Holographic incoherent transport in Einstein-Maxwell-dilaton Gravity

TL;DR

This paper explores how conductivities in Einstein-Maxwell-dilaton gravity can be separated into coherent and incoherent parts, providing analytic results for low-frequency conductivity with slow momentum relaxation, aligning with memory matrix methods.

Contribution

It introduces a decoupled perturbation framework for Einstein-Maxwell-dilaton theory to analyze conductivity decomposition, offering new analytic insights into incoherent transport.

Findings

Derived decoupled perturbation equations for a broad class of solutions.

Obtained analytic low-frequency conductivity results consistent with memory matrix techniques.

Clarified the role of intrinsic current relaxation in holographic transport.

Abstract

Recent progress in the holographic approach makes it more transparent that each conductivity can be decomposed into the coherent contribution due to momentum relaxation and the incoherent contribution due to intrinsic current relaxation. In this paper we investigate this decomposition in the framework of Einstein-Maxwell-dilaton theory. We derive the perturbation equations, which are decoupled for a large class of background solutions, and then obtain the analytic results of conductivity with the slow momentum relaxation in low frequency approximation, which is consistent with the known results from memory matrix techniques.