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Multiconfigurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems
| Content Provider | Semantic Scholar |
|---|---|
| Author | Alon, Ofir E. Streltsov, Alexej I. Cederbaum, Lorenz S. |
| Copyright Year | 2008 |
| Abstract | 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. |
| Starting Page | 033613 |
| Ending Page | 033613 |
| Page Count | 1 |
| File Format | PDF HTM / HTML |
| DOI | 10.1103/PhysRevA.77.033613 |
| Alternate Webpage(s) | https://arxiv.org/pdf/cond-mat/0703237v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1103/PhysRevA.77.033613 |
| Volume Number | 77 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
