Self-consistent derivation of the modified Gross-Pitaevskii equation with Lee-Huang-Yang correction
arXiv:1810.02636 · doi:10.3390/app8101998
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.
7 pages, invited contribution for the special issue "Optical Properties of Confined Quantum Systems" of the journal Applied Sciences, included the effect of anomalous density
References in corpus (6)
- Quantum liquid droplets in a mixture of Bose-Einstein condensates
- Bragg spectroscopy of a strongly interacting 85Rb Bose-Einstein condensate
- Localized modes in quasi-2D Bose-Einstein condensates with spin-orbit and Rabi couplings
- Effective Nonlinear Schrödinger Equations for Cigar-Shaped and Disk-Shaped Fermi Superfluids at Unitarity
- Vortex lattice in the crossover of a Bose gas from weak coupling to unitarity
- Quantum fluctuations and Gross-Pitaevskii theory
Cited by in corpus (10)
- Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
- Massive phonons and gravitational dynamics in a photon-fluid model
- Shell-shaped atomic gases
- Investigation of Quantum Droplet: An Analytical Approach
- Dropleton-Soliton Crossover mediated via Trap Modulation
- Cloud shape of a molecular Bose-Einstein condensate in a disordered trap: a case study of the dirty boson problem
- Quantum field theory for multipolar composite bosons with mass defect and relativistic corrections
- Beyond-mean-field corrections to the blueshift of a driven-dissipative exciton-polariton condensate
- Localization landscape for interacting Bose gases in one-dimensional speckle potentials
- Effective action approach to quantum and thermal effects: from one particle to Bose-Einstein condensates