Sebastian Merk | Searcharxiv

arXiv2026

Meshfree versus grid-based Schr\"odinger solvers for modeling the interactions between free-electron wave packets and light

The interaction of free-electron wave packets with electromagnetic fields provides a powerful route toward coherent electron control, enabling the generation of energy combs, momentum-state superpositions, and aberration-engineered electron beams. Existing theoretical descriptions, however, often rely on eikonal or no-recoil approximations. Here, we present a mesh-free numerical framework that directly solves the time-dependent single-particle Schr\"odinger equation for arbitrary electromagnetic potentials. Comparison with a benchmark mesh-based Schr\"odinger solver reveals excellent quantitative agreement. By eliminating the need for spatial meshing, our method offers an efficient and scalable route for simulating electron wave packet dynamics in complex time-dependent and static electromagnetic environments, while the simulation time is significantly improved by up to 800 times faster. These capabilities establish a versatile computational tool for quantum electron optics and free-electron-light interactions beyond eikonal approximations.

physics.optics↗

arXiv2026

Structure-Preserving Integration for Magnetic Gaussian Wave Packet Dynamics

We develop structure-preserving time integration schemes for Gaussian wave packet dynamics associated with the magnetic Schr\"odinger equation. The variational Dirac--Frenkel formulation yields a finite-dimensional Hamiltonian system for the wave packet parameters, where the presence of a magnetic vector potential leads to a non-separable structure and a modified symplectic geometry. By introducing kinetic momenta through a minimal substitution, we reformulate the averaged dynamics as a Poisson system that closely parallels the classical equations of charged particle motion. This representation enables the construction of Boris-type integrators adapted to the variational setting. In addition, we propose explicit high-order symplectic schemes based on splitting methods and partitioned Runge--Kutta integrators. The proposed methods conserve the quadratic invariants characterizing the Hagedorn parametrization, preserve linear and angular momentum under symmetry assumptions, and exhibit near-conservation of the averaged Hamiltonian over long time intervals. Rigorous error estimates are derived for both the wave packet parameters and observable quantities, with bounds uniform in the semiclassical parameter. Numerical experiments demonstrate the favorable long-time behavior and structure preservation of the integrators.

math.NA↗