On the linearized system of equations for the condensate-normal fluid interaction at very low temperature

The linearization around one of its equilibrium of a system that describes the correlations between the superfluid component and the normal fluid part of a condensed Bose gas in the approximation of very low temperature and small condensate density is studied. A simple and transparent argument gives a necessary and sufficient condition for the existence of global solutions satisfying the conservation of the total number of particles and energy. The global solutions describe the evolution in time of the density of the thermal cloud and, unlike in previous work, that of the condensate's density. Their convergence to a suitable stationary state is also shown and rates of convergence for the normal fluid and superfluid components are obtained.

Automated summary

We study the linearization of a system that describes the correlations between the superfluid component and the normal fluid part of a condensed Bose gas at very low temperature and small condensate density, around one of its equilibrium points. Using a simple and transparent argument, we give a necessary and sufficient condition for the existence of global solutions that satisfy the conservation of the total number of particles and energy. The global solutions describe the time evolution of the density of the thermal cloud and the condensate's density, unlike previous work, and we also demonstrate the convergence of these global solutions to a suitable stationary state, obtaining convergence rates for the normal fluid and superfluid components.