 Then we assume formula_50 and formula_51 to be plane waves of momentum formula_59, which leads to the energy spectrum

For large formula_59, the dispersion relation is quadratic in formula_59 as one would expect for usual non interacting single particle excitations.For small formula_59, the dispersion relation is linear

with formula_65 being the speed of sound in the condensate, also known as second sound.The fact that formula_66 shows, according to Landau's criterion, that the condensate is a superfluid, meaning that if an object is moved in the condensate at a velocity inferior to s, it will not be energetically favorable to produce excitations and the object will move without dissipation, which is a characteristic of a superfluid.