In the case of bosons, there is no Pauli exclusion principle to confine excitations close to the chemical potential (Fermi energy for fermions) so the entire Brillouin zone must be included. At low temperatures, the bosons will collect at the lowest energy point, the Γ Γ -point of the lower band. Energy must be added to excite the quasiparticles to the vicinity of the linear crossing point.