Finite-size effect of a weakly interacting Bose gas at zero-temperature

Phạm Thế Song

Pham Duy Thanh, Nguyen Van Thu

We investigate the effects of finite-range interatomic interactions on the equation of state (EoS) of a weakly interacting Bose gas. Within the Cornwall-Jackiw-Tomboulis effective action approach, we show that finite-range effects influence not only the EoS but also the thermodynamic properties of the system at zero temperature, leading to nonuniversal behavior.

Valery Isaakovich Klyatskin

Maksim Tomchenko

We diagonalize the second-quantized Hamiltonian of a one-dimensional Bose gas with a non-point repulsive interatomic potential and zero boundary conditions. At a weak coupling, the solutions for the ground-state energy E0 and the dispersion law E(k) coincide with the Bogoliubov solutions for a periodic system. In this case, the single-particle density matrix F1(x, x′) at T = 0 is close to the solution for a periodic system and, at T > 0, is significantly different from it. We also obtain that the wave function ⟨w(x, t)⟩ of the effective condensate is close to a constant √︀N0/L inside the system and vanishes on the boundaries (here, N0 is the number of atoms in the effective condensate, and L is the size of the system). We find the criterion of applicability of the method, according to which the method works for a finite system at very low temperature and with a weak coupling (a weak interaction or a large concentration).

Nguyễn Văn Thụ, Pham Duy Thanh

We investigate the effect of non-zero temperature to the condensate fraction of a homogeneous dilute weakly interacting Bose gas in very low-temperature region. Within inproved Hartree-Fock approximation, the Cornwall-Jackiw-Tomboulis effective action approach shows that the thermal fluctuations make the condensate fraction decrease as a second and fourth-order power law of temperature. The result is compared with experimental data. Indeed, the effect of non-infinite size of the trap is also integrated.

Bert Van Schaeybroeck