Pole skipping and chaos in anisotropic plasma: a holographic study

Abstract

Recently, a direct signature of chaos in many body system has been realized from the energy density retarded Green's function using the phenomenon of 'pole skipping'. Moreover, special locations in the complex frequency and momentum plane are found, known as the pole skipping points such that the retarded Green's function can not be defined uniquely there. In this paper, we compute the correction/shift to the pole skipping points due to a spatial anisotropy in a holographic system by performing near horizon analysis of EOMs involving different bulk field perturbations, namely the scalar, the axion and the metric field. For vector and scalar modes of metric perturbations we construct the gauge invariant variable in order to obtain the master equation. Two separate cases for every bulk field EOMs is considered with the fluctuation propagating parallel and perpendicular to the direction of anisotropy. We compute the dispersion relation for momentum diffusion along the transverse direction in the shear channel and show that it passes through the first three successive pole skipping points. The pole skipping phenomenon in the sound channel is found to occur in the upper half plane such that the parameters Lyapunov exponent λ L and the butterfly velocity v B are explicitly obtained thus establishing the connection with many body chaos.

Pole-skipping and hydrodynamic analysis in Lifshitz, AdS$_2$ and Rindler geometries

“…Ref. [22] show that the dispersion relation which arises from the pole of the retarded Green's function associated to the transverse momentum density passes through the lower half-plane pole skipping points in the backgound of anisotropic plasma. The pole-skipping points may be related to the hydrodynamic dispersion relation.…”

Analogue of the pole-skipping phenomenon in acoustic black holes

“…The locations of special points (ω n , k n ) can be easily extracted from the determinant of the In Ref. [6,13,14], the authors show that dispersion relation, which arises from the pole of the retarded Green's function (QNMs), passes through the lower half-plane pole-skipping points. We want to see if the relation between the pole-skipping points and the hydrodynamic dispersion relation still holds for acoustic black holes.…”

“…), where w = ω 2πT . These special points have been found in BTZ black hole [6], Schwarzschild-AdS spacetime [7], 2D CFT [8], a holographic system with the chiral anomaly [9], a holographic system at finite chemical potential [10], hyperbolic space [11], the large q limit of SYK chain [12], anisotropic plasma [13], Lifshitz, and Rindler geometries [14]. However, the physical interpretation of the pole-skipping phenomenon remains elusive.…”

Nonuniqueness of Green’s functions at special points

“…Since then, various aspects of the pole-skipping have been investigated (see, e.g., Refs. [23][24][25][26][27][28][29][30][31][32][33][34][35][36]). This phenomenon can be seen in various Green's functions, e.g., the Green's functions for conserved quantities such as energy density, momentum density, and charge density.…”