Institut für Chemie, Freie Universität Berlin, Altensteinstraße 23A, D-14195 Berlin, Germany.
Institut für Mathematik, Freie Universität Berlin, Arnimallee 3-9, D-14195 Berlin, Germany.
J Chem Phys. 2023 Apr 28;158(16). doi: 10.1063/5.0147314.
WaveTrain is an open-source software for numerical simulations of chain-like quantum systems with nearest-neighbor (NN) interactions only. The Python package is centered around tensor train (TT, or matrix product) format representations of Hamiltonian operators and (stationary or time-evolving) state vectors. It builds on the Python tensor train toolbox Scikit_tt, which provides efficient construction methods and storage schemes for the TT format. Its solvers for eigenvalue problems and linear differential equations are used in WaveTrain for the time-independent and time-dependent Schrödinger equations, respectively. Employing efficient decompositions to construct low-rank representations, the tensor-train ranks of state vectors are often found to depend only marginally on the chain length N. This results in the computational effort growing only slightly more than linearly with N, thus mitigating the curse of dimensionality. As a complement to the classes for full quantum mechanics, WaveTrain also contains classes for fully classical and mixed quantum-classical (Ehrenfest or mean field) dynamics of bipartite systems. The graphical capabilities allow visualization of quantum dynamics "on the fly," with a choice of several different representations based on reduced density matrices. Even though developed for treating quasi-one-dimensional excitonic energy transport in molecular solids or conjugated organic polymers, including coupling to phonons, WaveTrain can be used for any kind of chain-like quantum systems, with or without periodic boundary conditions and with NN interactions only. The present work describes version 1.0 of our WaveTrain software, based on version 1.2 of scikit_tt, both of which are freely available from the GitHub platform where they will also be further developed. Moreover, WaveTrain is mirrored at SourceForge, within the framework of the WavePacket project for numerical quantum dynamics. Worked-out demonstration examples with complete input and output, including animated graphics, are available.
WaveTrain 是一个用于数值模拟仅具有最近邻（NN）相互作用的链式量子系统的开源软件。这个 Python 包的核心是哈密顿算符和（静态或时变）态矢量的张量火车（TT 或矩阵乘积）格式表示。它建立在 Python 张量火车工具包 Scikit_tt 之上，该工具包为 TT 格式提供了高效的构造方法和存储方案。它的特征值问题和线性微分方程的求解器分别用于 WaveTrain 中的非时变和时变薛定谔方程。通过采用高效的分解来构建低秩表示，态矢量的张量火车阶数通常仅略微依赖于链长 N。这导致计算复杂度仅随 N 呈线性增长，从而减轻了维度诅咒。作为对全量子力学类的补充，WaveTrain 还包含用于二分量系统的完全经典和混合量子经典（Ehrenfest 或平均场）动力学的类。图形功能允许对量子动力学进行“实时”可视化，可根据约化密度矩阵选择几种不同的表示形式。尽管它是为处理分子固体或共轭有机聚合物中的准一维激子能量输运而开发的，包括与声子的耦合，但 WaveTrain 可以用于任何类型的链式量子系统，无论是否具有周期性边界条件，并且仅具有 NN 相互作用。本工作描述了我们的 WaveTrain 软件的 1.0 版本，该版本基于 scikit_tt 的 1.2 版本，这两个版本都可以从 GitHub 平台上免费获得，并且将在该平台上进一步开发。此外，WaveTrain 在 SourceForge 上进行了镜像，作为数值量子动力学的 WavePacket 项目的一部分。提供了带有完整输入和输出的工作示例，包括动画图形。
