Antoine Levitt

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<title>Antoine Levitt</title>

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![Me](photopetit.jpg)

I'm a professor at the Laboratoire de Mathématiques d'Orsay, Université Paris-Saclay (bureau 2G1). 

Contact me at antoine (dot) levitt (at) universite-paris-saclay (dot) fr.

## Publications

#### Nonprints
AI-generated papers that I'm confident are correct and interesting, but did not write and will not submit for publication. If you're interested in discussing them, feel free to get in touch!

* The Liouvillian of a gapped crystal and the decay of correlations (2026), [nonprint](nonprints/liouvillian.pdf)
* Scattering by periodic obstacles: complex deformation with integral equations (2026), [nonprint](nonprints/KKR.pdf)

#### Preprints
* C. Barat, A. Levitt, M. Torrent, Preconditioning Magnetic Systems in Kohn-Sham Density Functional Theory (2026), [preprint](https://hal.science/hal-05658631)
* E. Lallinec, A. Levitt, Numerical methods for the computation of densities of states of periodic operators (2026), [preprint](https://hal.science/hal-05572898)
* É. Cancès, A. Levitt, J. Thomas, Decay of Interatomic Force Constants in the Reduced Hartree-Fock Model (2025), [preprint](https://arxiv.org/abs/2506.09595)

#### Journal articles
* A. Levitt, D. Lundholm, N. Rougerie, Magnetic Thomas-Fermi theory for 2D abelian anyons (2026), SciPost Physics Core [preprint](https://hal.science/view/index/docid/5037710)
* X. Gonze, C. Tantardini, A. Levitt, Low-temperature behavior of density-functional theory for metals based on density-functional perturbation theory and Sommerfeld expansion (2025), Physical Review B (2026), [preprint](https://arxiv.org/abs/2512.14438)
* M-S. Dupuy, E. Letournel, A. Levitt, Linear response and resonances in adiabatic time-dependent density functional theory, Annales Henri Poincaré (2025), [preprint](https://arxiv.org/abs/2408.00009)
* T. Audinet, U. Morellini, A. Levitt, J. Toulouse, Vacuum polarization in a one-dimensional effective quantum-electrodynamics model, Journal of Physics A (2024), [preprint](https://hal.science/hal-04752718)
* 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](https://arxiv.org/abs/2305.16472)
* 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](https://hal.inria.fr/hal-03692851)
* 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](https://hal.science/hal-04094087)
* I. Duchemin, A. Levitt, Computing photoionization spectra in Gaussian basis sets, Journal of Chemical Physics (2023), [preprint](https://inria.hal.science/hal-04100359)
* 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](https://arxiv.org/abs/2210.04512)
* 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](https://hal.sorbonne-universite.fr/hal-03849878)
* A. Castellano, F. Bottin, J. Bouchet, A. Levitt, G. Stoltz, Ab initio Canonical Sampling based on Variational Inference, Physical Review B letter (2022), [preprint](https://arxiv.org/abs/2210.11531)
* 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](https://hal.inria.fr/hal-03408321)
* 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](https://hal.archives-ouvertes.fr/hal-03611185/document)
* 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](https://hal.sorbonne-universite.fr/hal-03605574/document)
* M. Herbst, A. Levitt, A robust and efficient line search for self-consistent field iterations, Journal of Computational Physics (2021), [preprint](https://arxiv.org/abs/2109.14018)
* M-S. Dupuy, A. Levitt, Finite-size effects in response functions of molecular systems, SMAI Journal of Computational Mathematics (2021), [preprint](https://arxiv.org/abs/2102.09841)
* E. Bernard, M. Fathi, A. Levitt, G. Stoltz, Hypocoercivity with Schur complements, Annales Henri Lebesgue (2021), [preprint](https://arxiv.org/abs/2003.00726)
* É. Cancès, C. Fermanian Kammerer, A. Levitt, S. Siraj-Dine, Coherent electronic transport in periodic crystals, Annales Henri Poincaré (2021), [preprint](https://arxiv.org/abs/2002.01990)
* É. Cancès, G. Kemlin, A. Levitt, Convergence analysis of direct minimization and self-consistent iterations, SIAM Journal on Matrix Analysis and Applications (2021), [preprint](https://arxiv.org/abs/2004.09088)
* M. Herbst, A. Levitt, Black-box inhomogeneous preconditioning for self-consistent field iterations in density functional theory, Journal of Physics: Condensed Matter (2020), [preprint](https://arxiv.org/abs/2009.01665)
* A. Levitt, Screening in the finite-temperature reduced Hartree-Fock model, Archive for Rational Mechanics and Analysis (2020), [preprint](https://arxiv.org/abs/1810.03342)
* M. Herbst, A. Levitt, É. Cancès, A posteriori error estimation for the non-self-consistent Kohn-Sham equations, Faraday Discussions (2020), [preprint](https://arxiv.org/abs/2004.13549)
* É. Cancès, V. Ehrlacher, D. Gontier, A. Levitt, D. Lombardi, Numerical quadrature in the Brillouin zone for periodic Schrodinger operators, Numerische Mathematik (2019), [preprint](https://arxiv.org/abs/1805.07144)
* D. Gontier, A. Levitt, S. Siraj-Dine, Numerical construction of Wannier functions through homotopy, Journal of Mathematical Physics (2019), [preprint](https://arxiv.org/abs/1812.06746)
* A. Damle, A. Levitt, L. Lin, Variational formulation for Wannier functions with entangled band structure, SIAM MMS (2019), [preprint](https://arxiv.org/abs/1801.08572)
* H. Cornean, D. Gontier, A. Levitt, D. Monaco, Localised Wannier functions in metallic systems, Annales Henri Poincaré (2019), [preprint](https://arxiv.org/abs/1712.07954)
* A. Levitt, C. Ortner, Convergence and Cycling in Walker-type Saddle Search Algorithms, SIAM Journal on Numerical Analysis (2017), [preprint](http://arxiv.org/abs/1607.08875)
* 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](https://arxiv.org/abs/1611.02045)
* É. Cancès, A. Levitt, G. Panati, G. Stoltz, Robust determination of maximally-localized Wannier functions, Phys. Rev. B, 95, 075114 (2017), [preprint](http://arxiv.org/abs/1605.07201)
* 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](https://hal.archives-ouvertes.fr/hal-01395833/)
* A. Levitt, M. Torrent, Parallel eigensolvers in plane-wave Density Functional Theory. Computer Physics Communications, 187:98–105 (2015), [preprint](http://arxiv.org/abs/1406.4350)
* A. Levitt, Solutions of the multiconfiguration Dirac-Fock equations. Reviews in Mathematical Physics, 26(07):1450014 (2014), [preprint](http://arxiv.org/abs/1305.3739)
* A. Levitt, Best constants in Lieb-Thirring inequalities: a numerical investigation. Journal of Spectral Theory 4.1 (2014), [preprint](http://arxiv.org/abs/1206.1473)
* A. Levitt, Convergence of gradient-based algorithms for the Hartree-Fock equations. ESAIM Math. Model. Numer. Anal. 46.06 (2012), [preprint](http://arxiv.org/abs/1109.5473/)
* 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](jlf.pdf)

