Quantum corrections to the ground state energy of a trapped Bose-Einstein condensate: A diffusion Monte Carlo calculation

The diffusion Monte Carlo method is applied to describe a trapped atomic Bose-Einstein condensate at zero temperature, fully quantum mechanically and nonperturbatively. For low densities, $n(0)a^3 \le 2 \cdot 10^{-3}$ [n(0): peak density, a: s-wave scattering length], our calculations confirm that the exact ground state energy for a sum of two-body interactions depends on only the atomic physics parameter a, and no other details of the two-body model potential. Corrections to the mean-field Gross-Pitaevskii energy range from being essentially negligible to about 20% for N=2-50 particles in the trap with positive s-wave scattering length a=100-10000 a.u.. Our numerical calculations confirm that inclusion of an additional effective potential term in the mean-field equation, which accounts for quantum fluctuations [see e.g. E. Braaten and A. Nieto, Phys. Rev. B 56}, 14745 (1997)], leads to a greatly improved description of trapped Bose gases.Comment: 7 pages, 4 figure

Thermodynamic perturbation theory for dipolar superparamagnets

Thermodynamic perturbation theory is employed to derive analytical expressions for the equilibrium linear susceptibility and specific heat of lattices of anisotropic classical spins weakly coupled by the dipole-dipole interaction. The calculation is carried out to the second order in the coupling constant over the temperature, while the single-spin anisotropy is treated exactly. The temperature range of applicability of the results is, for weak anisotropy (A/kT << 1), similar to that of ordinary high-temperature expansions, but for moderately and strongly anisotropic spins (A/kT > 1) it can extend down to the temperatures where the superparamagnetic blocking takes place (A/kT \sim 25), provided only the interaction strength is weak enough. Besides, taking exactly the anisotropy into account, the results describe as particular cases the effects of the interactions on isotropic (A = 0) as well as strongly anisotropic (A \to \infty) systems (discrete orientation model and plane rotators).Comment: 15 pages, 3 figure