Holographic D.C. conductivity

Holographic D.C. conductivity describes the zero-frequency electric response of a boundary system using a bulk gauge field. In a clean normal state at nonzero charge density, the electric current generally overlaps with conserved momentum. A constant electric field then continuously accelerates that momentum, producing a zero-frequency delta function rather than an ordinary finite D.C. response.

Introducing relaxation of momentum can broaden this contribution and yield finite conductivity when no other protected dissipationless channel remains. That qualification matters: a superfluid can retain a delta function even when translations are broken. One must specify the phase, conserved quantities and frequency limit before interpreting a bulk calculation as a measured D.C. conductivity.