The hierarchy of excitation lifetimes in two-dimensional Fermi gases

Momentum-conserving quasiparticle collisions in two-dimensional Fermi gases give rise to a large family of exceptionally long-lived excitation modes. The lifetimes of these modes exceed by a factor (TF∕T)2≫1 the conventional Landau Fermi-liquid lifetimes τ∼TF∕T2. The long-lived modes have a distinct angular structure, taking the form of cosmθ and sinmθ with odd m values for a circular Fermi surface, with relaxation rate dependence on m of the form m4logm, valid at not-too-large m. In contrast, the even-m harmonics feature conventional lifetimes with a weak m dependence. The long-time dynamics, governed by these modes, occurs at “non-Fermi-liquid” timescales, taking values as large as τ∼TF3∕T4. The hierarchy of timescales, short and long, leads to unusual long-time memory effects, defining an intriguing transport regime that lies between the conventional ballistic and hydrodynamic regimes.