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Register a new userSpectral decomposition of the Lippmann-Schwinger equation applied to cylinders
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We derive the spectral decomposition of the Lippmann-Schwinger equation for electrodynamics, obtaining the fields as a sum of eigenmodes. The method is applied to cylindrical geometries.
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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 merges a qualitative and a quantitative method to optimize the way of exploiting the a priori information on the background within the inversion procedure, thus improving the quality of the reconstruction and reducing the data amount necessary for a satisfactory result. In the qualitative step, this a priori knowledge is utilized to implement the linear sampling method in its near-field formulation for an inhomogeneous background, in order to identify the region where the scatterer is located. On the other hand, the same a priori information is also encoded in the quantitative step by extending and applying the contrast source inversion method to what we call the `inhomogeneous Lippmann-Schwinger equation: the latter is a generalization of the classical Lippmann-Schwinger equation to the case of an inhomogeneous background, and in our paper is deduced from the differential formulation of the direct scattering problem to provide the reconstruction algorithm with an appropriate theoretical basis. Then, the point values of the refractive index are computed only in the region identified by the linear sampling method at the previous step. The effectiveness of this hybrid approach is supported by numerical simulations presented at the end of the paper.
We propose a new method to describe three-body breakups of nuclei, in which the Lippmann-Schwinger equation is solved combining with the complex scaling method. The complex-scaled solutions of the Lippmann-Schwinger equation (CSLS) enables us to treat boundary conditions of many-body open channels correctly and to describe a many-body breakup amplitude from the ground state. The Coulomb breakup cross section from the 6He ground state into 4He+n+n three-body decaying states as a function of the total excitation energy is calculated by using CSLS, and the result well reproduces the experimental data. Furthermore, the two-dimensional energy distribution of the E1 transition strength is obtained and an importance of the 5He(3/2-) resonance is confirmed. It is shown that CSLS is a promising method to investigate correlations of subsystems in three-body breakup reactions of the weakly-bound nuclei.
In this work the Lippmann-Schwinger equation is used to model seismic waves in strongly scattering acoustic media. We consider the Helmholtz equation, which is the scalar wave equation in the frequency domain with constant density and variable velocity, and transform it to an integral equation of the Lippmann-Schwinger type. To directly solve the discretized problem with matrix inversion is time-consuming, therefore we use iterative methods. The Born series is a well-known scattering series which gives the solution with relatively small cost, but it has limited use as it only converges for small scattering potentials. There exist other scattering series with preconditioners that have been shown to converge for any contrast, but the methods might require many iterations for models with high contrast. Here we develop new preconditioners based on randomized matrix approximations and hierarchical matrices which can make the scattering series converge for any contrast with a low number of iterations. We describe two different preconditioners; one is best for lower frequencies and the other for higher frequencies. We use the fast Fourier transform both in the construction of the preconditioners and in the iterative solution, and this makes the methods efficient. The performance of the methods are illustrated by numerical experiments on two 2D models.
The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced. A system of integro-differential equations for the cutoff-dependent potential is obtained. As an illustration, a perturbative solution of these equations with two cutoff parameters for a simple case of an S-wave low-energy potential in the form of a Taylor series in momenta is obtained. The relevance of the obtained results for the effective field theory approach to nucleon-nucleon scattering is discussed.
We develop a first-principles electron-transport simulator based on the Lippmann--Schwinger (LS) equation within the framework of the real-space finite-difference scheme. In our fully real-space based LS (grid LS) method, the ratio expression technique for the scattering wave functions and the Greens function elements of the reference system is employed to avoid numerical collapse. Furthermore, we present analytical expressions and/or prominent calculation procedures for the retarded Greens function, which are utilized in the grid LS approach. In order to demonstrate the performance of the grid LS method, we simulate the electron-transport properties of the semiconductor/oxide interfaces sandwiched between semi-infinite metal electrodes. The results confirm that the leakage current through the (001)Si/SiO$_2$ model becomes much larger when the dangling-bond (DB) state is induced by a defect in the oxygen layer while that through the (001)Ge/GeO$_2$ model is insensitive to the DB state.
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