Zero-sound collective modes in a clean or disordered Fermi liquid are mapped across the Pomeranchuk instability, including silent poles on unphysical Riemann sheets and a special l=1 current channel whose instability survives a vanishing residue.
Comparing the results for for the l = 0, 1, 2 modes, we see a difference between even and odd l
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Collective modes near a Pomeranchuk instability
Zero-sound collective modes in a clean or disordered Fermi liquid are mapped across the Pomeranchuk instability, including silent poles on unphysical Riemann sheets and a special l=1 current channel whose instability survives a vanishing residue.