ABSTRACT
So far we have studied various properties of the Fermi liquid in thermodynamic equilibrium. Even in the case of a dynamical phenomenon such as the propagation of a sound wave, we worked in the low frequency limit ωτ ≪ 1; here the quasiparticles had sufficient time to relax before the completion of one period. The condition ωτ ≪ 1 is equivalent to saying that the quasiparticles are able to equilibrate in a region of dimension l ∼ sτ that is much smaller than the wavelength λ = 2 π s / ω $ \lambda = 2\pi s/\omega $ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781351121996/b629fd18-6a2d-463e-9a28-616371388344/content/inline-math3_1.tif"/> of the sound wave. Such sound waves are a collective, hydrodynamic process. As the temperature is lowered, the relaxation time τ of the quasiparticles increases as τ ∝ 1/T 2, and it becomes increasingly difficult to equilibrate the quasiparticles before the completion of a period of oscillation. In other words, at a sufficiently low temperature, or at high enough frequency, the inequality ωτ ≪ 1 can no longer be satisfied, and the hydrodynamic approximation is not appropriate.
