Phenomenological Construction of New Dictionaries for Holographic Conductors

TL;DR

This paper introduces new holographic dictionaries to compute carrier densities and mean velocities in holographic conductors, bridging phenomenological models with holographic results.

Contribution

It develops a phenomenological model to define non-conjugate quantities and establishes a new dictionary linking these to holographic computations.

Findings

Carrier density differs from charge density.

Mean velocity matches the velocity of an analog black hole.

The spectrum of fluctuations reveals the mean velocity.

Abstract

We propose new dictionaries for holographic conductors that enable us to compute carrier densities and mean velocities of charge carriers in the system. The carrier density, which differs from the charge density, is the total number density of both the positive and the negative charge carriers. The mean velocity is the mean value of the velocities of all charge carriers. These quantities are not conjugate to the sources that are given by boundary values of bulk fields, and we cannot compute them by using the conventional method in holography. In the present work, we introduce a phenomenological model of charge transport, and we establish the dictionary by comparing the results of the phenomenological model and those from the holography. We show that the mean velocity agrees with the velocity of an analog black hole on the worldvolume of the probe D-brane, and it can be read from the spectrum of the fluctuations.