English

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

Mathematical Physics 2025-05-16 v3 Mesoscale and Nanoscale Physics Analysis of PDEs math.MP

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.

Keywords

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