Thermal diffusion and quantum chaos in neutral magnetized plasma

We calculate the thermal diffusion constant $D_T$ and butterfly velocity $v_B$ in neutral magnetized plasma using a holographic magnetic brane background. We find that the thermal diffusion constant satisfies Blake’s bound. The constant in the bound $D_{T}2\pi T/v_B^2$ is a decreasing function of magnetic field. It approaches one half in the large-magnetic-field limit. We also find the existence of a special point defined by the Lyapunov exponent and butterfly velocity at which the pole-skipping phenomenon occurs.

Figure 1

The ratio ${\lambda }_L{D}_T/v_B^2$ as a function of $B/T^2$. It is a monotonically decreasing function with an asymptotic value of $1/2$. The asymptotic value can be obtained from the dimensionally reduced metric $BTZ\times R^2$ in the large-$B$ limit.

Figure 2

The ratio ${\lambda }_L{D}_T/v_B^2$ approaches 1 when $B/T^2\approx 33.67$. We expect that near this region hydrodynamics is a good approximation.

Figure 3

The ratio ${\lambda }_L{D}_T/v_B^2$ as a function of $B/T^2$. The dashed line represents a constant value of 1. The bound is a monotonically decreasing function with an asymptotic value of 1.