Mathematics of Density Functional Theory

Existence of minimizers in generalized Gross-Pitaevskii theory with the Lee-Huang-Yang correction

Author(s): Triay, Arnaud
Published in: https://hal.archives-ouvertes.fr/hal-02104829, Issue 2, 2019
Publisher: Arxiv

Existence of minimizers in generalized Gross-Pitaevskii theory with the Lee-Huang-Yang correction

Author(s): Triay, Arnaud
Published in: ArXiV preprint, 2019
Publisher: ArXiV
DOI: 10.48550/arxiv.1904.10672

Analysis of the one dimensional inhomogeneous Jellium model with the Birkhoff-Hopf Theorem

Author(s): Ducatez, Raphael
Published in: 2018, Issue 1, 2018
Publisher: arxiv

Universal Functionals in Density Functional Theory

Author(s): Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert
Published in: ArXiV preprint, 2019
Publisher: ArXiV
DOI: 10.48550/arxiv.1912.10424

Differentiability of the van der Waals interaction between two atoms

Author(s): Anapolitanos, Ioannis; Lewin, Mathieu; Roth, Matthias
Published in: ArXiV preprint, 2019
Publisher: ArXiV
DOI: 10.48550/arxiv.1902.06683

Grand-Canonical Optimal Transport

Author(s): Simone Di Marino, Mathieu Lewin, Luca Nenna
Published in: ArXiV preprint, 2022
Publisher: ArXiV
DOI: 10.48550/arxiv.2201.06859

Analysis of the one dimensional inhomogeneous Jellium model with the Birkhoff-Hopf Theorem

Author(s): Ducatez, Raphael
Published in: ArXiV preprint, Issue 1, 2018
Publisher: ArXiV
DOI: 10.48550/arxiv.1806.07681

Derivation of the time-dependent Gross-Pitaevskii equation for the dipolar gases

Author(s): Triay, Arnaud
Published in: ArXiV preprint, 2019
Publisher: ArXiV
DOI: 10.48550/arxiv.1904.04000

Dirac-Coulomb operators with infinite mass boundary conditions in sectors

Author(s): Biagio Cassano; Fabio Pizzichillo; Matteo Gallone
Published in: J. Math. Phys., Issue 9, 2022, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/5.0089526

Dirac–Coulomb operators with general charge distribution I. Distinguished extension and min-max formulas

Author(s): Esteban, Maria J.; Lewin, Mathieu; Séré, Eric
Published in: Annales Henri Lebesgue, Issue 4, 2021, ISSN 2644-9463
Publisher: None
DOI: 10.5802/ahl.106

Boundary triples for the Dirac operator with Coulomb-type spherically symmetric perturbations

Author(s): Biagio Cassano, Fabio Pizzichillo
Published in: Journal of Mathematical Physics, Issue 60/4, 2019, Page(s) 041502, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/1.5063986

Improved Lieb-Oxford bound on the indirect and exchange energies

Author(s): Mathieu Lewin, Elliott H. Lieb, and Robert Seiringer
Published in: Lett. Math. Phys., Issue 112, 2022, Page(s) 92, ISSN 1573-0530
Publisher: springer
DOI: 10.1007/s11005-022-01584-5

Dirac–Coulomb operators with general charge distribution II. The lowest eigenvalue

Author(s): Maria J. Esteban; Mathieu Lewin; Eric Séré
Published in: https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/plms.12396, Issue 3, 2021, ISSN 1460-244X
Publisher: None
DOI: 10.1112/plms.12396

The reduced Hartree-Fock model with self-generated magnetic fields

Author(s): David Gontier, Salma Lahbabi
Published in: Journal of Mathematical Physics, Issue 60/8, 2019, Page(s) 081902, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/1.5100919

Classical field theory limit of many-body quantum Gibbs states in 2D and 3D

Author(s): Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie
Published in: Inventiones mathematicae, 2021, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-020-01010-4

Building Kohn-Sham potentials for ground and excited states

Author(s): Louis Garrigue
Published in: Archive for Rational Mechanics and Analysis, Issue 245, 2022, Page(s) 949-1003, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.48550/arxiv.2101.01127

Convergence analysis of adaptive DIIS algorithms with application to electronic ground state calculations

Author(s): Maxime Chupin; Mi-Song Dupuy; Guillaume Legendre; Eric Séré
Published in: 2020, Issue 4, 2020, ISSN 2804-7214
Publisher: EDP Sciences
DOI: 10.1051/m2an/2021069

The Hartree and Vlasov equations at positive density

Author(s): Mathieu Lewin, Julien Sabin
Published in: Communications in Partial Differential Equations, Issue 45/12, 2020, Page(s) 1702-1754, ISSN 0360-5302
Publisher: Marcel Dekker Inc.
DOI: 10.1080/03605302.2020.1803355

