Thermal Diffusion and Quantum Chaos in Neutral Magnetized Plasma

TL;DR

This work investigates the link between thermal diffusion and quantum chaos in a neutral magnetized plasma using a holographic magnetic brane. By combining magnetohydrodynamics and a holographic calculation, it demonstrates that the thermal diffusion constant obeys Blake's bound and that the diffusive diffusion is captured by horizon data, with the ratio $λ_L D_T / v_B^2$ decreasing toward $1/2$ as the magnetic field strengthens. It also uncovers a special point in the energy-density correlator, revealing pole-skipping phenomena in the magnetized background and illustrating how chaos quantities constrain transport in anisotropic holographic plasmas. The results illuminate the interplay between diffusion, chaos, and momentum damping in strongly coupled systems and point to extensions to charged backgrounds and higher dimensions.

Abstract

We calculate the thermal diffusion constant $D_T$ and butterfly velocity $v_B$ in neutral magnetized plasma using holographic magnetic brane background. We find the thermal diffusion constant satisfies Blake's bound. The constant in the bound $D_T2πT/v_B^2$ 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 Lyapunov exponent and butterfly velocity on which pole-skipping phenomenon occurs.

Figures (3)

• Figure 1: The ratio ${\lambda}_LD_T/v_B^2$ 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 dimensionally reduced metric $BTZ\times R^2$ in the large $B$ limit.
• Figure 2: The ratio ${\lambda}_LD_T/v_B^2$ approaches 1 when $B/T^2\approx33.67$. We expect near this region hydrodynamics is a good approximation.
• Figure 3: The ratio ${\lambda}_LD_T/v_B^2$ as a function of $B/T^2$. The dashed line represents constant $1$. The bound is a monotonically decreasing function with an asymptotic value of $1$.