Data di Pubblicazione:
2014
Citazione:
Deriving the Gross-Pitaevskii Equation / N. Benedikter - In: Mathematical Results in Quantum Mechanics / [a cura di] P. Exner, W. König, H. Neidhardt. - [s.l] : World Scientific, 2014 Dec. - ISBN 9789874618137. - pp. 207-212 (( Intervento presentato al 12. convegno QMath tenutosi a Berlin nel 2013 [10.1142/9789814618144_0014].
Abstract:
In experiments, Bose-Einstein condensates are prepared by cooling a dilute Bose gas in a trap. After the phase transition has been reached, the trap is switched off and the evolution of the condensate observed. The evolution is macroscopically described by the Gross-Pitaevskii equation. On the microscopic level, the dynamics of Bose gases are described by the N-body Schrödinger equation. We review our article [BdS12] in which we construct a class of initial data in Fock space which are energetically close to the ground state and prove that their evolution approximately follows the Gross-Pitaevskii equation. The key idea is to model two-particle correlations with a Bogoliubov transformation.
Tipologia IRIS:
03 - Contributo in volume
Keywords:
Bose-Einstein condensate; dilute Bose gas; Gross-Pitaevskii equation; correlations; many-body systems; Bogoliubov transformations; queezed coherent states
Elenco autori:
N. Benedikter
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Titolo del libro:
Mathematical Results in Quantum Mechanics