English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The evolution of Bose-Einstein condensates is amply described by thetime-dependent Gross-Pitaevskii mean-field theory which assumes all bosons toreside in a single time-dependent one-particle state throughout the propagationprocess. In this work, we go beyond mean-field and develop an essentially-exactmany-body theory for the propagation of the time-dependent Schr\"odingerequation of $N$ interacting identical bosons. In our theory, the time-dependentmany-boson wavefunction is written as a sum of permanents assembled fromorthogonal one-particle functions, or orbitals, where {\it both} the expansioncoefficients {\it and} the permanents (orbitals) themselves are {\ittime-dependent} and fully determined according to a standard time-dependentvariational principle. By employing either the usual Lagrangian formulation orthe Dirac-Frenkel variational principle we arrive at two sets of coupledequations-of-motion, one for the orbitals and one for the expansioncoefficients. The first set comprises of first-order differential equations intime and non-linear integro-differential equations in position space, whereasthe second set consists of first-order differential equations withtime-dependent coefficients. We call our theory multi-configurationaltime-dependent Hartree for bosons, or MCTDHB($M$), where $M$ specifies thenumber of time-dependent orbitals used to construct the permanents. Numericalimplementation of the theory is reported and illustrative numerical examples ofmany-body dynamics of trapped Bose-Einstein condensates are provided anddiscussed.Comment: 30 pages, 2 figure

Multiconfigurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems