An user-friendly software tool for the solution of the time-dependent Schrödinger and Gross-Pitaevskii equations

Abstract

Abstract. In this work we present TDStool, a general-purpose easy-to-use software tool for the solution of the time-dependent Schrödinger equation in 2D and 3D domains with arbitrary time-dependent potentials. The numerical algorithms adopted in the code, namely Fourier split-step and box-integration methods, are sketched and the main characteristics of the tool are illustrated. As an example, the dynamics of a single electron in systems of two and three coupled quantum dots is obtained. The code is released as an open-source project and has a build-in graphical interface for the visualization of the results. IntroductionThe astonishing development in semiconductor growth, characterization and processing technologies opened new horizons in the field of carriers control, up to the single electron level [1]. In fact, single-particle quantum interference is routinely achieved in advanced research laboratories and single electrons are not only confined, but also moved by varying electromagnetic fields [2]. The theoretical modeling of such systems is usually tackled with numerical instruments developed on a case-by-case basis. Although this allows for a great specificity, the development work is very expensive.Here we present a novel software tool for the numerical solution of the time-dependent (TD) Schrödinger equation. We named it TDStool and released it as an open-source project (binaries are available for Windows and Linux systems), free for non-commercial use [3]. The main characteristics of TDStool are: 2D and 3D solution domain; arbitrary TD electric potential landscape; uniform magnetic field; nonuniform (x-y-z separable) discretization grid; clean graphical user interface for input setup and results visualization; comprehensive documentation. Two different numerical algorithms are available, namely Fourier split-step and box-integration method.In addition to the linear Schrödinger case, the nonlinear system dynamics determined by TD Gross-Pitaevskii equation [4] can be simulated. In fact, many recent experimental results on the manipulation of quantum ultracold condensates exposed the quantum coherence of their dynamics [5] and confirmed the extra potential-like term g|ψ(r)| 2 in their equation of motion, proportional to the local particle density.In the next section we sketch the numerical algorithms adopted in the code. Then, in the remaining two sections, we present two examples of applications, namely the single-particle

Time-dependent simulation and analytical modelling of electronic Mach–Zehnder interferometry with edge-states wave packets

“…The time evolution of the WP is realized with the split-step Fourier method [39,42,44]. In summary, the evolution operator ˆ( )…”