of mass frame.…
We construct a family of solvable lattice models whose partition functions include $p$-adic Whittaker functions for general linear groups from two very different sources: from Iwahori-fixed vectors and from metaplectic covers. Interpolating…
The normalisation relation between the bound and scattering S-state wave functions, extrapolated to the bound state pole, is derived from the Schroedinger equation. It is shown that, unlike previous work, the result does not depend on the…
An inverse scattering transform method corresponding to a Riemann-Hilbert problem is formulated for CH2, the two-component generalization of the Camassa-Holm (CH) equation. As an illustration of the method, the multi - soliton solutions…
Starting from the Pauli Hamiltonian operator, we derive a scalar quantum kinetic equations for spin-1/2 systems. Here the regular Wigner two-state matrix is replaced by a scalar distribution function in extended phase space. Apart from…
A coupled system of volume integral and hydrodynamic equations is solved to analyze electromagnetic scattering from nanostructures consisting of metallic and dielectric parts. In the metallic part, the hydrodynamic equation relates the free…
Convergence and stability results for the inverse Born series [Moskow and Schotland, Inverse Problems, 24:065005, 2008] are generalized to mappings between Banach spaces. We show that by restarting the inverse Born series one obtains a…
Factorial Schur functions are generalizations of Schur functions that have, in addition to the usual variables, a second family of "shift" parameters. We show that a factorial Schur function times a deformation of the Weyl denominator may…
A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an…
We extend the recently developed Izergin-Korepin analysis on the wavefunctions of the $U_q(sl_2)$ six-vertex model to the reflecting boundary conditions. Based on the Izergin-Korepin analysis, we determine the exact forms of the symmetric…
We derive semiclassical approximations for wavefunctions, Green's functions and expectation values for classically chaotic quantum systems. Our method consists of applying singular and regular perturbations to quantum Hamiltonians. The…
We propose a new approach to quantum states in Fock space in terms of classical hydrodynamics. By conformal mapping of complex analytic function, representing the wave function of quantum states in Fock-Bargmann representation, we define…
This paper develops a general theory of the Fourier-Jacobi expansion of cusp forms on the real symplectic group of degree two including generic cusp forms. An explicit description of such expansion is available for cusp forms generating…
The multi-component nonlinear Schrodinger equation related to C.I=Sp(2p)/U(p) and D.III=SO(2p)/U(p)-type symmetric spaces with non-vanishing boundary conditions is solvable with the inverse scattering method (ISM). As Lax operator L we use…
This work shows that notable acceleration of the speed of calculating Chandrasekhar's H-functions for general laws of scattering with an iterative method can be realized by supplying a starting pproximation produced by the following…
This work studies the semiclassical methods in multi-dimensional quantum systems bounded by finite potentials. By replacing the Maslov index by the scattering phase, the modified transfer operator method gives rather accurate corrections to…
Integral representation for the eigenfunctions of quantum periodic Toda chain is constructed for N-particle case. The multiple integral is calculated using the Cauchy residue formula. This gives the representation which reproduces the…
An differential equation for wave functions is proposed, which is equivalent to Schr\"{o}dinger's wave equation and can be used to determine energy-level gaps of quantum systems. Contrary to Schr\"{o}dinger's wave equation, this equation is…
We show that the geometric lifting of the RSK correspondence introduced by A.N. Kirillov (2001) is volume preserving with respect to a natural product measure on its domain, and that the integrand in Givental's integral formula for…
This paper concerns the study and resolution of wave equations in the space of Schwartz distributions. Wave phenomena are widespread in many branches of physics and chemistry, such as optics, gravitation, quantum mechanics, chemical waves…