In this Colloquium, the wavefunction-based {M}ulticonfigurational {T}ime-{D}ependent {H}artree approaches to the dynamics of indistinguishable particles (MCTDH-F for {F}ermions and MCTDH-B for {B}osons) 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 Schrdinger 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. We briefly describe the historical developments that have lead to the formulation of the MCTDH-X methods and motivate the necessity for wavefunction-based approaches. We sketch the derivation of the unified MCTDH-F and MCTDH-B equations of motion for complete and also specific restricted configuration spaces. The strengths and limitations of the MCTDH-X approach are assessed via benchmarks against an exactly solvable model and via convergence checks. We highlight some applications to instructive and experimentally-realized quantum many-body systems: the dynamics of atoms in Bose-Einstein condensates in magneto-optical and optical traps and of electrons in atoms and molecules. We discuss the current development and frontiers in the field of MCTDH-X: 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 are discussed.

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，基于波函数的{M}多构型{T} ime- {D}偶极{H} artree逼近了不可分辨粒子的动力学（{F} ermions为MCTDH-F，{B} osons为MCTDH-B ）进行审核。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inger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用于构建多体基集的单粒子状态的时间依赖性和最优化，这产生了非线性工作方程。我们简要描述了导致MCTDH-X方法形成的历史发展，并激发了基于波函数的方法的必要性。我们绘制了完整的MCTDH-F和MCTDH-B统一的运动方程的推导，也给出了特定的受限配置空间。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。我们重点介绍了在教学和实验实现的量子多体系统中的一些应用：玻色-爱因斯坦磁光阱和光阱中的冷凝物以及原子和分子中的电子的动力学。我们讨论了MCTDH-X领域的最新发展和前沿：难以区分的粒子的理论和数值方法，