Pole-skipping and chaos in D3-D7 brane systems

In this paper, we analyse the pole-skipping phenomena of finite temperature Yang-Mills theory with quark flavors which is dual to D3-D7 brane systems in bulk. We also consider the external electric field in the boundary field theory which is dual to the world volume electric field on the D7 brane. We will work in the probe limit where the D7 branes do not back-react to the D3 brane background. In this scenario, we decode the characteristic parameters of the chaos namely, Lyapunov exponent $\lambda_{L}$ and butterfly velocity $v_b$ from the pole-skipping points by performing the near effective horizon analysis of the linearised Einstein equations. Unlike pure Yang-Mills, once charged quarks with a background electric field are added into the system, the characteristic parameters of the chaos show non-trivial dependence on the quark mass and external electric field. We have observed that $\lambda_{L}$ and $v_b$ decreases with increasing electric field. We further perform the pole-skipping analysis for the gauge invariant sound, shear, and tensor modes of the perturbation in the bulk and discuss their physical importance in the holographic context.