42 citations · 622 across the 80 of their papers we have counts for
55 papers · 1 filter
Almost invariant subspaces in the topologically non-trivial setting: a pedestrian approach
Horia Cornean, Gabriele Peluso, Mikkel Hviid Thorn
We present a self-contained, algorithmic construction of almost invariant subspaces [Panati et al. (2003), De Nittis and Panati (2010), Freund and Teufel (2016)] for Hofstadter-lik…
Magnetic Weyl Super Calculus: Schatten-class properties, commutator criterion, and complete positivity
Horia D. Cornean, Mikkel H. Thorn
We combine our previous results on magnetic pseudo-differential operators for Hörmander symbols dominated by tempered weights [arXiv:2511.07184] with the magnetic Weyl super calcul…
Universality of the Hall conductivity for a weakly interacting magnetic fermionic gas in the Hartree-Fock approximation
Horia D. Cornean, Emanuela Laura Giacomelli, Domenico Monaco +1
We consider a two-dimensional gas of interacting fermions in presence of an external constant magnetic field: the system is extended and homogeneous, and thus assumed to be invaria…
A fresh look at the Peierls-Onsager substitution
Horia D. Cornean, Bernard Helffer, Radu Purice
We formulate a general version of the Peierls-Onsager substitution for a finite family of Bloch eigenvalues under a local spectral gap hypothesis, via strongly localized tight-fram…
Green's functions for magnetic Dirac operators and bulk-edge correspondence
Jean-Marie Barbaroux, Horia D. Cornean, Loïc Le Treust +2
We study the resolvent kernel (Green's function) of magnetic Dirac operators on a half-plane with boundary conditions interpolating between infinite mass and zigzag cases, excludin…
On the magnetic perturbation theory for Chern insulators
Horia D. Cornean, Massimo Moscolari
The gauge covariant magnetic perturbation theory is tailored for one-body Schrödinger operators perturbed by long-range magnetic fields. In this work we present a self-contained ex…
A rigorous Peierls-Onsager effective dynamics for semimetals in long-range magnetic fields
Horia D. Cornean, Bernard Helffer, Radu Purice
We consider periodic (pseudo)differential {elliptic operators of Schrödinger type} perturbed by weak magnetic fields not vanishing at infinity, and extend our previous analysis in…
Magnetic Dirac systems: Violation of bulk-edge correspondence in the zigzag limit
Loïc Le Treust, Jean-Marie Barbaroux, Horia D. Cornean +2
We consider a Dirac operator with constant magnetic field defined on a half-plane with boundary conditions that interpolate between infinite mass and zigzag. By a detailed study of…
On the self-consistent Landauer-Büttiker formalism
Horia D. Cornean, Giovanna Marcelli
We provide sufficient conditions such that the time evolution of a mesoscopic tight-binding open system with a local Hartree-Fock non-linearity converges to a self-consistent non-e…
Sharp spectral stability for a class of singularly perturbed pseudo-differential operators
Horia D. Cornean, Radu Purice
Let be a real Hörmander symbol of the type , let be a smooth function with all its derivatives globally bounded, and let…
Bulk-edge correspondence for unbounded Dirac-Landau operators
Horia D. Cornean, Massimo Moscolari, Kasper S. Sørensen
We consider two-dimensional unbounded magnetic Dirac operators, either defined on the whole plane, or with infinite mass boundary conditions on a half-plane. Our main results use t…
Discrete approximations to Dirac operators and norm resolvent convergence
Horia D. Cornean, Henrik Garde, Arne Jensen
We consider continuous Dirac operators defined on , , together with various discrete versions of them. Both forward-backward and symmetric finite diffe…
From orbital magnetism to bulk-edge correspondence
Horia D. Cornean, Massimo Moscolari, Stefan Teufel
By extending the gauge covariant magnetic perturbation theory to operators defined on half-planes, we prove that for random ergodic magnetic Schrödinger operators, the zero-te…
On the two-dimensional quantum confined Stark effect in strong electric fields
Horia Cornean, David Krejcirik, Thomas Garm Pedersen +2
We consider a Stark Hamiltonian on a two-dimensional bounded domain with Dirichlet boundary conditions. In the strong electric field limit we derive, under certain local convexity…
Spectral analysis near a Dirac type crossing in a weak non-constant magnetic field
Horia D. Cornean, Bernard Helffer, Radu Purice
This is the last paper in a series of three in which we have studied the Peierls substitution in the case of a weak magnetic field. Here we deal with two Bloch eigenvalues whi…
Gap opening in the spectrum of some Dirac-like pseudo-differential operators
J. -M. Barbaroux, H. D. Cornean, S. Zalczer
In this paper, we study the opening of a spectral gap for a class of 2-dimensional periodic Hamiltonians which include those modelling multilayer graphene. The kinetic part of the…
A Dyson equation for non-equilibrium Green's functions in the partition-free setting
H. D. Cornean, V. Moldoveanu, C. -A. Pillet
We consider a small interacting sample coupled to several non-interacting leads. Initially, the system is at thermal equilibrium. At some instant the system is set into the s…
Localization for gapped Dirac Hamiltionians with random perturbations: Application to graphene antidot lattices
Jean-Marie Barbaroux, Horia D. Cornean, Sylvain Zalczer
In this paper we study random perturbations of first order elliptic operators with periodic potentials. We are mostly interested in Hamiltonians modeling graphene antidot lattices…
Resolvent convergence to Dirac operators on planar domains
Jean-Marie Barbaroux, Horia D. Cornean, Loïc Le Treust +1
Consider a Dirac operator defined on the whole plane with a mass term of size m supported outside a domain Omega. We give a simple proof for the norm resolvent convergence, as m go…
Beyond Diophantine Wannier diagrams: Gap labelling for Bloch-Landau Hamiltonians
Horia D. Cornean, Domenico Monaco, Massimo Moscolari
It is well known that, given a purely magnetic Landau Hamiltonian with a constant magnetic field which generates a magnetic flux per unit area, then any spectral islan…
Impurity-bound excitons in one and two dimensions
Horia Cornean, Hynek Kovarik, Thomas G. Pederesen
We study three-body Schrödinger operators in one and two dimensions modelling an exciton interacting with a charged impurity. We consider certain classes of multiplicative interact…
Localised Wannier functions in metallic systems
Horia Cornean, David Gontier, Antoine Levitt +1
The existence and construction of exponentially localised Wannier functions for insulators is a well-studied problem. In comparison, the case of metallic systems has been much less…
Peierls' substitution for low lying spectral energy windows
Horia D. Cornean, Bernard Helffer, Radu Purice
We consider a magnetic Schrödinger operator perturbed by a weak magnetic field which slowly varies around a positive mean. In a previous paper we proved the appearance of a `L…
A mathematical account of the NEGF formalism
H. D. Cornean, V. Moldoveanu, C. -A. Pillet
The main goal of this paper is to put on solid mathematical grounds the so-called Non-Equilibrium Green's Function (NEGF) transport formalism for open systems. In particular, we de…