Slow Shear Waves Defy Physics in New Holographic Simulations
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Scientists are increasingly interested in understanding anomalous transport phenomena in strongly coupled non-relativistic matter, and new research sheds light on shear fluctuations within non-relativistic holographic systems. Yan Liu from Beihang University, Zhi-Ling Wang and Xin-Meng Wu from Shanghai Jiao Tong University demonstrate a universal subdiffusive shear mode characterised by a quartic dispersion relation, a significant departure from conventional hydrodynamic diffusion. They derive this result analytically via a systematic higher-order matched asymptotic expansion and corroborate it with numerical quasinormal mode calculations, revealing a gapped, purely imaginary first non-hydrodynamic mode and pole-skipping points for both hydrodynamic and non-hydrodynamic modes. This work highlights the efficacy of Lifshitz holography as a framework for modelling such complex behaviours and advances our understanding of transport in these systems. This breakthrough challenges conventional hydrodynamic diffusion, revealing a quartic dispersion relation, ω = −iD⁴k⁴, that deviates significantly from the standard Fickian behaviour described by ω = −iDk². The research, utilising asymptotically Lifshitz spacetimes within an Einstein-Maxwell-dilaton gravity framework, demonstrates that momentum transport can exhibit slower scaling under specific constraints. Researchers achieved this by meticulously analysing shear fluctuations in holographic systems coupled to torsional Newton-Cartan geometry, a configuration relevant to condensed matter physics. This work establishes a systematic higher-order matched asymptotic expansion, successfully connecting near-horizon and far-region solutions to derive the subdiffusive result analytically. Verification was subsequently obtained through direct numerical quasinormal mode calculations, confirming the analytical predictions with high precision. Numerical analysis reveals the first non-hydrodynamic mode to be purely imaginary and gapped, following the dispersion relation ω = −iω₀ −iDk², and importantly, both the hydrodynamic and this first non-hydrodynamic mode exhibit pole-skipping points. These pole-skipping points are indicative of the system’s complex response to perturbations and provide further insight into its anomalous transport properties. The study highlights the efficacy of Lifshitz holography as a framework for investigating anomalous transport phenomena in strongly coupled non-relativistic systems. By employing this holographic approach, researchers circumvent the challenges associated with directly studying momentum dynamics, a conserved quantity often difficult to analyse. This discovery opens avenues for understanding exotic late-time dynamics in non-equilibrium systems, where relaxation rates deviate from conventional scaling laws. The findings have implications for diverse areas of physics, including the study of fluids with enhanced symmetries and systems exhibiting ergodicity breaking. Furthermore, the research demonstrates that the observed subdiffusion is not limited to conserved charges, but can also manifest in transverse momentum transport. This expands the scope of subdiffusive phenomena and suggests that it may be more prevalent in strongly correlated systems than previously thought. The combination of analytical and numerical techniques employed in this study provides a robust and reliable method for characterising anomalous transport in complex quantum materials, paving the way for future investigations into related phenomena. Determining shear mode dispersion via matched asymptotic expansion of holographic fluctuations reveals a characteristic power-law behavior Researchers investigated shear fluctuations within non-relativistic holographic systems employing asymptotically Lifshitz spacetimes and Einstein-Maxwell-dilaton gravity. The study commenced with analysis of transverse fluctuations to characterise shear diffusion, utilising linear perturbation theory to describe deviations from equilibrium. Specifically, the team calculated the response of the holographic system to external perturbations in the transverse direction, focusing on the shear mode which represents distortions in the fluid’s shape. A key methodological innovation involved a systematic higher-order matched asymptotic expansion connecting near-horizon and far-region solutions. This technique allowed for precise determination of the dispersion relation governing the shear mode, circumventing limitations of purely local or global analyses. The near-horizon analysis captured the behaviour of the system close to the black hole, while the far-region analysis described the dynamics at large distances, and matching these solutions provided a complete picture of the shear mode’s propagation. Analytical results predicted a universal subdiffusive shear mode with a quartic dispersion relation, differing significantly from conventional hydrodynamic diffusion. To corroborate the analytical findings, researchers performed direct numerical quasinormal mode calculations. A 72-qubit superconducting processor was not used in this study; instead, numerical solutions to the perturbed field equations were obtained using established computational techniques. These calculations confirmed the subdiffusive behaviour and revealed that the first non-hydrodynamic mode is purely imaginary and gapped, following the dispersion relation . Furthermore, both the hydrodynamic and first non-hydrodynamic modes exhibited pole-skipping points, indicating a breakdown of the standard hydrodynamic description. These results demonstrate Lifshitz holography as an effective framework for modelling anomalous transport in strongly coupled non-relativistic matter. Subdiffusive modes and gapless excitations in non-relativistic holography reveal emergent phenomena in strongly correlated systems Shear fluctuations in non-relativistic holographic systems exhibit a universal subdiffusive mode characterised by the dispersion relation ω = −iDk², diverging from conventional hydrodynamic diffusion. Analytical derivations, utilising higher-order matched asymptotic expansions connecting near-horizon and far-region solutions, confirm this result alongside direct numerical quasinormal mode calculations. Numerical analysis demonstrates the first non-hydrodynamic mode is purely imaginary and gapped, following the dispersion relation ω = −iω₀ −iDk², where ω₀ represents a constant gap parameter. Both the hydrodynamic and the first non-hydrodynamic modes exhibit pole-skipping points, indicating a breakdown of the standard diffusive approximation. The purely imaginary component of the first non-hydrodynamic mode reaches a value of −iω₀, signifying a gapped excitation within the system. These findings establish Lifshitz holography as an effective framework for investigating anomalous transport in strongly coupled non-relativistic quantum matter. The research focuses on systems coupled to torsional Newton-Cartan geometry, employing asymptotically Lifshitz spacetimes within an Einstein-Maxwell-dilaton framework. Calculations reveal that the dispersion relation ω = −iDk² governs the subdiffusive shear mode, contrasting with the typical ω = −iDk² observed in standard hydrodynamic behaviour. The analytical approach involved systematically matching solutions in the near-horizon and far-region limits, providing a robust verification of the numerical quasinormal mode analysis.
Subdiffusive Shear Mode Characteristics and Quasinormal Mode Analysis reveal complex wave behavior Researchers have identified a universal subdiffusive shear mode in non-relativistic holographic systems coupled to torsional Newton-Cartan geometry, demonstrating a departure from conventional hydrodynamic diffusion. This subdiffusive behaviour is characterised by a quartic dispersion relation, indicating a slower relaxation time compared to standard diffusive processes. The findings were obtained through analytical calculations using matched asymptotic expansion and confirmed with numerical quasinormal mode calculations. The study establishes Lifshitz holography as an effective framework for investigating anomalous transport in strongly coupled non-relativistic matter, offering insights into systems where microscopic dynamics exhibit additional symmetries or constraints. Numerical analysis revealed that the first non-hydrodynamic mode is purely imaginary and possesses a gap, following a specific dispersion relation, and both hydrodynamic and non-hydrodynamic modes exhibit pole-skipping points. The authors acknowledge a limitation in focusing on shear fluctuations, leaving the exploration of other transport channels for future work. Further research could investigate the implications of these findings for specific condensed matter systems and explore the broader applicability of Lifshitz holography to other anomalous transport phenomena. 👉 More information 🗞 Shear subdiffusion in non-relativistic holography 🧠 ArXiv: https://arxiv.org/abs/2602.01971 Tags: