Linear response beyond hydrodynamic poles

TL;DR

This paper develops a linearised effective theory that accurately reproduces charge current correlators with multiple poles, bridging hydrodynamics and quasihydrodynamics, and applies it to D3/D5 brane charge fluctuations.

Contribution

It introduces a framework for constructing effective linear theories with multiple poles that align with the Mittag-Leffler expansion, enhancing the understanding of quasihydrodynamics.

Findings

Framework reproduces correlators with arbitrary simple poles

Maintains compatibility with hydrostatic thermodynamics

Quantifies transport coefficient behavior at large charge density

Abstract

We consider the problem of writing an effective, linearised theory in small derivatives that reproduces the Mittag-Leffler expansion of a charge current correlator with an arbitrary number of simple poles. We demonstrate how such a framework: can be compatible with hydrostaticity without modification of thermodynamics, properly accounts for the differing notions of smallness in time and space derivatives including setting the lowest order effective equation of motion, and corrects the effective equations in derivatives. As an application, we apply the results to charge fluctuations of the D3/D5 probe brane and quantify how the transport coefficients behave when quasihydrodynamics emerges at large charge density.