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arXiv · 1906.07123

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

Egor I. Kiselev·Jörg Schmalian
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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.

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Egor I. Kiselev, Jörg Schmalian. 2019-06-17. L\'evy flights and hydrodynamic superdiffusion on the Dirac cone of Graphene. https://doi.org/10.1103/physrevlett.123.195302

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