Self-Consistent Derivation of the Modified Gross-Pitaevskii Equation with Lee-Huang-Yang Correction

Year: 2018

Authors: Salasnich L.

Autors Affiliation: [Salasnich, Luca] Univ Padua, Dipartimento Fis & Astron Galileo Galilei, Via Marzolo 8, I-35131 Padua, Italy.
[Salasnich, Luca] Univ Padua, CNISM, Via Marzolo 8, I-35131 Padua, Italy.
[Salasnich, Luca] CNR, INO, Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy.

Abstract: We consider a dilute and ultracold bosonic gas of weakly-interacting atoms. Within the framework of quantum field theory, we derive a zero-temperature modified Gross-Pitaevskii equation with beyond-mean-field corrections due to quantum depletion and anomalous density. This result is obtained from the stationary equation of the Bose-Einstein order parameter coupled to the Bogoliubov-de Gennes equations of the out-of-condensate field operator. We show that, in the presence of a generic external trapping potential, the key steps to get the modified Gross-Pitaevskii equation are the semiclassical approximation for the Bogoliubov-de Gennes equations, a slowly-varying order parameter and a small quantum depletion. In the uniform case, from the modified Gross-Pitaevskii equation, we get the familiar equation of state with Lee-Huang-Yang correction


Volume: 8 (10)      Pages from: 1988-1  to: 1988-7

KeyWords: Bose-Einstein condensation; quantum field theory; Gross-Pitaevskii equation
DOI: 10.3390/app8101998

Citations: 5
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