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At zero temperature, the charge current operator appears to be conserved,within linear response, in certain holographic probe brane models of strangemetals. At small but finite temperature, we analytically show that the weaknon-conservation of this current leads to both a collective "zero sound" modeand a Drude peak in the electrical conductivity. This simultaneously resolvestwo outstanding puzzles about probe brane theories. The nonlinear dynamics ofthe current operator itself appears qualitatively different.

Origin of the Drude peak and of zero sound in probe brane holography