# Fiend -- Finite Element Quantum Dynamics

## TL;DR

Fiend is a Python-based simulation package for solving the 3D time-dependent Schrödinger equation in cylindrically symmetric systems, enabling detailed studies of electron dynamics under complex electromagnetic fields with advanced numerical methods.

## Contribution

It introduces a finite element method-based solver with full minimal coupling for inhomogeneous vector potentials, supporting flexible and accurate quantum dynamics simulations.

## Key findings

- Supports inhomogeneous vector potentials beyond dipole approximation
- Uses FEM for spatial discretization and advanced time-stepping methods
- Provides user-friendly API with extensive documentation

## 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.