Low-energy Fermi-liquid quasiparticle lifetime (${\tau }^{-1}\propto (ϵ-\mu {)}^2+(\pi k_{B}T{)}^2$)

The Pauli exclusion principle restricts final states available to a low-energy Landau quasiparticle and the particle–hole pair it excites. In a regular three-dimensional Fermi liquid, this phase-space restriction makes the decay rate quadratic in excitation energy or temperature. The excitation's width divided by its energy therefore vanishes at the Fermi surface, allowing an asymptotically sharp quasiparticle despite interactions.

A particle loss rate can include the factor $1-f(\xi )$, whereas a spectral decay width also contains the complementary inverse collision process. Their sum has the regular quadratic low-energy scale ${\xi }^2+(\pi k_{B}T{)}^2$. Particle and hole decay must not be confused with an occupied-state loss probability.