Related papers: A time-dependent scattering approach to core-level…
Rigorous quantum dynamics calculations provide essential insights into complex scattering phenomena across atomic and molecular physics, chemical reaction dynamics, and astrochemistry. However, the application of the gold-standard quantum…
In this work, we investigate time-dependent wave scattering by multiple small particles of arbitrary shape. To approximate the solution of the associated boundary-value problem, we derive an asymptotic model that is valid in the limit as…
We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both…
Time-resolved ultrafast x-ray scattering from photo-excited matter is an emerging method to image ultrafast dynamics in matter with atomic-scale spatial and temporal resolutions. For a correct and rigorous understanding of current and…
We propose a method for realizing true, real-space imaging of charge dynamics in a periodic system, with angstrom spatial resolution and attosecond time resolution. In this method, inelastic x-ray scattering (IXS) is carried out with a…
In this paper, we study the time-independent Schr\"odinger equation within the formalism of position dependent effective mass. For a generalized decomposition of the non-central effective potential, the deformed Schr\"odinger equation can…
Inelastic x-ray scattering (IXS) now a widely used technique for studying the dynamics of electrons in condensed matter. We previously posed a solution to the phase problem for IXS [P. Abbamonte, et. al., Phys. Rev. Lett. {\bf 92}, 237401…
We consider the cubic nonlinear Schr\"odinger equation with an exceptional potential. We obtain a sharp time decay for the global in time solution and we get the large time asymptotic profile of small solutions. We prove the existence of…
We present a time-dependent Schr\"odinger equation (TDSE) approach within a non-relativistic quantum electrodynamics (QED) framework to investigate resonant x-ray scattering under intense x-ray pulses. This method enables us to explore how…
This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…
The coherent control of scattering processes is considered, with electron impact dissociation of H$_2^+$ used as an example. The physical mechanism underlying coherently controlled stationary state scattering is exposed by analyzing a…
Phase retrieval is at the heart of adaptive optics and modern high-resolution imaging. Without phase information, optical systems are limited to intensity-only measurements, hindering full reconstruction of object structures and wavefront…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
In this paper we introduce a method for solving linear and nonlinear scattering problems for wave equations using a new hybrid approach. This new approach consists of a reformulation of the governing equations into a form that can be solved…
We present scattering from many body systems in a new light. In place of the usual van Hove treatment, (applicable to a wide range of scattering processes using both photons and massive particles) based on plane waves, we calculate the…
Understanding quantum materials -- solids in which quantum-mechanical interactions among constituent electrons yield a great variety of novel emergent phenomena -- is a forefront challenge in modern condensed matter physics. This goal has…
Spectral analysis of the {\em adjoint} propagator in a suitable Hilbert space (and Lie algebra) of quantum observables in Heisenberg picture is discussed as an alternative approach to characterize infinite temperature dynamics of non-linear…
We have developed an improved method of time-resolved x-ray reflectivity (XRR) using monochromatic synchrotron radiation. Our method utilizes a polycapillary x-ray optic to create a range of incident angles and an area detector to collect…
The transition-matrix ($T$-matrix) approach provides a general formalism to study scattering problems in various areas of physics, including acoustics (scalar fields) and electromagnetics (vector fields), and is related to the theory of the…
Absorbing boundary conditions in the form of a complex absorbing potential are routinely introduced in the Schr\"odinger equation to limit the computational domain or to study reactive scattering events using the multi-configurational…