A new second-order upper bound for the ground state energy of dilute Bose gases

We establish an upper bound for the ground state energy per unit volume of a dilute Bose gas in the thermodynamic limit, capturing the correct second-order term, as predicted by the Lee–Huang–Yang formula. This result was first established in [20] by H.-T. Yau and J. Yin. Our proof, which applies to repulsive and compactly supported $V \in L^3 (\mathbb {R}^3)$ , gives better rates and, in our opinion, is substantially simpler.

Bose Gas in Classical Environment at Low Temperatures

The properties of a dilute Bose gas with the non-Gaussian quenched disorder are analyzed. Being more specific, we have considered a system of bosons immersed in the classical bath consisting of the non-interacting particles with infinite mass. Making use of perturbation theory up to the second order, we have studied the impact of environment on the ground-state thermodynamic and superfluid characteristics of the Bose component.

Condensate Density of a Bose Gas Confined between Two Parallel Plates in Canonical Ensemble within Improved Hartree-Fock Approximation

By means of Cornwall-Jackiw-Tomboulis (CJT) effective action approach, the condensate density of a dilute Bose gas is investigated in the canonical ensemble. Our results show that the condensate density is proportional to a half-integer power law of the s-wave scattering length and distance between two plates. Apart from that, these quantities also depend on the particle number and area of each plate.

THE FREE ENERGY OF THE TWO-DIMENSIONAL DILUTE BOSE GAS. I. LOWER BOUND

We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density $\unicode[STIX]{x1D70C}$ and inverse temperature $\unicode[STIX]{x1D6FD}$ differs from the one of the noninteracting system by the correction term $4\unicode[STIX]{x1D70B}\unicode[STIX]{x1D70C}^{2}|\ln \,a^{2}\unicode[STIX]{x1D70C}|^{-1}(2-[1-\unicode[STIX]{x1D6FD}_{\text{c}}/\unicode[STIX]{x1D6FD}]_{+}^{2})$ . Here, $a$ is the scattering length of the interaction potential, $[\cdot ]_{+}=\max \{0,\cdot \}$ and $\unicode[STIX]{x1D6FD}_{\text{c}}$ is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit $a^{2}\unicode[STIX]{x1D70C}\ll 1$ and if $\unicode[STIX]{x1D6FD}\unicode[STIX]{x1D70C}\gtrsim 1$ .