Anomalously long lifetimes in two-dimensional Fermi liquids

A precise characterization of the recently discovered crossover to hydrodynamic transport in electron liquids, and in particular of a conjectured exotic tomographic transport regime, requires a full solution of the Fermi-liquid collision integral at all temperatures beyond state-of-the-art analytic leading-logarithmic approximations. We develop a general basis expansion of the linearized collision integral applicable at all temperatures, and employ this to determine the decay rates of Fermi surface perturbations in two-dimensional electron liquids. In particular, we provide exhaustive data on the decay rates for a new tomographic regime, in which parity-even Fermi surface deformations decay rapidly but odd-parity modes are anomalously long-lived, and which exists at fairly large temperatures $T \lesssim 0.1 T_F$, putting this regime within the reach of current experiments.