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Unique Continuation for Many-Body Schrödinger Operators and the Hohenberg-Kohn Theorem

- Louis Garrigue
- MathematicsMathematical Physics, Analysis and Geometry
- 20 April 2018

We prove the strong unique continuation property for many-body Schrödinger operators with an external potential and an interaction potential both in Llocp(ℝd)$L^{p}_{\text {loc}}(\mathbb {R}^{d})$,… Expand

Hohenberg–Kohn Theorems for Interactions, Spin and Temperature

- Louis Garrigue
- MathematicsJournal of Statistical Physics
- 7 June 2019

We prove Hohenberg-Kohn theorems for several models of quantum mechanics. First, we show that for possibly degenerate systems of several types of particles, the pair correlation functions of any… Expand

Unique continuation for many-body Schr\"odinger operators and the Hohenberg-Kohn theorem. II. The Pauli Hamiltonian

- Louis Garrigue
- Mathematics
- 10 January 2019

We prove the strong unique continuation property for many-body Pauli operators with external potentials, interaction potentials and magnetic fields in $L^p_{\rm loc}(\mathbb{R}^d)$, and with magnetic… Expand

Building Kohn–Sham Potentials for Ground and Excited States

- Louis Garrigue
- MathematicsArchive for Rational Mechanics and Analysis
- 4 January 2021

. We analyze the inverse problem of Density Functional Theory using a regularized variational method. First, we show that given k and a target density ρ , there exist potentials having k th bound… Expand

Some Properties of the Potential-to-Ground State Map in Quantum Mechanics

- Louis Garrigue
- MathematicsCommunications in Mathematical Physics
- 7 December 2020

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 that the map is… Expand

Second-order homogenization of periodic Schr\"odinger operators with highly oscillating potentials

- 'Eric Cances, Louis Garrigue, D. Gontier
- Mathematics
- 22 December 2021

We consider the homogenization at second-order in ε of Lperiodic Schrödinger operators with rapidly oscillating potentials of the form H = −∆+ε−1v(x, ε−1x)+W (x) on L(R), where L is a Bravais lattice… Expand

Mixed state representability of entropy-density pairs

- Louis Garrigue
- Physics
- 30 March 2022

One of the basic questions arising in the variational approach of manybody quantum mechanics, and raised by Coleman [2], is whether some quantities like one-body or two-body density matrices, or… Expand

A simple derivation of moir\'e-scale continuous models for twisted bilayer graphene

- É. Cancès, Louis Garrigue, D. Gontier
- Physics
- 12 June 2022

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 TBG Kohn-Sham… Expand