Fiend -- Finite Element Quantum Dynamics

Abstract

We present Fiend - a simulation package for three-dimensional single-particle time-dependent Schr\"odinger equation for cylindrically symmetric systems. Fiend has been designed for the simulation of electron dynamics under inhomogeneus vector potentials such as in nanostructures, but it can also be used to study, e.g., nonlinear light-matter interaction in atoms and linear molecules. The light-matter interaction can be included via the minimal coupling principle in its full rigour, beyond the conventional dipole approximation. The underlying spatial discretization is based on the finite element method (FEM), and time-stepping is provided either via the generalized-{\alpha} or Crank-Nicolson methods. The software is written in Python 3.6, and it utilizes state-of-the-art linear algebra and FEM backends for performance-critical tasks. Fiend comes along with an extensive API documentation, a user guide, simulation examples, and allows for easy installation via Docker or the Python Package Index.