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Images of Wave Function Solutions for the Electron and Positron Generated by Vectpotential 3D Finite Element Modeling Software

Declan Traill

Published Jun 1, 2013• 0 citations
OpenAlex

Abstract

The images [fig 1-9] in this paper are graphical representations of the fields generated by these wave functions using a 3D finite element vector modeling program [ref 1] I wrote to aid in the visualization and testing of proposed wave function solutions.

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Advancement in the field of superconductor circuits requires better designing tools and computer-aided programs. The JOINUS program is developed as part of the ColdFlux/SuperTools project. It features a user-friendly environment with several useful tools to design superconductor circuits based on Josephson junctions. The program can work with different Josephson simulator engines and embeds several new functionalities.We pursue two main goals to develop the software with a multi-platform capability. The first goal is to provide a graphical user interface environment that is easy to use and can be handled quickly with a simple user guide and some helpful examples. That also includes the automation of some tasks to perform in the course of a design sequence. The objective is to make newcomers to the field of superconducting electronics more interested and inclined to start using and designing simple digital circuits in a short time and a simple way. The second goal is to improve already established models that are sometimes inaccurate or even inappropriate. The software is not just a user-friendly interface, it also provides improved models and many new functionalities.
We present a general-purpose, open-source software suite, SQUIRREL (Streamlined Quantum Unified Interface for Researching Real-time Excitations with Light), for propagating the time-dependent Schrödinger equation on complex geometries in the presence of time-dependent electric and/or magnetic fields. To handle large systems that can be executed on a conventional desktop computer, the SQUIRREL software suite uses a suite of efficient propagation methods for various quantum dynamics applications, including a new perturbation-based element-dropping algorithm that improves computational performance with minimal loss of accuracy. We analyze the efficacy of these optimizations for Crank-Nicolson, scaled Taylor series approximation, and split-operator propagation methods and discuss the range of their applicability to a variety of quantum dynamics problems. In addition, we provide several examples of time-dependent dynamics calculations and extensive documentation for generating custom geometries, potentials, and time-propagation approaches. Our numerical benchmarks and results demonstrate the versatility of the SQUIRREL software suite for efficiently calculating quantum dynamics in complex nanoscale geometries, particularly in the presence of time-dependent magnetic fields, which have received less attention in previous quantum dynamics studies. Program summary Program Title: SQUIRREL CPC Library link to program files: https://doi.org/10.17632/kfvs5s88sj.1 Licensing provisions: GNU General Public License 3 Programming language: MATLAB Supplementary material: Additional details on calculations with an anisotropic effective mass, determination of timesteps, propagation timings, and element-dropping timings. Nature of problem: The SQUIRREL software suite solves the time-dependent Schrödinger equation for electronic states in the presence of time-dependent electric and/or magnetic fields. The code is well-suited for calculating electron dynamics of complex nanostructures in the effective mass approximation, using various propagation and sparse-matrix techniques to reduce the computational complexity of these problems. The program provides a user-friendly interface for testing these optimizations and generating custom geometries and potentials for systems of interest. Solution method: The SQUIRREL software suite uses Crank-Nicolson, split-operator, Padé approximant, and scaled-Taylor-series-based propagation methods to calculate electron dynamics on a finite-element basis. The code includes a novel perturbation-based element-dropping method, which enables sparse representations of the typically dense finite element Hamiltonian matrix. This capability enables a highly efficient and flexible approach for calculating driven dynamics in quantum systems with complex geometries and time-dependent electric/magnetic fields.