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MCTDH-X: The Multiconfigurational Time-Dependent Hartree Method for Indistinguishable Particles High-Performance Computation Project

Axel U. J. Lode, Ofir E. Alon, M. A. Bastarrachea-Magnani, Anal Bhowmik, Andreas Buchleitner, Lorenz S. Cederbaum, R. Chitra, Elke Faßhauer, Laurent de Forges de Parny, Sudip Kumar Haldar, Camille Lévêque, Rui Lin, Lars Bojer Madsen, Paolo Molignini, Luca Papariello, Frank Schäfer, Alexej I. Streltsov, Marios C. Tsatsos, Storm Weiner

Published Jan 1, 2021• 3 citations
Publisher
DOI
10.1007/978-3-030-80602-6_2

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Colloquium: Multiconfigurational time-dependent Hartree approaches for indistinguishable particles

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In this Colloquium, the wavefunction-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. 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 nonadia-batic dynamics of atomic and molecular systems, the so-called multilayer generalizations to the MCTDH-F and MCTDH-B methods, and the time-dependent orbital-adaptive coupled cluster theory are discussed.

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Multiconfigurational time-dependent Hartree method to describe particle loss due to absorbing boundary conditions

Simen Kvaal

Absorbing boundary conditions in the form of a complex absorbing potential are routinely introduced in the Schr\"odinger equation to limit the computational domain or to study reactive scattering events using the multiconfigurational time-dependent Hartree (MCTDH) method. However, it is known that a pure wave-function description does not allow the modeling and propagation of the remnants of a system of which some parts are removed by the absorbing boundary. It was recently shown [S. Selst\o{} and S. Kvaal, J. Phys. B: At. Mol. Opt. Phys. 43, 065004 (2010)] that a master equation of Lindblad form was necessary for such a description. We formulate a MCTDH method for this master equation, usable for any quantum system composed of any mixture of species. The formulation is a strict generalization of pure-state propagation using standard MCTDH for identical particles and mixtures. We demonstrate the formulation with a numerical experiment.

arXiv:1102.3899•Physical Review A•Aug 29, 2011•30 citations
In this Colloquium, the wavefunction-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. 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 nonadia-batic dynamics of atomic and molecular systems, the so-called multilayer generalizations to the MCTDH-F and MCTDH-B methods, and the time-dependent orbital-adaptive coupled cluster theory are discussed.
Absorbing boundary conditions in the form of a complex absorbing potential are routinely introduced in the Schr\"odinger equation to limit the computational domain or to study reactive scattering events using the multiconfigurational time-dependent Hartree (MCTDH) method. However, it is known that a pure wave-function description does not allow the modeling and propagation of the remnants of a system of which some parts are removed by the absorbing boundary. It was recently shown [S. Selst\o{} and S. Kvaal, J. Phys. B: At. Mol. Opt. Phys. 43, 065004 (2010)] that a master equation of Lindblad form was necessary for such a description. We formulate a MCTDH method for this master equation, usable for any quantum system composed of any mixture of species. The formulation is a strict generalization of pure-state propagation using standard MCTDH for identical particles and mixtures. We demonstrate the formulation with a numerical experiment.