caa a22 4500 44536534X CHVBK 20180317142928.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s10909-011-0366-9 doi (NATIONALLICENCE)springer-10.1007/s10909-011-0366-9 Isotherms, Order Parameter and Density Profiles for Weakly Interacting Bose Gases within Three Mean-Field Theories [Elektronische Daten] [L. Olivares-Quiroz, V. Romero-Rochin] In this work we consider three mean field approximations of standard use in the literature to describe the weakly interacting Bose gas confined in a box of volume V. For these approximations we calculate the corresponding isotherms μ=μ(ρ,T), where μ is the chemical potential, ρ the particle density and T the absolute temperature. In particular we address this calculation at the nanokelvin regime for a gas parameter $\gamma= \rho a_{s}^{3}\leq 1$ where the Bose-Einstein Condensation in alkali atoms is observed. The non singled value observed for the equation of state μ=μ(ρ,T) suggests strongly that the approximations considered here do not capture properly the thermodynamic behavior in the vicinity of the BEC transition. In order to support this statement we calculate the so-called order parameter Φ(T)=N 0(T)/N from 0≤T≤T c where N 0 represents the number of particles within the condensate, N the total number of particles and T c the critical temperature. Both results suggest that the three mean-field theories considered here, Hartree-Fock (HF), Popov (P) and Yukalov-Yukalova (Ykv) do not predict a second order phase transition as the BEC transition in weakly interacting gases is expected to show. Using the Local Density Approximation (LDA) we extend these calculation to obtain the density profiles $\rho(\vec{r})$ for an inhomogeneous Bose gas trapped in a harmonic external potential $V_{ext}(\vec{r})$. As expected the density profiles show that the confinement is not enough to override the anomalies observed in the thermodynamic quantities for the gas confined in a box of volume V. Springer Science+Business Media, LLC, 2011 Bose-Einstein condensation nationallicence Hartree-Fock theory nationallicence Popov approximation nationallicence Yukalov-Yukalova approximation nationallicence Local density approximation nationallicence Olivares-Quiroz L. Universidad Autónoma de la Ciudad de México, Av La Corona 320, Col Loma La Palma, C.P. 07160, Mexico, D.F., Mexico aut Romero-Rochin V. Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000, México, D.F., Mexico aut Journal of Low Temperature Physics Springer US; http://www.springer-ny.com 164/1-2(2011-07-01), 23-40 0022-2291 164:1-2<23 2011 164 10909 https://doi.org/10.1007/s10909-011-0366-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10909-011-0366-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Olivares-Quiroz L. Universidad Autónoma de la Ciudad de México, Av La Corona 320, Col Loma La Palma, C.P. 07160, Mexico, D.F., Mexico aut NATIONALLICENCE 700 1- Romero-Rochin V. Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000, México, D.F., Mexico aut NATIONALLICENCE 773 0- Journal of Low Temperature Physics Springer US; http://www.springer-ny.com 164/1-2(2011-07-01), 23-40 0022-2291 164:1-2<23 2011 164 10909 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer