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We develop the $\bar{\partial}$ -approach to inverse scattering at zero energy in dimensions $d \geq 3$ of [Beals, Coifman 1985], [Henkin, Novikov 1987] and [Novikov 2002]. As a result we give, in particular, uniqueness theorem, precise reconstruction procedure, stability estimate and approximate reconstruction for the problem of finding a sufficiently small potential $v$ in the Schrödinger equation from a fixed non-overdetermined (“backscattering” type) restriction ${h |}_{Γ}$ of the Faddeev generalized scattering amplitude $h$ in the...

Properties of non-hermitian quantum field theories

Carl M. Bender (2003)

Annales de l’institut Fourier

In this paper I discuss quantum systems whose Hamiltonians are non-Hermitian but whose energy levels are all real and positive. Such theories are required to be symmetric under $𝒞 𝒫 𝒯$ , but not symmetric under $𝒫$ and $𝒯$ separately. Recently, quantum mechanical systems having such properties have been investigated in detail. In this paper I extend the results to quantum field theories. Among the systems that I discuss are $- φ^{4}$ and $i φ^{3}$ theories. These theories all have unexpected and remarkable properties. I discuss...

Riemann-Lebesgue properties of Green's functions with applications to inverse scattering.

Ford, Richard (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Scattering and spectral theory for Stark Hamiltonians in one dimension.

Yang Liu (1993)

Mathematica Scandinavica

Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations

Tanya Christiansen, M. S. Joshi (2003)

Annales de l’institut Fourier

The scattering matrix is defined on a perturbed stratified medium. For a class of perturbations, its main part at fixed energy is a Fourier integral operator on the sphere at infinity. Proving this is facilitated by developing a refined limiting absorption principle. The symbol of the scattering matrix determines the asymptotics of a large class of perturbations.

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Back-scattering and nonlinear Radon transformation

Bethe ansatz solutions of the Bose-Hubbard dimer.

Darboux transformation for the nonstationary Schrödinger equation.

Gauge transformations and inverse quantum scattering with medium-range magnetic fields.

Inverse scattering problems in several dimensions

Inverse scattering theory for Dirac operators

Matrice de scattering et résonances associées à une orbite hétérocline

On non-overdetermined inverse scattering at zero energy in three dimensions

Properties of non-hermitian quantum field theories

Riemann-Lebesgue properties of Green's functions with applications to inverse scattering.

Scattering and spectral theory for Stark Hamiltonians in one dimension.

Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations

Structured matrix numerical solution of the nonlinear Schrödinger equation by the inverse scattering transform.

The inverse $N$ -body problem. A geometrical approach

The measurable distinction between the spin and orbital angular momenta of electromagnetic radiation.

The Role of Green’s Functions in Inverse Scattering at Fixed Energy

Гармонический анализ в многосвязной области I

Гармонический анализ в многосвязной области II

Корреляционные функции в квантовом методе обратной задачи рассеяния

Метод обратной задачи для системы Захарова-Манакова

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