Publications

Preprints

  1. Edge states for tight-binding operators with soft walls.
    Camilo Gómez Araya, David Gontier, Hanne Van Den Bosch
    submitted. (arXiv).

Articles (published or accepted)

  1. Exponential decay of the critical points in a discrete model of polyacetylene..
    David Gontier, Adechola E. K. Kouande, Éric Séré
    Nonlinearity 38 015002 (2024). (journal, arXiv, HAL).
  2. Keller and Lieb-Thirring estimates of the eigenvalues in the gap of Dirac operators.
    Jean Dolbeault, David Gontier, Fabio Pizzichillo, Hanne Van Den Bosch
    Rev. Mat. Iberoam. (2023). (journal, arXiv, HAL).
  3. Density Functional Theory for two-dimensional homogeneous materials with magnetic fields.
    David Gontier, Salma Lahbabi, Abdallah Maichine
    J. Funct. Anal. 285 (2023) 110100. (journal, arXiv, HAL).
  4. Optimizers for the finite-rank Lieb-Thirring inequality.
    Rupert L. Frank, David Gontier, and Mathieu Lewin
    accepted in American Journal of Mathematics. (arXiv).
  5. Phase transition in the Peierls model for polyacetylene.
    David Gontier, Adéchola Kouande, Éric Séré
    Ann. Henri Poincaré (2023). (journal, arXiv, HAL).
  6. A simple derivation of moiré-scale continuous models for twisted bilayer graphene.
    Éric Cancès, Louis Garrigue, David Gontier
    Phys. Rev. B. 107, 155403 (2023). (journal, arXiv, HAL).
  7. Edge states for second order elliptic operators in a channel.
    Davic Gontier
    J. Spectr. Theory 12 (2023), 1155–1202. (journal, arXiv, HAL).
  8. Second-order homogenization of periodic Schrödinger operators with highly oscillating potentials.
    Éric Cancès, Louis Garrigue, David Gontier
    SIAM Journal on Mathematical Analysis, 55.3 (2023): 2288-2323. (journal, arXiv, HAL).
  9. Symmetric Fermi projections and Kitaev's table: topological phases of matter in low dimensions.
    David Gontier, Domenico Monaco, Solal Perrin-Roussel
    J. Math. Phys. 63, 041902 (2022). (journal, arXiv, HAL).
  10. Spectral properties of periodic systems cut with an angle.
    David Gontier
    Comptes Rendus Mathématique, Tome 359 (2021) no. 8, pp. 949-958. (journal, arXiv, HAL).
  11. Density Functional Theory for two-dimensional homogeneous materials.
    David Gontier, Salma Lahbabi, Abdallah Maichine
    Commun. Math. Phys. (2021). (journal, arXiv, HAL).
  12. The nonlinear Schrödinger equation for orthonormal functions: II. Application to Lieb-Thirring inequalities.
    Rupert L. Frank, David Gontier, Mathieu Lewin
    Commun. Math. Phys. 384, 1783–1828 (2021). (journal, arXiv, HAL).
  13. The nonlinear Schrödinger equation for orthonormal functions: I. Existence of ground states.
    David Gontier, Mathieu Lewin, Faizan Q. Nazar
    Arch. Rational Mech. Anal. 240, 1203–1254 (2021). (journal, arXiv, HAL).
  14. Edge states in ordinary differential equations for dislocations.
    David Gontier
    J. Math. Phys. 61, 043507 (2020). (journal, arXiv, HAL).
  15. Numerical quadrature in the Brillouin zone for periodic Schrödinger operators.
    Éric Cancès, Virginie Ehrlacher, David Gontier, Antoine Levitt, Damiano Lombardi
    Numer. Math. (2020). (journal, arXiv, HAL).
  16. Numerical reconstruction of the first band(s) in an inverse Hill's problem.
    Athman Bakhta, Virginie Ehrlacher, David Gontier
    ESAIM: COCV, 26 (2020) 59. (journal, arXiv, HAL).
  17. The reduced Hartree-Fock model with self-generated magnetic fields.
    David Gontier, Salma Lahbabi
    J. Math. Phys., 60, 081902 (2019). (journal, arXiv, HAL).
  18. Spin symmetry breaking in the translation-invariant Hartree-Fock uniform electron gas.
    David Gontier, Mathieu Lewin
