The multi-configurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems
| dc.creator | Alon, Ofir E. | |
| dc.creator | Streltsov, Alexej I. | |
| dc.creator | Cederbaum, Lorenz S. | |
| dc.date | 2007-03-09 | |
| dc.date.accessioned | 2026-07-07T09:27:12Z | |
| dc.date.available | 2026-07-07T09:27:12Z | |
| dc.description | 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 Schrödinger 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. | |
| dc.description | 30 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0703237 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0703237 | |
| dc.identifier | Phys. Rev. A 77, 033613 (2008) | |
| dc.identifier | doi:10.1103/PhysRevA.77.033613 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157013 | |
| dc.subject | Other Condensed Matter | |
| dc.title | The multi-configurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems | |
| dc.type | text |