I'm a "professeur junior" (CPJ) at the Laboratoire de Mathématiques d'Orsay, Université Paris-Saclay (bureau 2G1). Before Nov 2022, I was a researcher (CR) at Inria Paris, in the MATHERIALS project-team, located at CERMICS, Ecole des Ponts.
Research interests
Development and analysis of numerical methods in quantum chemistry and materials science
Publications
Preprints
- A. Levitt, D. Lundholm, N. Rougerie, Magnetic Thomas-Fermi theory for 2D abelian anyons (2025), preprint
- M-S. Dupuy, E. Letournel, A. Levitt, Linear response and resonances in adiabatic time-dependent density functional theory (2024), preprint
Journal articles
- T. Audinet, U. Morellini, A. Levitt, J. Toulouse, Vacuum polarization in a one-dimensional effective quantum-electrodynamics model, Journal of Physics A (2024), preprint
- É. Cancès, F. Faulstich, A. Kirsch, É. Letournel, A. Levitt, Some mathematical insights on Density Matrix Embedding Theory, Communications on Pure and Applied Mathematics (2024), preprint
- A. Castellano et al., Machine learning assisted canonical sampling (MLACS), Phys. Rev. B (2024), preprint
- É. Cancès, G. Kemlin, A. Levitt, A priori error analysis of linear and nonlinear periodic Schrödinger equations with analytic potentials, Journal of Scientific Computing (2023), preprint
- T. Nottoli, I. Giannı̀, A. Levitt, F. Lipparini, A robust, open-source implementation of the locally optimal block preconditioned conjugate gradient for large eigenvalue problems in quantum chemistry, Theoretical Chemistry Accounts (2023), preprint
- I. Duchemin, A. Levitt, Computing photoionization spectra in Gaussian basis sets, Journal of Chemical Physics (2023), preprint
- É. Cancès, M. Herbst, G. Kemlin, A. Levitt, B. Stamm, Numerical stability and efficiency of response property calculations in density functional theory, Letters in Mathematical Physics (2023), preprint
- J. Toulouse, K. Schwinn, F. Zapata, A. Levitt, É. Cancès, E. Luppi, Photoionization and core resonances from range-separated time-dependent density-functional theory for open-shell states: Example of the lithium atom, Journal of Chemical Physics (2022), preprint
- A. Castellano, F. Bottin, J. Bouchet, A. Levitt, G. Stoltz, Ab initio Canonical Sampling based on Variational Inference, Physical Review B letter (2022), preprint
- É. Cancès, G. Dusson, G. Kemlin, A. Levitt, Practical error bounds for properties in plane-wave electronic structure calculations, SIAM Journal on Scientific Computing (2022), preprint
- I. Duchemin, L. Genovese, E. Letournel, A. Levitt, S. Ruget, Efficient extraction of resonant states in systems with defects, Journal of Computational Physics (2022), preprint
- K. Schwinn, F. Zapata, A. Levitt, É. Cancès, E. Luppi, J. Toulouse, Photoionization and core resonances from range-separated density-functional theory: General formalism and example of the beryllium atom, Journal of Chemical Physics (2022), preprint
- M. Herbst, A. Levitt, A robust and efficient line search for self-consistent field iterations, Journal of Computational Physics (2021), preprint
- M-S. Dupuy, A. Levitt, Finite-size effects in response functions of molecular systems, SMAI Journal of Computational Mathematics (2021), preprint
- E. Bernard, M. Fathi, A. Levitt, G. Stoltz, Hypocoercivity with Schur complements, Annales Henri Lebesgue (2021), preprint
- É. Cancès, C. Fermanian Kammerer, A. Levitt, S. Siraj-Dine, Coherent electronic transport in periodic crystals, Annales Henri Poincaré (2021), preprint
- É. Cancès, G. Kemlin, A. Levitt, Convergence analysis of direct minimization and self-consistent iterations, SIAM Journal on Matrix Analysis and Applications (2021), preprint
- M. Herbst, A. Levitt, Black-box inhomogeneous preconditioning for self-consistent field iterations in density functional theory, Journal of Physics: Condensed Matter (2020), preprint
- A. Levitt, Screening in the finite-temperature reduced Hartree-Fock model, Archive for Rational Mechanics and Analysis (2020), preprint
- M. Herbst, A. Levitt, É. Cancès, A posteriori error estimation for the non-self-consistent Kohn-Sham equations, Faraday Discussions (2020), preprint
