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

Year: 2018

Authors: Salasnich L.

Autors Affiliation: Univ Padua, Dipartimento Fis & Astron Galileo Galilei, Via Marzolo 8, I-35131 Padua, Italy; Univ Padua, CNISM, Via Marzolo 8, I-35131 Padua, Italy; 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

Journal/Review: APPLIED SCIENCES-BASEL

Volume: 8 (10)      Pages from: 1998-1  to: 1998-7

More Information: This research was funded by Italian Ministry of Education, University and Research, grant Fondo per il finanziamento delle attivita base di ricerca (FFABR, 2017).
KeyWords: Bose-Einstein condensation; quantum field theory; Gross-Pitaevskii equation
DOI: 10.3390/app8101998

Citations: 11
data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-10-27
References taken from IsiWeb of Knowledge: (subscribers only)
Connecting to view paper tab on IsiWeb: Click here
Connecting to view citations from IsiWeb: Click here