Pole skipping and chaos in anisotropic plasma: a holographic study

TL;DR

This paper investigates how spatial anisotropy affects pole skipping phenomena in holographic models, revealing shifts in chaos-related parameters like Lyapunov exponent and butterfly velocity, thus linking chaos signatures to anisotropic systems.

Contribution

It provides a detailed analysis of pole skipping shifts due to anisotropy in holographic systems, including explicit calculations of chaos parameters in different directions.

Findings

Pole skipping points are shifted by anisotropy.

Lyapunov exponent and butterfly velocity are explicitly computed.

Chaos parameters depend on the direction relative to anisotropy.

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 $\lambda_{L}$ and the butterfly velocity $v_{B}$ are explicitly obtained thus establishing the connection with many body chaos.