Hydrodynamics of a relativistic charged fluid in the presence of a periodically modulated chemical potential

TL;DR

This paper investigates the behavior of a relativistic charged fluid in a periodic lattice, revealing novel mode interactions and level repulsion phenomena through analytical and numerical methods within fluid-gravity duality.

Contribution

It introduces the study of hydrodynamic fluctuations as Bloch waves in a periodic chemical potential, uncovering new mode mixing effects and providing explicit examples with numerical verification.

Findings

Discovery of level repulsion at unit cell boundaries.

Identification of novel mode mixing between charge and sound.

Verification of theoretical results via fluid-gravity duality simulations.

Abstract

We study charged hydrodynamics in a periodic lattice background. Fluctuations are Bloch waves rather than single momentum Fourier modes. At boundaries of the unit cell where hydrodynamic fluctuations are formally degenerate with their Umklapped copy, level repulsion occurs. Novel mode mixings between charge, sound, and their Umklapped copies appear at finite chemical potential -- both at zero and finite momentum. We provide explicit examples for an ionic lattice, i.e. a periodic external chemical potential, and verify our results with numerical computations in fluid-gravity duality.