27 citations · 178 across the 25 of their papers we have counts for
27 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-regularised Dirac field coupled to electromagnetic fields at thermal equilibrium
William Borrelli, Umberto Morellini
In this paper we consider a model for the Dirac field in a classical electromagnetic field at thermal equilibrium. 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 di…
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…
On the nodal set of solutions to Dirac equations
William Borrelli, Ruijun Wu
Motivated by various geometric problems, we study the nodal set of solutions to Dirac equations on manifolds, of general form. We prove that such set has Hausdorff dimension less t…
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…