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Colloquium: Multiconfigurational time-dependent Hartree approaches for indistinguishable particles
Reviews of Modern Physics ( IF 38.296 ) Pub Date : 
Axel U. J. Lode, Camille Lévêque, Lars Bojer Madsen, Alexej I. Streltsov, and Ofir E. Alon

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.
更新日期:2019-12-02

 

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