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We consider pion condensation in cold and dense QCD using chiral perturbationtheory ($\chi$PT). Thermodynamic quantities are calculated at next-to-leadingorder in the low-energy expansion. In the nonrelatistivtic limit, we recoverthe classic result by Lee and Yang for the energy density of a dilute Bose gaswith an $s$-wave scattering length that includes loop corrections from$\chi$PT. In the chiral limit, we calculate the thermodynamic functions tonext-to-leading order in the low-energy expansion. We use Son's prescription towrite down an effective field theory for the massless Goldstone boson thatresults from the spontaneous breakdown of the global internal symmetry$U(1)_{I_3}$ at finite isospin density $n_I$. In the ultrarelativistic limit,the phonons propagate with the speed of light up to renormalization effects.The damping rate of the phonons behaves as $p^5$ for small momenta in agreementwith Beliaev's old result for a weakly interacting Bose gas.

Pion condensation in dense QCD, the dilute Bose gas, and speedy Goldstone bosons