Related papers: Factorized structure of the long-range two-electro…
Coulomb explosion imaging (CEI) is a powerful experimental technique that maps a molecule's geometric structure onto the momenta of ionic molecular fragments produced by rapid multiple ionization. Here, we apply CEI induced by pulses from…
Knowledge of the molecular structure is key to understanding the function of participating molecules in photo-induced chemical reactions. Visualizing the nuclear dynamics of a photochemical reaction requires an ultrafast measurement…
In this work, we perform Bayesian inference tasks for the chemical master equation in the tensor-train format. The tensor-train approximation has been proven to be very efficient in representing high dimensional data arising from the…
Linear-scaling electronic structure methods based on the calculation of moments of the underlying electronic Hamiltonian offer a computationally efficient and numerically robust scheme to drive large-scale atomistic simulations, in which…
Semi-empirical quantum models such as Density Functional Tight Binding (DFTB) are attractive methods for obtaining quantum simulation data at longer time and length scales than possible with standard approaches. However, application of…
The paper is devoted to the efficient computation of high-order cubature formulas for volume potentials obtained within the framework of approximate approximations. We combine this approach with modern methods of structured tensor product…
Numerical homogenization for mechanical multiscale modeling by means of the finite element method (FEM) is an elegant way of obtaining structure-property relations, if the behavior of the constituents of the lower scale is well understood.…
Quantum computing shows promise for addressing computationally intensive problems but is constrained by the exponential resource requirements of general quantum state tomography (QST), which fully characterizes quantum states through…
We derive distance-dependent estimators for two-center and three-center electron repulsion integrals over a short-range Coulomb potential, $\textrm{erfc}(\omega r_{12})/r_{12}$. These estimators are much tighter than one based on the…
Coulomb explosion imaging (CEI) with x-ray free electron lasers has recently been shown to be a powerful method for obtaining detailed structural information of gas-phase planar ring molecules [R. Boll et al. Nat. Phys. 18, 423-428 (2022)].…
We propose the novel numerical scheme for solution of the multidimensional Fokker-Planck equation, which is based on the Chebyshev interpolation and the spectral differentiation techniques as well as low rank tensor approximations, namely,…
We extend the FE-DMN method to fully coupled thermomechanical two-scale simulations of composite materials. In particular, every Gauss point of the macroscopic finite element model is equipped with a deep material network (DMN). Such a DMN…
Explicitly correlated quantum chemical calculations require calculations of five types of molecular integrals beyond the standard electron repulsion integrals. We present a novel scheme, which utilises general ideas of the…
We present a tensor-structured algorithm for efficient large-scale DFT calculations by constructing a Tucker tensor basis that is adapted to the Kohn-Sham Hamiltonian and localized in real-space. The proposed approach uses an additive…
We generalize Tweed's seminal Born~I formalism for the electron-impact double ionization of two-electron atomic systems ($\text{H}^-$, $\text{He}$, $\text{Li}^+$) to non-extensive plasma environments described by Tsallis $q$-statistics. The…
The computation of strongly correlated quantum systems is challenging because of its potentially exponential scaling in the number of electron configurations. Variational calculation of the two-electron reduced density matrix (2-RDM)…
In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become…
A practical experimental scheme for a quantum simulator of strongly correlated electrons is proposed. Our scheme employs electrons confined in a two dimensional electron gas in a GaAs/AlGaAs heterojunction. Two surface acoustic waves are…
Semi-empirical interatomic potentials have been developed for Al, alpha-Ti, and gamma-TiAl within the embedded atomic method (EAM) by fitting to a large database of experimental as well as ab-initio data. The ab-initio calculations were…
With growing demand for time-domain simulations of correlated many-body systems, the development of efficient and stable integration schemes for the time-dependent Schr\"odinger equation is of keen interest in modern electronic structure…