Global well-posedness in a Hartree-Fock model for graphene
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.
Cite
@article{arxiv.2411.14028,
title = {Global well-posedness in a Hartree-Fock model for graphene},
author = {William Borrelli and Umberto Morellini},
journal= {arXiv preprint arXiv:2411.14028},
year = {2025}
}
Comments
23 pages. The case of time-dependent external density has been included. Minor corrections