#### Book chapters
* D. Cianchino, I. Gianni, A. Levitt, T. Nottoli, F. Pes, F. Lipparini, Robust and efficient
design of Algorithms in quantum chemistry, in Handbook of Electronic Structure Theory (2026)
* É. Cancès, A. Levitt, Y. Maday, C. Yang, Numerical Methods for Kohn–Sham Models: Discretization, Algorithms, and Error Analysis (2023), [link](https://link.springer.com/book/10.1007/978-3-031-22340-2)


#### Code papers
* A. Castellano et al., Machine learning assisted canonical sampling (MLACS), Computer Physics Communications (2025), [preprint](https://hal.science/hal-04854064)
* X. Quan, A. Levitt, MatrixFuns.jl: Matrix functions in Julia, The journal of open source software (2025), [link](
https://joss.theoj.org/papers/10.21105/joss.08396)
* M. Herbst, A. Levitt, É Cancès, DFTK: A Julian approach for simulating electrons in solids, Proceedings of the JuliaCon conferences 3.26 (2021), [link](https://proceedings.juliacon.org/papers/10.21105/jcon.00069.pdf)
* X. Gonze, F. Jollet et al., Recent developments in the ABINIT software package. Computer Physics Communications, 205:106-131 (2016), [journal](http://www.sciencedirect.com/science/article/pii/S0010465516300923)


## Teaching materials
* 2025 [Algèbre linéaire avancée et numérique](algebre_lineaire.pdf), L3
* 2024 [Calcul scientifique](MAO.pdf), M1
* 2023 [Mathematical methods in quantum mechanics](MMQM), M2
* 2021 [Introduction to functional analysis](OMPI.pdf), L3
* 2021 [Practical scientific computing](calsci.pdf), L3
* 2019 Mini-course: [Complex analysis for quantum physicists and chemists](complex_analysis.pdf)
* 2016- [Analyse de Fourier](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](dispersion.pdf)
* 2022 [What is the response function of an oscillatory system?](response_oscillatory.pdf)
* 2021 [The many disguises of the Schur complement](schur.pdf)
* 2020 [The adjoint trick and automatic differentiation](adjoint.pdf)
* 2019 [Ewald summation](ewald.pdf)

## 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](talks/italy.pdf)
* 2022 Response functions and resonances, Collège de France, [link](talks/collegedefrance.pdf)
* 2021 Direct minimization vs SCF for nonlinear eigenspace problems, SIAM linear algebra, [link](talks/SIAM_LA.pdf)
* 2020 Numerical analysis and properties of crystals, internal MATHERIALS seminar, [link](talks/MATHERIALS.pdf)
* 2020 HDR defence [link](talks/HDR.pdf)
* 2019 Screening and charge sloshing in crystals, ICIAM minisymposium [link](talks/ICIAM.pdf)
* 2019 Wannier functions for insulators and metals, Copenhagen [link](talks/copenhagen.pdf)
* 2018 Numerical integration in the Brillouin zone, Beijing [link](talks/beijing.pdf)

## Software
* [DFTK.jl](https://github.com/mfherbst/DFTK.jl), the density functional toolkit
* Computation of [Wannier functions](https://github.com/antoine-levitt/wannier)

## Misc links
* (very out of date...) [resume](cv.pdf)
* [HDR thesis](hdr.pdf) and [PhD thesis](https://hal.archives-ouvertes.fr/tel-00881031)
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