# L\'evy flights and hydrodynamic superdiffusion on the Dirac cone of Graphene

## TL;DR

This paper demonstrates that electron collisions in graphene at neutrality point lead to superdiffusive behavior of collective excitations, modeled as Le9vy flights in momentum space, with broader implications for quantum-critical systems.

## Contribution

It introduces a fractional Fokker-Planck equation to describe superdiffusion in graphene, linking electron collisions to Le9vy flights and highlighting their significance in quantum-critical dynamics.

## Key findings

- Electron-electron collisions cause superdiffusive collective excitations.
- Superdiffusion modeled as Le9vy flights in momentum space.
- Implications for out-of-equilibrium quantum-critical systems.

## Abstract

We show that hydrodynamic collision processes of graphene at the neutrality point can be described in terms of a Fokker-Planck equation with fractional derivative, corresponding to a L\'evy flight in momentum space. Thus, electron-electron collisions give rise to frequent small-angle scattering processes that are interrupted by rare large-angle events. The latter give rise to superdiffusive dynamics of collective excitations. We argue that such superdiffusive dynamics is of more general importance to the out-of-equilibrium dynamics of quantum-critical systems.