- É. Cancès, V. Ehrlacher, D. Gontier, A. Levitt, D. Lombardi, Numerical quadrature in the Brillouin zone for periodic Schrodinger operators, Numerische Mathematik (2019), preprint
- D. Gontier, A. Levitt, S. Siraj-Dine, Numerical construction of Wannier functions through homotopy, Journal of Mathematical Physics (2019), preprint
- A. Damle, A. Levitt, L. Lin, Variational formulation for Wannier functions with entangled band structure, SIAM MMS (2019), preprint
- H. Cornean, D. Gontier, A. Levitt, D. Monaco, Localised Wannier functions in metallic systems, Annales Henri Poincaré (2019), preprint
- A. Levitt, C. Ortner, Convergence and Cycling in Walker-type Saddle Search Algorithms, SIAM Journal on Numerical Analysis (2017), preprint
- X. Antoine, A. Levitt, Q. Tang, Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by the preconditioned nonlinear conjugate gradient method, Journal of Computational Physics 343 (2017), preprint
- É. Cancès, A. Levitt, G. Panati, G. Stoltz, Robust determination of maximally-localized Wannier functions, Phys. Rev. B, 95, 075114 (2017), preprint
- F. Aviat, A. Levitt, et. al., Truncated Conjugate Gradient (TCG): an optimal strategy for the analytical evaluation of the many-body polarization energy and forces in molecular simulations, J. Chem. Theory Comput., 13 (1), pp 180–190 (2017), preprint
- X. Gonze, F. Jollet et al., Recent developments in the ABINIT software package. Computer Physics Communications, 205:106-131 (2016), journal
- A. Levitt, M. Torrent, Parallel eigensolvers in plane-wave Density Functional Theory. Computer Physics Communications, 187:98–105 (2015), preprint
- A. Levitt, Solutions of the multiconfiguration Dirac-Fock equations. Reviews in Mathematical Physics, 26(07):1450014 (2014), preprint
- A. Levitt, Best constants in Lieb-Thirring inequalities: a numerical investigation. Journal of Spectral Theory 4.1 (2014), preprint
- A. Levitt, Convergence of gradient-based algorithms for the Hartree-Fock equations. ESAIM Math. Model. Numer. Anal. 46.06 (2012), preprint
- G. James, A. Levitt, C. Ferreira, Continuation of discrete breathers from infinity in a nonlinear model for DNA breathing. Applicable Analysis 89.9 (2010), preprint
Book chapters
- É. Cancès, A. Levitt, Y. Maday, C. Yang, Numerical Methods for Kohn–Sham Models: Discretization, Algorithms, and Error Analysis (2023), link
Proceedings
- M. Herbst, A. Levitt, É Cancès, DFTK: A Julian approach for simulating electrons in solids, Proceedings of the JuliaCon conferences 3.26 (2021), link
Teaching materials
- 2024 Calcul scientifique, M1
- 2023 Mathematical methods in quantum mechanics, M2
- 2021 Introduction to functional analysis, L3
- 2021 Practical scientific computing, L3
- 2019 Mini-course: Complex analysis for quantum physicists and chemists
- 2016- Analyse de Fourier, M1
Notes
These are unreviewed notes on basic techniques that I made for my own usage and that may (or may not) be helpful and/or correct. Use at your own risk and please report any mistakes or omissions.
- 2023 Van der Waals interactions from first principles
- 2022 What is the response function of an oscillatory system?
- 2021 The many disguises of the Schur complement
- 2020 The adjoint trick and automatic differentiation
- 2019 Ewald summation
Talks
Slides of selected talks at conferences or seminars that may or may not be clearer than papers. Again, no warranty.
- 2023 Review on numerical methods for quantum dynamics, Italian maths of QM online seminar, link
- 2022 Response functions and resonances, Collège de France, link
- 2021 Direct minimization vs SCF for nonlinear eigenspace problems, SIAM linear algebra, link
- 2020 Numerical analysis and properties of crystals, internal MATHERIALS seminar, link
- 2020 HDR defence link
- 2019 Screening and charge sloshing in crystals, ICIAM minisymposium link
- 2019 Wannier functions for insulators and metals, Copenhagen link
- 2018 Numerical integration in the Brillouin zone, Beijing link
Software
- DFTK.jl, the density functional toolkit
- Computation of Wannier functions
Misc links
- (very out of date...) resume
- HDR thesis and PhD thesis
Contact
antoine (dot) levitt (at) universite-paris-saclay (dot) fr