Spectral weight, excitation stability and critical velocity in a Bose-condensed gas

We study the excitation spectrum of a spatially homogeneous Bose-condensed gas. Using finite-temperature field theory, we derive the dependence of the excitation spectrum on both the gaseous parameter and the temperature. In particular, we derive the asymptotic forms of the spectral weight at finite temperature. We then discuss the effects of the interaction between the excitations on the dispersion relation, in particular on its curvature for small momentum. From the gaseous parameter dependence of the curvature at zero temperature, we find that there exists a threshold for the gaseous parameter, above which the spectrum becomes stable and no damping processes occur. The excitation stability is analyzed at finite temperature, and it is found that the effect of the finite temperature is to increase the stability of the excitation. We numerically calculated the ratio of the critical velocity to the sound velocity, finding that the critical velocity is small compared to the sound velocity for specific gaseous parameters and temperatures.