The Gaussian Approximation to Homogeneous Bose Gas

Paolo Tommasini, Paulo Laerte Natti, A. F. R. de Toledo Piza

Anna Okopińska

The effective action formalism of quantum field theory is used to study the properties of the non-relativistic interacting Bose gas. The Gaussian approximation is formulated by calculating the effective action to the first order of the optimized expansion. In the homogeneous limit the method respects the Hughenholz-Pines theorem, leading to the gapless spectrum both for excitations and for density fluctuations. Renormalization is carried out by adopting dimensional regularization. The results for critical temperature are compared with that obtained in the loop expansion.

Abdulla Rakhimov, Chul Koo Kim, Sang‐Hoon Kim +1 more

The properties of the uniform Bose gas are studied within the optimized variational perturbation theory (Gaussian approximation) in a self-consistent way. It is shown that the atomic Bose-Einstein condensate with a repulsive interaction becomes unstable when the gas parameter $\ensuremath{\gamma}=\ensuremath{\rho}{a}^{3}$ exceeds a critical value ${\ensuremath{\gamma}}_{crit}\ensuremath{\approx}0.01$. The quantum corrections beyond the Bogoliubov-Popov approximation to the energy density, chemical potential, and pressure in powers of $\sqrt{\ensuremath{\gamma}}$ expansions are presented.

Eric Braaten, Agustín Nieto

Maxine Pitter Lunn

Nguyễn Văn Thụ

Motivated by the recent experiment [R. Lopes et. al., Phys. Rev. Lett. 119, 190404 (2017)] with a homogeneous Bose gas, we investigate a homogeneous dilute Bose gas to reproduce the quantum depletion density. By means of Cornwall-Jackiw-Tomboulis effective action approach within improved Hartree-Fock approximation, the quantum depletion density is recovered in an easier manner.Additionally, the higher-order terms are taken into account for the condensed fraction.