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arXiv · 2602.01971

Shear subdiffusion in non-relativistic holography

Yan Liu·Zhi-Ling Wang·Xin-Meng Wu
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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.

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Yan Liu, Zhi-Ling Wang, Xin-Meng Wu. 2026-02-02. Shear subdiffusion in non-relativistic holography. https://arxiv.org/abs/2602.01971

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