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

Author(s): Louis Garrigue
Published in: Comm Math Phys, Issue 4, 2021, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-021-04140-9

A forward-backward random process for the spectrum of 1D Anderson operators

Author(s): Raphael Ducatez
Published in: Electronic Communications in Probability, Issue 24/0, 2019, ISSN 1083-589X
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/19-ecp232

Coulomb and Riesz gases: The known and the unknown

Author(s): Mathieu Lewin
Published in: Journal of Mathematical Physics, Issue 63, 2022, Page(s) pp.061101, ISSN 1089-7658
Publisher: AIP
DOI: 10.1063/5.0086835

Classical Density Functional Theory: Representability and Universal Bounds

Author(s): Michal Jex, Mathieu Lewin, Peter S. Madsen
Published in: Journal of Statistical Physics, Issue 190, 2023, ISSN 1572-9613
Publisher: Springer
DOI: 10.1007/s10955-023-03086-7

Self-adjointness of two-dimensional Dirac operators on corner domains

Author(s): Fabio Pizzichillo; Hanne Van Den Bosch
Published in: JSP, Issue 5, 2019, ISSN 1664-039X
Publisher: EMS
DOI: 10.4171/jst/365

The Scott Correction in Dirac–Fock Theory

Author(s): Søren Fournais, Mathieu Lewin, Arnaud Triay
Published in: Communications in Mathematical Physics, Issue 378/1, 2020, Page(s) 569-600, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-020-03781-6

The diatomic Hartree model at dissociation

Author(s): Cazalis, Jean
Published in: Nonlinearity, Issue 35, 2022, Page(s) 2633, ISSN 1361-6544
Publisher: IOP
DOI: 10.1088/1361-6544/ac665a

A remark on the attainable set of the Schrödinger equation

Author(s): Jonas Lampart
Published in: Evolution Equations & Control Theory, Issue 0/0, 2019, Page(s) 0-0, ISSN 2163-2480
Publisher: AIMS
DOI: 10.3934/eect.2020075

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

Author(s): Louis Garrigue
Published in: Mathematical Physics, Analysis and Geometry, Issue 21/3, 2018, ISSN 1385-0172
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11040-018-9287-z

Lower bound on the Hartree-Fock energy of the electron gas

Author(s): David Gontier, Christian Hainzl, Mathieu Lewin
Published in: Physical Review A, Issue 99/5, 2019, ISSN 2469-9926
Publisher: APS
DOI: 10.1103/physreva.99.052501

Existence of Hartree–Fock excited states for atoms and molecules

Author(s): Mathieu Lewin
Published in: Letters in Mathematical Physics, 2018, ISSN 0377-9017
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11005-017-1019-y

Domains for Dirac–Coulomb min-max levels

Author(s): Maria Esteban, Mathieu Lewin, Éric Séré
Published in: Revista Matemática Iberoamericana, 2019, ISSN 0213-2230
Publisher: Universidad Autonoma de Madrid
DOI: 10.4171/rmi/1074

Semi-classical limit of the Levy–Lieb functional in Density Functional Theory

Author(s): Mathieu Lewin
Published in: Comptes Rendus Mathematique, Issue 356/4, 2018, Page(s) 449-455, ISSN 1631-073X
Publisher: Elsevier Masson
DOI: 10.1016/j.crma.2018.03.002

The local density approximation in density functional theory

Author(s): Mathieu Lewin, Elliott H. Lieb, Robert Seiringer
Published in: Pure and Applied Analysis, Issue 2/1, 2020, Page(s) 35-73, ISSN 2578-5885
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/paa.2020.2.35

Statistical mechanics of the uniform electron gas

Author(s): Mathieu Lewin, Elliott H. Lieb, Robert Seiringer
Published in: Journal de l’École polytechnique — Mathématiques, Issue 5, 2018, Page(s) 79-116, ISSN 2270-518X
Publisher: Ecole Polytechnique
DOI: 10.5802/jep.64

Derivation of the Dipolar Gross--Pitaevskii Energy

Author(s): Arnaud Triay
Published in: SIAM Journal on Mathematical Analysis, Issue 50/1, 2018, Page(s) 33-63, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/17m112378x

Compactness of Molecular Reaction Paths in Quantum Mechanics

Author(s): Ioannis Anapolitanos, Mathieu Lewin
Published in: Archive for Rational Mechanics and Analysis, Issue 236/2, 2020, Page(s) 505-576, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-019-01475-5

Spin Symmetry Breaking in the Translation-Invariant Hartree--Fock Electron Gas

Author(s): David Gontier, Mathieu Lewin
Published in: SIAM Journal on Mathematical Analysis, Issue 51/4, 2019, Page(s) 3388-3423, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m1243142

