Pseudospectra of holographic diffusion: gauge fields breaking free from the master scalar

TL;DR

This paper investigates the pseudospectra of quasinormal modes and complex momenta of gauge fields in black brane backgrounds, introducing a new computational approach and analyzing spectral stability in the hydrodynamic regime.

Contribution

It presents a novel method for computing pseudospectra directly from gauge fields and clarifies the energy norm issue in the master scalar approach.

Findings

Pseudospectra of both approaches coincide.

Hydrodynamic quasinormal frequencies are spectrally stable.

Hydrodynamic complex momenta exhibit enhanced spectral instability.

Abstract

We study pseudospectra of quasinormal frequencies and complex linear momenta of a U(1) gauge field in a Schwarzschild black branes in Anti-de Sitter. We present a novel approach for computing the pseudospectra which uses directly the gauge field variables and contrast it to a conventional master scalar field approach. Upon clarifying a subtlety in the energy norm of the master scalar we show that the pseudospectra of both approaches conincide. In the hydrodynamic regime we find that the hydrodynamic quasinormal frequency, the diffusive mode, is spectrally stable to a very good approximation. On the other hand hydrodynamic complex linear momenta show enhanced spectral instability as a consequence of a pole-collision at zero frequency.