Shear subdiffusion in non-relativistic holography

TL;DR

This paper uncovers a universal subdiffusive shear mode with quartic dispersion in non-relativistic holographic systems, contrasting with standard diffusion, and verifies it through analytical and numerical methods, revealing complex mode structures and pole-skipping phenomena.

Contribution

It introduces and analytically derives a universal subdiffusive shear mode in Lifshitz holography, supported by numerical verification, advancing understanding of anomalous transport in non-relativistic quantum matter.

Findings

Identification of a universal quartic dispersion shear mode

Verification of mode structure through numerical quasinormal modes

Observation of pole-skipping points in both hydrodynamic and non-hydrodynamic modes

Abstract

We study shear fluctuations in non-relativistic holographic systems coupled to torsional Newton-Cartan geometry, using asymptotically Lifshitz spacetimes in Einstein-Maxwell-dilaton gravity. We identify a universal subdiffusive shear mode characterized by the quartic dispersion relation $\omega=-iD_4 k^4$, in sharp contrast to the conventional hydrodynamic diffusion. We derive this result analytically through a systematic higher-order matched asymptotic expansion connecting near-horizon and far-region solutions, and we verify it with direct numerical quasinormal mode calculations. Our numerics demonstrate that the first non-hydrodynamic mode is purely imaginary and gapped, following the dispersion relation $\omega=-i\omega_0-i D k^2$, and that both the hydrodynamic and the first non-hydrodynamic modes pass through pole-skipping points. These results highlight Lifshitz holography as an efficient framework for anomalous transport in strongly coupled non-relativistic quantum matter.