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arXiv · 2411.14028

Global well-posedness in a Hartree-Fock model for graphene

William Borrelli·Umberto Morellini
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Abstract

Graphene is a monolayer graphitic film in which electrons behave like two-dimensional Dirac fermions without mass. Its study has attracted a wide interest in the domain of condensed matter physics. In particular, it represents an ideal system to test the comprehension of 2D massless relativistic particles in a laboratory, the Fermi velocity being 300 times smaller than the speed of light. In this work, we present a global well-posedness result for graphene in the Hartree- Fock approximation. The model allows to describe the time evolution of graphene in the presence of external time-dependent electric potentials, such as those induced by local charge defects in the monolayer of carbon atoms. Our approach is based on a well established non-perturbative framework originating from the study of three-dimensional quantum electrodynamics.

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William Borrelli, Umberto Morellini. 2024-11-21. Global well-posedness in a Hartree-Fock model for graphene. https://arxiv.org/abs/2411.14028

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