On the order of BEC transition in weakly interacting gases predicted by mean-field theory

Abstract

Predictions from Hartree-Fock (HF), Popov (P), Yukalov-Yukalova (YY) and $t$-matrix approximations regarding the thermodynamics from the normal to the BEC phase in weakly interacting Bose gases are considered. By analyzing the dependence of the chemical potential $\mu$ on temperature $T$ and particle density $\rho$ we show that none of them predicts a second-order phase transition as required by symmetry-breaking general considerations. In this work we find that the isothermal compressibility ${\kappa }_T$ predicted by these theories does not diverge at criticality as expected in a true second-order phase transition. Moreover the isotherms $\mu =\mu (\rho ,T)$ typically exhibit a non-singled valued behavior in the vicinity of the BEC transition, a feature forbidden by general thermodynamic principles. This behavior can be avoided if a first order phase transition is appealed. The facts described above show that although these mean field approximations give correct results near zero temperature they are endowed with thermodynamic anomalies in the vicinity of the BEC transition. We address the implications of these results in the interpretation of current experiments with ultracold trapped alkali gases.

arXiv comment16 pages, 5 figures

References in corpus (13)

• Theory of Bose-Einstein condensation in trapped gases
• Formation and Propagation of Matter Wave Soliton Trains
• Theory of the Weakly Interacting Bose Gas
• The Excitation Spectrum of a Bose-Einstein Condensate
• Condensate fraction and critical temperature of a trapped interacting Bose gas
• Feshbach resonances in ultracold K(39)
• Justification of c-Number Substitutions in Bosonic Hamiltonians
• Bose-Einstein condensation and gauge symmetry breaking
• Bose-Einstein-condensed gases with arbitrary strong interactions
• Thermodynamics of ultracold trapped gases. Generalized mechanical variables, equation of state and heat capacity
• Condensate and superfluid fractions for varying interactions and temperature
• Linear density response in the random phase approximation for confined Bose vapours at finite temperature
• Achievement of Quantum Degeneracy in a Na-QUIC trap in Brazil: an in situ observation

Cited by in corpus (14)

• Cosmological dynamics of dark matter Bose-Einstein Condensation
• The Equation of State of Dark Matter Superfluids
• Isothermal compressibility determination across Bose-Einstein condensation
• Cosmological perturbations during the Bose-Einstein condensation of dark matter
• Cross-over to quasi-condensation: mean-field theories and beyond
• Bose-Einstein condensation in self-consistent mean-field theory
• Equation of state and phase transition in spin-orbit-coupled Bose gases at finite temperature: A perturbation approach
• Normal-Superfluid Phase Separation in Spin-Half Bosons at Finite Temperature
• Bose-Einstein Condensation and Symmetry Breaking of a Complex Charged Scalar Field
• Dark matter as the Bose-Einstein condensation in loop quantum cosmology
• Semi-classical and quantum description of an ideal Bose gas in a uniform gravitational field
• Evidence for the breakdown of momentum independent many-body t-matrix approximation in the normal phase of Bosons
• Thermodynamical properties of a trapped interacting Bose gas
• Bose-Einstein Condensation and Dissipative Dynamics in a Relativistic Pion Gas