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The real part (imaginary part inset) of the charge-charge correlator at zero frequency as a function of temperature noramlised wave-vector. The blue dots are data from solving the holographic model, and the red dashed line is the fitted hydrodynamic correlator. We see the excellent fit between our model and the data.
Probe branes are rather remarkable theories. Despite coming from an action principle their low energy effective theory, at large charge density, seems to be described by quasihydrodynamics i.e. a non-conservative theory. Similar phenomena have been found in other bottom-up holographic models with higher powers of the electromagnetic field strength but a deep explanation is still lacking.
What we do know is that in the presence of an electric field a steady state emerges. The existence of this steady state has important consequences for fluctuations of the system and the full formalism to describe them is at present lacking. In this initial foray, I examined low frequency and wavevector perturbations around these steady states and obtained an effective linearised quasihydrodynamic theory which describes these perturbations.
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