5 papers
On two-dimensional Dirac operators with critical delta-shell interactions
William Borrelli, Pietro Carimati, Davide Fermi
We study two-dimensional Dirac operators with singular interactions of electrostatic and Lorentzscalar type, supported either on a straight line or a circle. For certain critical v…
The Pauli-Villars-regularized Dirac vacuum in electromagnetic fields at positive temperature
William Borrelli, Umberto Morellini
In this paper we consider a model of the Dirac vacuum in classical electromagnetic fields at positive temperature. We adopt the Pauli-Villars regularisation technique in order to p…
Dirac solitons in one-dimensional nonlinear Schrödinger equations
William Borrelli, Elena Danesi, Simone Dovetta +1
In this paper we study a family of one-dimensional stationary cubic nonlinear Schrödinger (NLS) equations with periodic potentials and linear part displaying Dirac points in the d…
Global well-posedness in a Hartree-Fock model for graphene
William Borrelli, Umberto Morellini
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 condense…
Pauli Hamiltonians with an Aharonov-Bohm Flux
William Borrelli, Michele Correggi, Davide Fermi
We study a two-dimensional Pauli operator describing a charged quantum particle with spin moving on a plane in presence of an orthogonal Aharonov-Bohm magnetic flux. We class…