Calculus of Variations and Geometric Measure Theory

W. Borrelli - U. Morellini

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

created by borrelli on 24 Nov 2024

[BibTeX]

Submitted Paper

Inserted: 24 nov 2024
Last Updated: 24 nov 2024

Pages: 21
Year: 2024

ArXiv: 2411.14028 PDF

Abstract:

Graphene is a monolayer graphitic film where 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 electric fields, such as those induced by local 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.