    SIAM J. Math. Anal., 51(4), 3388–3423 (2019). (journal, arXiv, HAL).
  19. Lower bound on the Hartree-Fock energy of the electron gas.
    David Gontier, Christian Hainzl, Mathieu Lewin
    Phys. Rev. A 99, 052501 (2019). (journal, arXiv, HAL).
  20. Numerical construction of Wannier functions through homotopy.
    David Gontier, Antoine Levitt, Sami Siraj-Dine
    J. Math. Phys. 60, 031901 (2019). (journal, arXiv, HAL).
  21. Localised Wannier functions in metallic systems.
    Horia Cornean, David Gontier, Antoine Levitt, Domenico Monaco
    Ann. Henri Poincaré (2019). (journal, arXiv, HAL).
  22. Minnaert resonances for acoustic waves in bubbly media.
    Habib Ammari, Brian Fitzpatrick, David Gontier, Hyundae Lee, Hai Zhang
    Ann. Inst. H. Poincaré C, 35,7 (2018), 1975-1998. (journal, arXiv, HAL).
  23. Sub-wavelength focusing of acoustic waves in bubbly media.
    Habib Ammari, Brian Fitzpatrick, David Gontier, Hyundae Lee, Hai Zhang
    Proc. R. Soc. A 473 (2017), 20170469. (journal, arXiv, HAL).
  24. A mathematical and numerical framework for bubble meta-screens.
    Habib Ammari, Brian Fitzpatrick, David Gontier, Hyundae Lee, Hai Zhang
    SIAM J. Appl. Math., 77 (2017), 1827–1850. (journal, arXiv, HAL).
  25. Supercell calculations in the reduced Hartree-Fock model for crystals with local defects.
    David Gontier, Salma Lahbabi
    Appl. Math. Res. Express, (2017) 1-64. (journal, arXiv, HAL).
  26. A mathematical analysis of the GW0 method for computing electronic excited energies of molecules.
    Éric Cancès, David Gontier, Gabriel Stoltz
    Rev. Math. Phys. 28, 1650008 (2016). (journal, arXiv, HAL).
  27. Convergence rates of supercell calculations in the reduced Hartree-Fock model.
    David Gontier, Salma Lahbabi
    Math. Model. Num. Anal., 50,5 (2016) 1403-1424. (journal, arXiv, HAL).
  28. Pure-state N-representability in current-spin-density functional theory.
    David Gontier
    Commun. Math. Sci., 24,4 (2016) 987–1003. (journal, arXiv, HAL).
  29. Existence of minimizers for Kohn-Sham within the Local Spin Density Approximation.
    David Gontier
    Nonlinearity 28 (2015) 57-76. (journal, arXiv, HAL).
  30. Sampling based on timing: Time encoding machines on shift-invariant subspaces.
    David Gontier, Martin Vetterli
    ACHA 36,1 (2014) 63-78. (journal, arXiv, HAL).
  31. N-representability in non-collinear spin-polarized density functional theory.
    David Gontier
    Phys. Rev. Lett. 111, 153001 (2013). (journal, arXiv, HAL).
  32. Stabilization of rigid bodies with frictional supports against dynamic perturbations.
    Peter L. Várkonyi, David Gontier, Joel W. Burdick
    2012 IEEE International Conference on Robotics and Automation. (journal, HAL).

Book chapters

  1. Thermodynamic Limits of Electronic Systems.
    D. Gontier, J. Lu, and Ch. Ortner
    Density Functional Theory. Modeling, Mathematical Analysis, Computational Methods, and Applications. (journal, arXiv, HAL).
  2. The periodic Lieb-Thirring inequality.
    R.L. Frank, D. Gontier, M. Lewin
    Partial Differential Equations, Spectral Theory, and Mathematical Physics. The Ari Laptev Anniversary Volume, volume 18 of EMS Series of Congress Reports, chapter The periodic Lieb–Thirring inequality, pages 135–154. EMS Publishing House, June 2021. (journal, arXiv, HAL).

Autres

  1. Periodic and half periodic fermionic systems
    HDR (2024). (pdf, présentation).
  2. Contributions mathématiques aux calculs de structures électroniques
    Thèse (2015). (pdf, présentation).


Slides and pictures are sometimes more useful than articles. Here are some oral presentations.