In this Colloquium, the wave-function-based multiconfigurational time-dependent Hartree approaches to the dynamics of indistinguishable particles (MCTDH-F for fermions and MCTDH-B for bosons) are reviewed. MCTDH-B and MCTDH-F or, together, MCTDH-X are methods for describing correlated quantum systems of identical particles by solving the time-dependent Schrödinger equation from first principles. MCTDH-X is used to accurately model the dynamics of real-world quantum many-body systems in atomic, molecular, and optical physics. The key feature of these approaches is the time dependence and optimization of the single-particle states employed for the construction of a many-body basis set, which yields nonlinear working equations. The historical developments that have led to the formulation of the MCTDH-X method and motivate the necessity for wave-function-based approaches are briefly described. The derivation of the unified MCTDH-F and MCTDH-B equations of motion for complete and also specific restricted configuration spaces are sketched. The strengths and limitations of the MCTDH-X approach are assessed via benchmarks against an exactly solvable model and via convergence checks. Applications to some instructive and experimentally realized quantum many-body systems are highlighted: the dynamics of atoms in Bose-Einstein condensates in magneto-optical and optical traps and of electrons in atoms and molecules. The current development and frontiers in the field of MCTDH-X are discussed: theories and numerical methods for indistinguishable particles, for mixtures of multiple species of indistinguishable particles, the inclusion of nuclear motion for the nonadiabatic dynamics of atomic and molecular systems, as well as the multilayer and second-quantized-representation approaches, and the orbital-adaptive time-dependent coupled-cluster theory.

中文翻译：

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座谈会：难以区分粒子的多配置时间相关Hartree方法

在本次座谈会上，回顾了基于波函数的基于时间的多构型Hartree方法，对不可区分的粒子（费米子为MCTDH-F，玻色子为MCTDH-B）进行了动力学研究。MCTDH-B和MCTDH-F或MCTDH-X一起是通过从第一原理求解时间相关的薛定er方程来描述相同粒子的相关量子系统的方法。MCTDH-X用于在原子，分子和光学物理学中准确地模拟现实世界中的量子多体系统的动力学。这些方法的关键特征是时间依赖性和对用于构建多体基集的单粒子状态的优化，这产生了非线性工作方程。简要介绍了导致制定MCTDH-X方法并激发基于波函数的方法的必要性的历史发展。概述了完整的MCTDH-F和MCTDH-B完整的运动方程以及特定的受限配置空间的运动方程。MCTDH-X方法的优势和局限性是通过针对可完全解决的模型的基准测试以及通过收敛性检查来评估的。着重介绍了在一些具有指导意义和实验意义上实现的量子多体系统的应用：磁光阱和光阱中玻色-爱因斯坦凝聚物中原子的动力学以及原子和分子中电子的动力学。讨论了MCTDH-X领域的最新发展和前沿：不可区分粒子的理论和数值方法，