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In parallel with the evolution of femtosecond and attosecond laser as well as free-electron laser technology, a variety of theoretical methods have been developed to describe the behavior of atoms, molecules, clusters, and solids under the…
We propose a new discrete element method supporting general polyhedral meshes. The method can be understood as a lowest-order discontinuous Galerkin method parametrized by the continuous mechanical parameters (Young's modulus and Poisson's…
We derive an analytical formula for the ionization rate of neutral atoms and molecules in a strong monochromatic field. Our model is based on the strong-field approximation with transition amplitudes calculated by an extended saddle point…
This paper mainly considers three iterations based on charge-conservative finite element approximation in Lipschitz domain for the stationary thermally coupled inductionless MHD equations. Based on the hybrid finite element method, the…
We apply relativistic many-body methods to compute static differential polarizabilities for transitions inside the ground-state hyperfine manifolds of monovalent atoms and ions. Knowing this transition polarizability is required in a number…
We relax the usual diagonal constraint on the matrix representation of the eigenvalue wave equation by allowing it to be tridiagonal. This results in a larger solution space that incorporates an exact analytic solution for the non-central…
We show that a pseudospectral representation of the wavefunction using multiple spatial domains of variable size yields a highly accurate, yet efficient method to solve the time-dependent Schr\"odinger equation. The overall spatial domain…
We investigate bright solitons in the one-dimensional Schr\"odinger equation in the framework of an extended variational approach. We apply the latter to the stationary ground state of the system as well as to coherent collisions between…
A novel unified Hamiltonian approach is proposed to solve Maxwell-Schrodinger equation for modeling the interaction between classical electromagnetic (EM) fields and particles. Based on the Hamiltonian of electromagnetics and quantum…
The exactly solvable quantum many-particle model with harmonic one- and two-particle interaction terms is extended to include time-dependency. We show that when the external trap potential and finite-range interparticle interaction have a…
The time-dependent Schr\"{o}dinger equation for the hydrogen atom and its interaction with coherent intense high-frequency short laser pulses is solved numerically exactly by propagating the single-electron wave packets. Thereby, the…
We study one of multidimensional inverse scattering problems for quantum systems in a constant electric field, by utilization of the Enss-Weder time-dependent method. The main purpose of this paper is to propose some methods of sharpening…
We use three dimensional time-dependent Schr\"odinger equation (3D--TDSE) to calculate angular electron momentum distributions and photoelectron spectra of atoms driven by spatially inhomogeneous fields. An example for such inhomogeneous…
A physical and numerical model of the Townsend discharge in molecular hydrogen and deuterium has been developed to meet the needs of designing a plasma-based switching device for power grid application. The model allows to predict the…
Relativistic strong-field ionization of hydrogen-like atoms or ions in a constant crossed electromagnetic field is studied. The transition amplitude is formulated within the strong-field approximation in G\"oppert-Mayer gauge, with initial…
Quantum theory has been remarkably successful in providing an understanding of physical systems at foundational scales. Solving the Schr\"odinger equation provides full knowledge of all dynamical quantities of the physical system. However…
The influence of inner electrons on the ionization dynamics in strong laser fields is investigated in a wavelength regime where the inner electron dynamics is usually assumed to be negligible. The role of inner electrons is of particular…
We present a space-time ultra-weak discontinuous Galerkin discretization of the linear Schr\"odinger equation with variable potential. The proposed method is well-posed and quasi-optimal in mesh-dependent norms for very general discrete…
In this paper we discuss how through the process of applying the Fourier transform to solutions of the Schr\"odinger equation in the Close Coupling approach, good results for the ionization differential cross section in energy for electrons…
Charge dynamics in an ultra-cold setup involving a laser dressed atom and an ion is studied here. This transfer of charge is enabled through molecular Rydberg states that are accessed via a laser. The character of the charge exchange…