Multiconfigurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems
By Ofir E. Alon, Alexej I. Streltsov, Lorenz S. Cederbaum. 2007
279 citations recorded by the source corpus.
The evolution of Bose-Einstein condensates is amply described by the time-dependent Gross-Pitaevskii mean-field theory which assumes all bosons to reside in a single time-dependent one-particle state throughout the propagation process. In this work, we go beyond mean-field and develop an essentially-exact many-body theory for the propagation of the time-dependent Schr\"odinger equation of $N$ interacting identical bosons. In our theory, the time-dependent many-boson wavefunction is written as a sum of permanents assembled from orthogonal one-particle functions, or orbitals, where {\it both} the expansion coefficients {\it and} the permanents (orbitals) themselves are {\it time-dependent} and fully determined according to a standard time-dependent variational principle. By employing either the usual Lagrangian formulation or the Dirac-Frenkel variational principle we arrive at two sets of coupled equations-of-motion, one for the orbitals and one for the expansion coefficients. The first set comprises of first-order differential equations in time and non-linear integro-differential equations in position space, whereas the second set consists of first-order differential equations with time-dependent coefficients. We call our theory multi-configurational time-dependent Hartree for bosons, or MCTDHB($M$), where $M$ specifies the number of time-dependent orbitals used to construct the permanents. Numerical implementation of the theory is reported and illustrative numerical examples of many-body dynamics of trapped Bose-Einstein condensates are provided and discussed.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/fa4ecc83d48b9e0ce27ace6d1587dbe5f0aaac80
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In Atomic and Molecular Physics, and Optics
- Z. Idziaszek
- Michal Tomza
- A. Cidrim
- P. Tavares
- M. Caracanhas
- V. Bagnato
- Francisco Ednilson Alves dos Santos
- Hans-Dieter Meyer
Citations in the corpus
- Cold hybrid ion-atom systems (2017, methodology): “…the ground-state properties of ultracold bosons in interaction with a static (i.e., tightly trapped) ion impurity have been investigated by (Schurer et al., 2014) by means of the multiconfiguration timedependent Hartree method for bosons (Alon et al., 2008; Cao et al., 2013; Krönke et al., 2013).”
- Studying molecular quantum dynamics with the multiconfiguration time‐dependent Hartree method (2012, background): “(29) is satisfied for sufficiently long relaxation times.”
- Quantum turbulence in trapped atomic Bose-Einstein condensates (2015, methodology): “A consistent way to go beyond the GP picture is the multi-configurational time-dependent Hartree for bosons (MCTDHB) and the equations bearing the same name [116, 117, 118].”
- Efficient time-stepping scheme for dynamics on TT-manifolds (2012, unknown): “Equations of the form (1) appear in the computation of the molecular spectra [24] [1].”