29 citations · 110 across the 12 of their papers we have counts for
13 papers
A sharp gradient-corrected Lieb--Thirring inequality in one dimension with applications to density functional theory
Thiago Carvalho Corso, Louis Garrigue
We first prove a sharp Lieb-Thirring inequality with semi-classical constant and gradient correction in one dimension. In the periodic setting, the corresponding inequality also in…
Some effective operators for graphene monolayer superlattices, from variational perturbation theory
Louis Garrigue
Our goal is to provide precise effective operators for monolayer graphene at Fermi energy. We consider the microscopic potential created by a lattice, and add a macroscopic potenti…
On reduced basis methods for eigenvalue problems, and on its coupling with perturbation theory
Louis Garrigue, Benjamin Stamm
In this article, we study eigenvalue problems associated to self-adjoint operators and their approximation obtained by subspace projection, as used in the reduced basis method for…
Coefficients of almost-degenerate density matrix perturbation theory for eigenvalue problems
Charles Arnal, Louis Garrigue
We investigate almost-degenerate perturbation theory of eigenvalue problems, using spectral projectors, also named density matrices. When several eigenvalues are close to each othe…
A multipoint perturbation formula for eigenvalue problems
Geneviève Dusson, Louis Garrigue, Benjamin Stamm
Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known…
A simple derivation of moiré-scale continuous models for twisted bilayer graphene
Eric Cancès, Louis Garrigue, David Gontier
We provide a formal derivation of a reduced model for twisted bilayer graphene (TBG) from Density Functional Theory. Our derivation is based on a variational approximation of the T…
Mixed state representability of entropy-density pairs
Louis Garrigue
We show the representability of density-entropy pairs with canonical and grand-canonical states, and we provide bounds on the kinetic energy of the representing states.
Second-order homogenization of periodic Schrödinger operators with highly oscillating potentials
Éric Cancès, Louis Garrigue, David Gontier
We consider the homogenization at second-order in of -periodic Schrödinger operators with rapidly oscillating potentials of the form $H^\varepsilon =-Δ+ \…
Building Kohn-Sham potentials for ground and excited states
Louis Garrigue
We analyze the inverse problem of Density Functional Theory using a regularized variational method. First, we show that given and a target density , there exist potentials h…
Some properties of the potential-to-ground state map in quantum mechanics
Louis Garrigue
We analyze the map from potentials to the ground state in static many-body quantum mechanics. We first prove that the space of binding potentials is path-connected. Then we show th…
Hohenberg-Kohn theorems for interactions, spin and temperature
Louis Garrigue
We prove Hohenberg-Kohn theorems for several models of quantum mechanics. First, we show that the pair correlation function of any ground state contains the information of the inte…
Unique continuation for many-body Schrödinger operators and the Hohenberg-Kohn theorem. II. The Pauli Hamiltonian
Louis Garrigue
We prove the strong unique continuation property for many-body Pauli operators with external potentials, interaction potentials and magnetic fields in $L^p\loc(\R^d)$, and with mag…
Unique continuation for many-body Schrödinger operators and the Hohenberg-Kohn theorem
Louis Garrigue
We prove the strong unique continuation property for many-body Schrödinger operators with an external potential and an interaction potential both in ,…