Title: Hierarchy of Information Scrambling, Thermalization, and Hydrodynamic Flow in Graphene,
Abstract: We determine the information scrambling rate $\lambda_{L}$ due to
electron-electron Coulomb interaction in graphene. $\lambda_{L}$ characterizes
the growth of chaos and has been argued to give information about the
thermalization and hydrodynamic transport coefficients of a many-body system.
We demonstrate that $\lambda_{L}$ behaves for strong coupling similar to
transport and energy relaxation rates. A weak coupling analysis, however,
reveals that scrambling is related to dephasing or single particle relaxation.
Furthermore, $\lambda_{L}$ is found to be parametrically larger than the
collision rate relevant for hydrodynamic processes, such as electrical
conduction or viscous flow, and the rate of energy relaxation, relevant for
thermalization. Thus, while scrambling is obviously necessary for
thermalization and quantum transport, it does generically not set the time
scale for these processes. In addition we derive a quantum kinetic theory for
information scrambling that resembles the celebrated Boltzmann equation and
offers a physically transparent insight into quantum chaos in many-body
systems.