Pole skipping and chaos in anisotropic plasma: a holographic study

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