Related papers: Fiend -- Finite Element Quantum Dynamics
A precise domain triangulation is recognized as indispensable for the accurate numerical approximation of differential operators within collocation methods, leading to a substantial reduction in discretization errors. An efficient finite…
Confocal fluorescence microscopy is widely applied for the study of point-like emitters such as biomolecules, material defects, and quantum light sources. Confocal techniques offer increased optical resolution, dramatic fluorescence…
The Finite Elements with Switch Detection (FESD) is a high-accuracy method for the numerical simulation and solution of optimal control problems subject to discontinuous ODEs. In this article, we extend the FESD method [Nurkanovi\'c et al.,…
We extend our analysis on the Oldroyd-B model in Barrett and Boyaval [1] to consider the finite element approximation of the FENE-P system of equations, which models a dilute polymeric fluid, in a bounded domain $D $\subset$ R d , d = 2 or…
We present and analyze a linearized finite element method (FEM) for the dynamical incompressible magnetohydrodynamics (MHD) equations. The finite element approximation is based on mixed conforming elements, where Taylor--Hood type elements…
The simulation of lattice gauge theories with tensor network (TN) methods is becoming increasingly fruitful. The vision is that such methods will, eventually, be used to simulate theories in $(3+1)$ dimensions in regimes difficult for other…
High-fidelity electron microscopy simulations required for quantitative crystal structure refinements face a fundamental challenge: while physical interactions are well-described theoretically, real-world experimental effects are…
We consider a system of ultracold atoms in an optical lattice as a quantum simulator for electron-positron pair production in quantum electrodynamics (QED). For a setup in one spatial dimension, we investigate the nonequilibrium phenomenon…
It is now established that nuclear quantum motion plays an important role in determining water's hydrogen bonding, structure, and dynamics. Such effects are important to include in density functional theory (DFT) based molecular dynamics…
We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach extends each of the aforementioned methods and unifies them within a single…
We study a new method - called Schrodingerisation introduced in [Jin, Liu, Yu, arXiv: 2212.13969] - for solving general linear partial differential equations with quantum simulation. This method converts linear partial differential…
Developing new methods for the accurate and efficient calculations of real-time quantum correlation functions is deemed one of the most challenging problems of modern condensed matter theory. Many popular methods, such as centroid molecular…
We present a new formulation of the correlated electron-ion dynamics (CEID) scheme, which systematically improves Ehrenfest dynamics by including quantum fluctuations around the mean-field atomic trajectories. We show that the method can…
Dynamical mass generation in a three-dimensional version of finite-temperature QED is studied with the help of Schwinger-Dyson equations in the real-time formalism. We go beyond the bare-vertex approximation and include wave-function…
Fluid-Structure Interaction (FSI) can be investigated by means of non-linear Finite Element Models (FEM), suitable to capture large deflections of structural parts interacting with fluids, and Computational Fluid Dynamics (CFD). High…
Physics-Informed Neural Networks present a novel approach in SciML that integrates physical laws in the form of partial differential equations directly into the NN through soft constraints in the loss function. This work studies the…
We present a full-vector finite element method (FEM) mode solver for dielectric waveguides based on a mixed Nedelec-Lagrange discretization of Maxwell's curl equations in the frequency domain. The formulation combines edge elements for…
MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and…
Field emission coupled with molecular dynamics simulation (FEcMD) software package is a computational tool for studying atomic structure evolution, structural deformation, phase transitions, recrystallization as well as electron emission…
Particle breakage due to collisional interactions plays a vital role in the development of several phenomena in science and engineering. The nonlinear collisional breakage equations (NCBEs) are a significant set of equations in this…