Superfluid-supersolid phase transition of elongated dipolar Bose-Einstein condensates at finite temperatures

We analyze the finite-temperature phase diagram of a dipolar Bose-Einstein condensate confined in a tubular geometry. The effect of thermal fluctuations is accounted for by means of Bogoliubov theory employing the local density approximation. In the considered geometry, the superfluid-supersolid phase transition can be of first and second order. We discuss how the corresponding transition point is affected by the finite temperature of the system.