The breakdown of magneto-hydrodynamics near AdS${}_2$ fixed point and energy diffusion bound

Abstract

We investigate the breakdown of magneto-hydrodynamics at low temperature ($T$) with black holes whose extremal geometry is AdS${}_2\times$R${}^2$. The breakdown is identified by the equilibration scales (${\omega }_{\text{eq}},k_{\text{eq}}$) defined as the collision point between the diffusive hydrodynamic mode and the longest-lived non-hydrodynamic mode. We show (${\omega }_{\text{eq}},k_{\text{eq}}$) at low $T$ is determined by the diffusion constant $D$ and the scaling dimension $\Delta (0)$ of an infra-red operator: ${\omega }_{\text{eq}}=2\pi T\Delta (0),k_{\text{eq}}^2={\omega }_{\text{eq}}/D$, where $\Delta (0)=1$ in the presence of magnetic fields. For the purpose of comparison, we have analytically shown $\Delta (0)=2$ for the axion model independent of the translational symmetry breaking pattern (explicit or spontaneous), which is complementary to previous numerical results. Our results support the conjectured universal upper bound of the energy diffusion $D\le {\omega }_{\text{eq}}/k_{\text{eq}}^2:=v_{\text{eq}}^2{\tau }_{\text{eq}}$ where $v_{\text{eq}}:={\omega }_{\text{eq}}/k_{\text{eq}}$ and ${\tau }_{\text{eq}}:={\omega }_{\text{eq}}^{-1}$ are the velocity and the timescale associated to equilibration, implying that the breakdown of hydrodynamics sets the upper bound of the diffusion constant $D$ at low $T$.

arXiv commentv1:26 pages, 17 figures. arXiv admin note: text overlap with arXiv:2104.13084; v2: minor edits, references added

References in corpus (43)

• Gauge Theory Correlators from Non-Critical String Theory
• A bound on chaos
• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
• Emergent quantum criticality, Fermi surfaces, and AdS2
• Hydrodynamic gradient expansion in gauge theory plasmas
• Locally critical umklapp scattering and holography
• Ohm's Law at strong coupling: S duality and the cyclotron resonance
• Momentum dissipation and effective theories of coherent and incoherent transport
• Holographic Polarons, the Metal-Insulator Transition and Massive Gravity
• Black hole scrambling from hydrodynamics
• Many-body chaos and energy dynamics in holography
• Holographic Operator Mixing and Quasinormal Modes on the Brane
• The complex life of hydrodynamic modes
• Relativistic magnetohydrodynamics
• Thermal diffusivity and chaos in metals without quasiparticles
• Universal Diffusion in Incoherent Black Holes
• On the convergence of the gradient expansion in hydrodynamics
• Diffusion and Chaos from near AdS${}_2$ horizons
• Holographic Axion Model: a simple gravitational tool for quantum matter
• A Practical Mini-Course on Applied Holography
• Complexified quasinormal modes and the pole-skipping in a holographic system at finite chemical potential
• Diffusivities bounds and chaos in holographic Horndeski theories
• Short-lived modes from hydrodynamic dispersion relations
• Bounds on transport from univalence and pole-skipping
• Quasinormal modes in charged fluids at complex momentum
• Thermal diffusivity and butterfly velocity in anisotropic Q-Lattice models
• Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field
• Hydrodynamic gradient expansion in linear response theory
• Universal Bounds on Transport in Holographic Systems with Broken Translations
• Convergence of hydrodynamic modes: insights from kinetic theory and holography
• Nonlinear Magnetohydrodynamics from Gravity
• Hydrodynamic diffusion and its breakdown near AdS${}_2$ quantum critical points
• Thermal Diffusion and Quantum Chaos in Neutral Magnetized Plasma
• On the universality of AdS${}_2$ diffusion bounds and the breakdown of linearized hydrodynamics
• A hydrodynamical description for magneto-transport in the strange metal phase of Bi-2201
• Hydrodynamic magneto-transport in charge density wave states
• Magneto-thermal transport implies an incoherent Hall conductivity
• The Fate of the Sound and Diffusion in Holographic Magnetic Field
• Hydrodynamic dispersion relations at finite coupling
• Sound Waves in (2+1) Dimensional Holographic Magnetic Fluids
• Relativistic Conformal Magneto-Hydrodynamics from Holography
• Collective modes of polarizable holographic media in magnetic fields
• S-duality in AdS/CFT magnetohydrodynamics

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• T-linear resistivity, optical conductivity and Planckian transport for a holographic local quantum critical metal in a periodic potential
• Upper bound of the charge diffusion constant in holography
• Breakdown of hydrodynamics from holographic pole collision
• Relativistic Hydrodynamics: A Singulant Perspective
• Construction of bulk solutions for towers of pole-skipping points
• On pole-skipping with gauge-invariant variables in holographic axion theories
• Thermo-electric Transport of Dyonic Gubser-Rocha Black Holes
• A novel holographic quantum phase transition and butterfly velocity
• Perturbing a quantum black hole
• Long-time tails in the SYK chain from the effective field theory with a large number of derivatives
• Probing Pole Skipping through Scalar-Gauss-Bonnet coupling
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