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 λL and the butterfly velocity vB are explicitly obtained
thus establishing the connection with many body chaos.
