ZERO SOUND — FERMI LIQUID

Landau quasiparticle collective mode vs ordinary sound
Fermi liquid (T→0):
Zero sound: ω = s₀q
s₀ = v_F·s, s > 1

From kinetic eq.:
1 = F₀ˢ·Π(s)
Π(s) = ½(s/√(s²-1) - 1)

Ordinary sound (T≫0):
adiabatic, s_ord = v_F/√3
(for non-interacting)

Zero sound persists when
ωτ ≫ 1 (collisionless)
F₀ˢ > 0 needed for mode