Semi-classical limit of large fermionic systems at positive temperature

Author(s): Mathieu Lewin, Peter S. Madsen, Arnaud Triay
Published in: Journal of Mathematical Physics, Issue 60/9, 2019, Page(s) 091901, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/1.5094397

Hohenberg–Kohn Theorems for Interactions, Spin and Temperature

Author(s): Louis Garrigue
Published in: Journal of Statistical Physics, Issue 177/3, 2019, Page(s) 415-437, ISSN 0022-4715
Publisher: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10955-019-02365-6

Derivation of renormalized Gibbs measures from equilibrium many-body quantum Bose gases

Author(s): Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie
Published in: Journal of Mathematical Physics, Issue 60/6, 2019, Page(s) 061901, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/1.5094331

The Nonlinear Schrödinger Equation for Orthonormal Functions II: Application to Lieb–Thirring Inequalities

Author(s): Rupert L. Frank; Rupert L. Frank; David Gontier; Mathieu Lewin
Published in: CMP, Issue 9, 2019, ISSN 1432-0916
Publisher: Springer
DOI: 10.1007/s00220-021-04039-5

The Nonlinear Schrödinger Equation for Orthonormal Functions: Existence of Ground States

Author(s): David Gontier; Mathieu Lewin; Faizan Q. Nazar
Published in: ISSN: 0003-9527, Issue 2, 2019, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-021-01634-7

DFT Exchange: Sharing Perspectives on the Workhorse of Quantum Chemistry and Materials Science

Author(s): Andrew M. Teale; Trygve Helgaker; Andreas Savin; Carlo Adamo; Bálint Aradi; Alexei V. Arbuznikov; Paul W. Ayers; Evert Jan Baerends; Vincenzo Barone; Patrizia Calaminici; Eric Cancès; Emily A. Carter; Pratim Kumar Chattaraj; Henry Chermette; Ilaria Ciofini; T. Daniel Crawford; Frank De Proft; John F. Dobson; Claudia Draxl; Thomas Frauenheim; Emmanuel Fromager; Patricio Fuentealba; Laura Gagliard
Published in: Physical Chemistry Chemical Physics, Issue 15, 2022, ISSN 1463-9084
Publisher: none
DOI: 10.1039/d2cp02827a

The double-power nonlinear Schrödinger equation and its generalizations: uniqueness, non-degeneracy and applications

Author(s): Mathieu Lewin, Simona Rota Nodari
Published in: Calculus of Variations and Partial Differential Equations, Issue 59/6, 2020, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-020-01863-w

Floating Wigner crystal with no boundary charge fluctuations

Author(s): Mathieu Lewin, Elliott H. Lieb, Robert Seiringer
Published in: Physical Review B, Issue 100/3, 2019, ISSN 2469-9950
Publisher: APS
DOI: 10.1103/physrevb.100.035127

Fast Diffusion leads to partial mass concentration in Keller-Segel type stationary solutions

Author(s): Carrillo, José A.; Delgadino, Matias G.; Frank, Rupert L.; Lewin, Mathieu
Published in: EISSN: 0218-2025, Issue 11, 2022, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/s021820252250018x

Optimizers for the finite-rank Lieb-Thirring inequality

Author(s): Frank, Rupert L.; Gontier, David; Lewin, Mathieu
Published in: Amer. J. Math., 2023, ISSN 1080-6377
Publisher: Johns Hopkins Univ. Press
DOI: 10.48550/arxiv.2109.05984

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

Author(s): Garrigue, Louis
Published in: Doc. Math., Issue 25, 2020, Page(s) 869-898, ISSN 1431-0635
Publisher: Deutsche Mathematiker-Vereinigung
DOI: 10.25537/dm.2020v25.869-898

The periodic Lieb-Thirring inequality

Author(s): Frank, Rupert L.; Gontier, David; Lewin, Mathieu
Published in: Partial Differential Equations, Spectral Theory, and Mathematical Physics. The Ari Laptev Anniversary Volume, Issue 4, 2021
Publisher: EMS Press
DOI: 10.4171/ecr/18

Blow-Up Profile of Rotating 2D Focusing Bose Gases

Author(s): Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie
Published in: Macroscopic Limits of Quantum Systems - Munich, Germany, March 30 - April 1, 2017, Issue 270, 2018, Page(s) 145-170, ISBN 978-3-030-01601-2
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-01602-9_7

Dirac operators and shell interactions: a survey

Author(s): Thomas Ourmières-Bonafos; Fabio Pizzichillo
Published in: https://hal.archives-ouvertes.fr/hal-02016328, Issue 4, 2020, ISBN 978-3-030-60453-0
Publisher: 2020
DOI: 10.1007/978-3-030-60453-0_5

The interacting 2D Bose gas and nonlinear Gibbs measures

Author(s): Lewin , Mathieu; Nam , Phan Thành; Rougerie , Nicolas
Published in: Oberwolfach Reports, 2018
Publisher: EMS

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