Related papers: Space-time propagator and exact solution for wave …
Using a generalized transfer matrix method we exactly solve the Schr\"odinger equation in a time periodic potential, with discretized Euclidean space-time. The ground state wave function propagates in space and time with an oscillating…
We study the inverse problem of locating point sources from far-field data under plane wave incidence. A direct computational method is developed based on multiple scattering theory, using a novel indicator function to avoid iterative…
The paper considers the wave equation, with constant or variable coefficients in $\R^n$, with odd $n\geq 3$. We study the asymptotics of the distribution $\mu_t$ of the random solution at time $t\in\R$ as $t\to\infty$. It is assumed that…
In electromagnetism, acoustics, and quantum mechanics, scattering problems can routinely be solved numerically by virtue of perfectly matched layers (PMLs) at simulation domain boundaries. Unfortunately, the same has not been possible for…
We develop a scattering theory to investigate the multi-photon transmission in a one-dimensional waveguide in the presence of quantum emitters. It is based on a path integral formalism, uses displacement transformations, and does not…
In this paper we address a fundamental question in communication, that is, in the presence of various noise scenarios such as white/colored Gaussian noise and impulsive -type noises, how to efficiently and accurately transmit a set of…
We present an analysis of enhanced wave transmission through random media with mirror symmetry about a reflecting barrier. The mathematical model is the acoustic wave equation and we consider two setups, where the wave propagation is along…
The geometrical-optics expansion reduces the problem of solving wave equations to one of solving transport equations along rays. Here we consider scalar, electromagnetic and gravitational waves propagating on a curved spacetime in general…
The multiple scattering theory (MST) is a Green's function method that has been widely used in electronic structure calculations for crystalline disordered systems. The key property of the MST method is the scattering path matrix (SPM) that…
We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer…
Propagation of an ultrashort pulse of light through strongly scattering media generates an intricate spatio-spectral speckle that can be described by means of the multi-spectral transmission matrix (MSTM). In conjunction with a spatial…
Indoor sensing is challenging because of the multi-bounce effect, spherical wavefront, and spatial nonstationarity (SNS) of the near-field effect. This paper addresses radio-based environment sensing considering these issues. Specifically,…
This paper is concerned with the mathematical analysis of the time-domain electromagnetic scattering problem in an infinite rectangular waveguide. A transparent boundary condition is developed to reformulate the problem into an equivalent…
This work concerns the analysis of wave propagation in random media. Our medium of interest is sea ice, which is a composite of a pure ice background and randomly located inclusions of brine and air. From a pulse emitted by a source above…
A network of large-scale laser interferometers is currently employed for searches of gravitational waves from various astrophysical sources. The frequency dependence of the dynamic response of these detectors introduces corrections to their…
Simulating the propagation of elastic waves in multi-layered media has many applications. A common approach is to use matrix methods where the elastic wave-field within each material layer is represented by a sum of partial-waves along with…
A general solution to the "shutter" problem is presented. The propagation of an arbitrary initially bounded wavefunction is investigated, and the general solution for any such function is formulated. It is shown that the exact solution can…
The large-time behavior of solutions to Burgers equation with small viscosity is described using invariant manifolds. In particular, a geometric explanation is provided for a phenomenon known as metastability, which in the present context…
We study detection and imaging of small reflectors in heavy clutter, using an array of transducers that emits and receives sound waves. Heavy clutter means that multiple scattering of the waves in the heterogeneous host medium is strong and…
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…