The multi-configurational time-dependent Hartree approach revisited

Manthe U (2015)
The Journal of Chemical Physics 142(24): 244109.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
Abstract / Bemerkung
The multi-configurational time-dependent Hartree (MCTDH) approach facilitates accurate high-dimensional quantum dynamics simulations. In the approach, the wavefunction is expanded in a direct product of self-adapting time-dependent single-particle functions (SPFs). The equations of motion for the expansion coefficients and the SPFs are obtained via the Dirac-Frenkel variational principle. While this derivation yields well-defined differential equations for the motion of occupied SPFs, singularities in the working equations resulting from unoccupied SPFs have to be removed by a regularization procedure. Here, an alternative derivation of the MCTDH equations of motion is presented. It employs an analysis of the time-dependence of the single-particle density matrices up to second order. While the analysis of the first order terms yields the known equations of motion for the occupied SPFs, the analysis of the second order terms provides new equations which allow one to identify optimal choices for the unoccupied SPFs. The effect of the optimal choice of the unoccupied SPFs on the structure of the MCTDH equations of motion and their regularization is discussed. Generalized equations applicable in the multi-layer MCTDH framework are presented. Finally, the effects resulting from the initial choice of the unoccupied SPFs are illustrated by a simple numerical example. (C) 2015 AIP Publishing LLC.
Erscheinungsjahr
Zeitschriftentitel
The Journal of Chemical Physics
Band
142
Ausgabe
24
Seite(n)
244109
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Manthe U. The multi-configurational time-dependent Hartree approach revisited. The Journal of Chemical Physics. 2015;142(24):244109.
Manthe, U. (2015). The multi-configurational time-dependent Hartree approach revisited. The Journal of Chemical Physics, 142(24), 244109. doi:10.1063/1.4922889
Manthe, U. (2015). The multi-configurational time-dependent Hartree approach revisited. The Journal of Chemical Physics 142, 244109.
Manthe, U., 2015. The multi-configurational time-dependent Hartree approach revisited. The Journal of Chemical Physics, 142(24), p 244109.
U. Manthe, “The multi-configurational time-dependent Hartree approach revisited”, The Journal of Chemical Physics, vol. 142, 2015, pp. 244109.
Manthe, U.: The multi-configurational time-dependent Hartree approach revisited. The Journal of Chemical Physics. 142, 244109 (2015).
Manthe, Uwe. “The multi-configurational time-dependent Hartree approach revisited”. The Journal of Chemical Physics 142.24 (2015): 244109.

9 Zitationen in Europe PMC

Daten bereitgestellt von Europe PubMed Central.

On regularizing the MCTDH equations of motion.
Meyer HD, Wang H., J Chem Phys 148(12), 2018
PMID: 29604814
On regularizing the ML-MCTDH equations of motion.
Wang H, Meyer HD., J Chem Phys 149(4), 2018
PMID: 30068178
A unified ab initio approach to the correlated quantum dynamics of ultracold fermionic and bosonic mixtures.
Cao L, Bolsinger V, Mistakidis SI, Koutentakis GM, Krönke S, Schurer JM, Schmelcher P., J Chem Phys 147(4), 2017
PMID: 28764383

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