We formulate a conserving gapless mean-field theory for Bose-Einstein condensates on the basis of a Luttinger-Ward thermodynamic functional. It is applied to a weakly interacting uniform gas with density $n$ and s-wave scattering length $a$ to clarify its fundamental thermodynamic properties. It is found that the condensation here occurs as a first-order transition. The shift of the transition temperature $ΔT_c$ from the ideal-gas result $T_{0}$ is positive and given to the leading order by $ΔT_c = 2.33a n^{1/3}T_0$ , in agreement with a couple of previous estimates. The theory is expected to form a new theoretical basis for trapped Bose-Einstein condensates at finite temperatures.We formulate a conserving gapless mean-field theory for Bose-Einstein condensates on the basis of a Luttinger-Ward thermodynamic functional. It is applied to a weakly interacting uniform gas with density $n$ and s-wave scattering length $a$ to clarify its fundamental thermodynamic properties. It is found that the condensation here occurs as a first-order transition. The shift of the transition temperature $ΔT_c$ from the ideal-gas result $T_{0}$ is positive and given to the leading order by $ΔT_c = 2.33a n^{1/3}T_0$, in agreement with a couple of previous estimates. The theory is expected to form a new theoretical basis for trapped Bose-Einstein condensates at finite temperatures.

arXiv:cond-mat/0411296Journal of the Physical Society of JapanJul 1, 200520 citations

Basic Mean-Field Theory for Bose-Einstein Condensates

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González

Springer eBooksDec 29, 20078 citations

Particle creation in Bose-Einstein condensates: Theoretical formulation based on conserving gapless mean-field theory

Yasunari Kurita, Michikazu Kobayashi, Hideki Ishihara +1 more

We formulate particle-creation phenomena in Bose-Einstein condensates in terms of conserving gapless mean-field theory for weakly interacting Bose gases. The particle-creation spectrum is calculated by rediagonalizing the Bogoliubov--de Gennes (BdG) Hamiltonian in mean-field theory. The conservation implies that quasiparticle creation is accompanied by quantum back reaction to the condensates. Particle creation in this mean-field theory is found to be equivalent to that in quantum field theory (QFT) in curved space-time. An expression is obtained for an effective metric affected by quantum back reaction. The formula for the particle-creation spectrum obtained in terms of QFT in curved space-time is shown to be the same as that given by rediagonalizing the BdG Hamiltonian.We formulate particle-creation phenomena in Bose-Einstein condensates in terms of conserving gapless mean-field theory for weakly interacting Bose gases. The particle-creation spectrum is calculated by rediagonalizing the Bogoliubov--de Gennes (BdG) Hamiltonian in mean-field theory. The conservation implies that quasiparticle creation is accompanied by quantum back reaction to the condensates. Particle creation in this mean-field theory is found to be equivalent to that in quantum field theory (QFT) in curved space-time. An expression is obtained for an effective metric affected by quantum back reaction. The formula for the particle-creation spectrum obtained in terms of QFT in curved space-time is shown to be the same as that given by rediagonalizing the BdG Hamiltonian.

arXiv:1007.0073Physical Review ANov 2, 20109 citations

Mean-field studies of Bose-Einstein condensates

William Hoston

Dec 1, 20000 citations

Conserving Gapless Mean-Field Theory of a Multi-Component Bose–Einstein Condensate

Yoshiyuki Kondo, Takafumi Kita

We develop a mean-field theory for Bose-Einstein condensation of spin-1 atoms with internal degrees of freedom. It is applicable to nonuniform systems at finite temperatures with a plausible feature of satisfying the Hugenholtz-Pines theorem and various conservation laws simultaneously. Using it, we clarify thermodynamic properties and the excitation spectra of a uniform gas. The condensate is confirmed to remain in the same internal state from T=0 up to $T_{c}$ for both antiferromagnetic and ferromagnetic interactions. The excitation spectra of the antiferromagnetic (ferromagnetic) interaction are found to have only a single gapless mode, contrary to the prediction of the Bogoliubov theory where three (two) of them are gapless. We present a detailed discussion on those single-particle excitations in connection with the collective excitations.We develop a mean-field theory for Bose-Einstein condensation of spin-1 atoms with internal degrees of freedom. It is applicable to nonuniform systems at finite temperatures with a plausible feature of satisfying the Hugenholtz-Pines theorem and various conservation laws simultaneously. Using it, we clarify thermodynamic properties and the excitation spectra of a uniform gas. The condensate is confirmed to remain in the same internal state from T=0 up to $T_{c}$ for both antiferromagnetic and ferromagnetic interactions. The excitation spectra of the antiferromagnetic (ferromagnetic) interaction are found to have only a single gapless mode, contrary to the prediction of the Bogoliubov theory where three (two) of them are gapless. We present a detailed discussion on those single-particle excitations in connection with the collective excitations.

arXiv:cond-mat/0608472Journal of the Physical Society of JapanFeb 13, 20071 citation

n

and s-wave scattering length

a

to clarify its fundamental thermodynamic properties. It is found that the condensation here occurs as a first-order transition. The shift of the transition temperature

ΔT_c

from the ideal-gas result

T_{0}

is positive and given to the leading order by

ΔT_c = 2.33a n^{1/3}T_0

, in agreement with a couple of previous estimates. The theory is expected to form a new theoretical basis for trapped Bose-Einstein condensates at finite temperatures.

T_{c}

for both antiferromagnetic and ferromagnetic interactions. The excitation spectra of the antiferromagnetic (ferromagnetic) interaction are found to have only a single gapless mode, contrary to the prediction of the Bogoliubov theory where three (two) of them are gapless. We present a detailed discussion on those single-particle excitations in connection with the collective excitations.