Robotic Assisted Laparoscopic Hysterectomy

Sakhel, Khaled

doi:10.5772/6900

Cited by 1 publication

(3 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The references [62,63] explain that, for a general potential, (29) and (30) give quasi-particle functions which are orthogonal to the condensate only in a generalized sense, [36,64]:…”

Section: E Quasi-particle Treatmentmentioning

confidence: 99%

“…Making use of the envelope functions from the previous section, the Bogoliubov-de Gennes equations, (29) and (30), take the algebraic form:…”

Section: Bogoliubov Spectrummentioning

confidence: 99%

“…One approach is to use quantum Monte Carlo calculations which, in principle, fully include thermal fluctuations and quantum correlations. Applications of this approach have mainly been to the Bose-Hubbard model [26,27,28], although recently a continuous space algorithm has also been developed for the full lattice potential [29]. Mean-field methods provide an ap-proximate treatment that is much simpler to use and are applicable in the superfluid regime where only weak correlations arise from inter-particle interactions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finite-temperature theory of superfluid bosons in optical lattices

Baillie

Blakie

2009

Phys. Rev. A

View full text Add to dashboard Cite

A practical finite temperature theory is developed for the superfluid regime of a weakly interacting Bose gas in an optical lattice with additional harmonic confinement. We derive an extended Bose-Hubbard model that is valid for shallow lattices and when excited bands are occupied. Using the Hartree-Fock-Bogoliubov-Popov mean-field approach, and applying local density and coarse-grained envelope approximations, we arrive at a theory that can be numerically implemented accurately and efficiently. We present results for a threedimensional system, characterizing the importance of the features of the extended Bose-Hubbard model and compare against other theoretical results and show an improved agreement with experimental data. PACS numbers: 67.85.Hj, 03.75.Hh, 05.30.Jp III. MEAN-FIELD APPROXIMATION A. Mean-field approach: condensate and non-condensateWe assume that the local number of condensate atoms is either macroscopic or zero [57,58], so that the field operator,Ψ(r), can be separated into a c-number condensate component (the order parameter), Φ(r), and a non-condensate field operator,ψ(r), defined by the usual broken symmetry approach, Φ(r) ≡ Ψ (r) ,ψ(r) ≡Ψ(r) − Φ(r) so that ψ (r) = 0.The assumption that Φ(r) is a c-number is inaccurate near the edges of the condensate, where the local condensate density, |Φ(r)| 2 , is small and just below the critical temperature, since fluctuations are important in such regions.

show abstract

“…The references [62,63] explain that, for a general potential, (29) and (30) give quasi-particle functions which are orthogonal to the condensate only in a generalized sense, [36,64]:…”

Section: E Quasi-particle Treatmentmentioning

confidence: 99%

“…Making use of the envelope functions from the previous section, the Bogoliubov-de Gennes equations, (29) and (30), take the algebraic form:…”

Section: Bogoliubov Spectrummentioning

confidence: 99%