Upper bound of the charge diffusion constant in holography

Abstract

We investigate the upper bound of charge diffusion constant in holography. For this purpose, we apply the conjectured upper bound proposal related to the equilibration scales (${\omega }_{\text{eq}},k_{\text{eq}}$) to the Einstein-Maxwell-Axion model. (${\omega }_{\text{eq}},k_{\text{eq}}$) is defined as the collision point between the diffusive hydrodynamic mode and the first non-hydrodynamic mode, giving rise to the upper bound of the diffusion constant $D$ at low temperature $T$ as $D={\omega }_{\text{eq}}/k_{\text{eq}}^2$. We show that the upper bound proposal also works for the charge diffusion and (${\omega }_{\text{eq}},k_{\text{eq}}$), at low $T$, is determined by $D$ and the scaling dimension $\Delta (0)$ of an infra-red operator as $({\omega }_{\text{eq}},k_{\text{eq}}^2)=(2\pi T\Delta (0),{\omega }_{\text{eq}}/D)$, as for other diffusion constants. However, for the charge diffusion, we find that the collision occurs at real $k_{\text{eq}}$, while it is complex for other diffusions. In order to examine the universality of the conjectured upper bound, we also introduce a higher derivative coupling to the Einstein-Maxwell-Axion model. This coupling is particularly interesting since it leads to the violation of the \textit{lower} bound of the charge diffusion constant so the correction may also have effects on the \textit{upper} bound of the charge diffusion. We find that the higher derivative coupling does not affect the upper bound so that the conjectured upper bound would not be easily violated.

v1: 23 pages, 10 figures; v2: minor edits, references added

References in corpus (26)

• Quantum criticality
• Viscosity Bound and Causality Violation
• Theory of universal incoherent metallic transport
• Quantum Criticality
• Momentum dissipation and effective theories of coherent and incoherent transport
• Thermal diffusivity and chaos in metals without quasiparticles
• On the convergence of the gradient expansion in hydrodynamics
• Spread of entanglement in a Sachdev-Ye-Kitaev chain
• An upper bound on transport
• Diffusion and Chaos from near AdS${}_2$ horizons
• Holographic Axion Model: a simple gravitational tool for quantum matter
• Charge diffusion and the butterfly effect in striped holographic matter
• Bounds on transport from univalence and pole-skipping
• Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field
• Universal Bounds on Transport in Holographic Systems with Broken Translations
• Quark-Gluon Plasma at RHIC and the LHC: Perfect Fluid too Perfect?
• Convergence of hydrodynamic modes: insights from kinetic theory and holography
• Hydrodynamic diffusion and its breakdown near AdS${}_2$ quantum critical points
• The breakdown of magneto-hydrodynamics near AdS${}_2$ fixed point and energy diffusion bound
• On the universality of AdS${}_2$ diffusion bounds and the breakdown of linearized hydrodynamics
• How small hydrodynamics can go
• Hydrodynamic dispersion relations at finite coupling
• Holographic renormalization and anisotropic black branes in higher curvature gravity
• Holographic Butterfly Effect and Diffusion in Quantum Critical Region
• Breakdown of hydrodynamics from holographic pole collision
• Constraints on hydrodynamics from many-body quantum chaos

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