Convergence of hydrodynamic modes: insights from kinetic theory and holography

We investigate the breakdown of magneto-hydrodynamics at low temperature (T) with black holes whose extremal geometry is AdS2×R2. The breakdown is identified by the equilibration scales (ωeq, keq) defined as the collision point between the diffusive hydrodynamic mode and the longest-lived non-hydrodynamic mode. We show (ωeq, keq) at low T is determined by the diffusion constant D and the scaling dimension ∆(0) of an infra-red operator: ωeq = 2πT∆(0),$$ {k}_{\mathrm{eq}}^2 $$ k eq 2 = ωeq/D, where ∆(0) = 1 in the presence of magnetic fields. For the purpose of comparison, we have analytically shown ∆(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 $$ D\le {\omega}_{\mathrm{eq}}/{k}_{\mathrm{eq}}^2:= {v}_{\mathrm{eq}}^2{\tau}_{\mathrm{eq}} $$ D ≤ ω eq / k eq 2 ≔ v eq 2 τ eq where veq := ωeq/keq and τeq := $$ {\omega}_{\mathrm{eq}}^{-1} $$ ω 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.

Section: Introductionmentioning

confidence: 99%

The breakdown of magneto-hydrodynamics near AdS2 fixed point and energy diffusion bound

Jeong

Kim

Sun

2022

“…It was proposed in [3][4][5][6] that, by viewing the hydrodynamic mode as complex spectral curve in C 2 of complexified frequency and momentum, the convergence radii (k eq , ω eq ) of the hydrodynamic dispersion series is set by the absolute value of the complex momentum and complex frequency where the hydrodynamic pole collides with the first non-hydrodynamic gapped pole, namely "pole collision". Along this line, the convergence of hydrodynamic dispersion series has been investigated using kinetic theory in [10], using field theory in [11,12] and using holographic duality in [13][14][15][16][17][18][19][20].…”

Section: Jhep01(2022)155mentioning

confidence: 99%

Breakdown of hydrodynamics from holographic pole collision

Liu

2022

We study the breakdown of diffusive hydrodynamics in holographic systems dual to neutral dilatonic black holes with extremal near horizon geometries conformal to AdS2 × R2. We find that at low temperatures by tuning the effective gauge coupling constant in the infra-red, the lowest non-hydrodynamic mode, which collides with the charge diffusive mode and sets the scales at which diffusive hydrodynamics breaks down, could be either an infra-red mode or a slow mode, resulting in different scaling behaviors of the local equilibrium scales. We confirm that the upper bound for the charge diffusion constant is always satisfied using the velocity and timescale of local equilibration from the pole collision. We also examine the breakdown of hydrodynamics at general temperature and find that the convergence radius has nontrivial dependence on temperature, in addition to the effective gauge coupling constant.

“…In general, a multitude of critical points is expected to exist in the complex q 2 -plane, representing level-crossings among two or more branches of the spectrum. Moreover, at finite N c or at weak coupling described by kinetic theory, one may also expect other types of singularities to appear [30].…”

Section: Critical Points Puiseux Series and Quasinormal Level-crossingmentioning

confidence: 99%

“…of hydrodynamic series in relativistic kinetic theory (in the relaxation time approximation) were recently studied in ref. [30].…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic dispersion relations at finite coupling

Grozdanov

Starinets²,

Tadić

2021

By using holographic methods, the radii of convergence of the hydrodynamic shear and sound dispersion relations were previously computed in the $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory at infinite ’t Hooft coupling and infinite number of colours. Here, we extend this analysis to the domain of large but finite ’t Hooft coupling. To leading order in the perturbative expansion, we find that the radii grow with increasing inverse coupling, contrary to naive expectations. However, when the equations of motion are solved using a qualitative non-perturbative resummation, the dependence on the coupling becomes piecewise continuous and the initial growth is followed by a decrease. The piecewise nature of the dependence is related to the dynamics of branch point singularities of the energy-momentum tensor finite-temperature two-point functions in the complex plane of spatial momentum squared. We repeat the study using the Einstein-Gauss-Bonnet gravity as a model where the equations can be solved fully non-perturbatively, and find the expected decrease of the radii of convergence with the effective inverse coupling which is also piecewise continuous. Finally, we provide arguments in favour of the non-perturbative approach and show that the presence of non-perturbative modes in the quasinormal spectrum can be indirectly inferred from the analysis of perturbative critical points.