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Bernard Helffer

Bernard Helffer

D-Index & Metrics

Mathematics

D-Index
56
Citations
10952
World Ranking
738
National Ranking
36

Bernard Helffer publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where Bernard Helffer sits on this spectrum.

42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 83 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientists 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientists 522–526 publications: 3 scientists 527–531 publications: 1 scientists 532–536 publications: 4 scientists 537+ publications: 100 scientists
42 publications 537+

This scientist: 368 publications — 92nd percentile

92% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

Bernard Helffer D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where Bernard Helffer sits on this spectrum.

30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 138 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 56 D-Index — 80th percentile

80% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

Overview

Bernard Helffer is affiliated with the University of Nantes in France. Their research primarily falls within the fields of Mathematics and Computer Science, with notable contributions across various specialized subfields. These subfields include Mathematical Physics, Computational Theory and Mathematics, Applied Mathematics, Atomic and Molecular Physics and Optics, and Geometry and Topology.

The main topics covered by Bernard Helffer's work are:

  • Spectral Theory in Mathematical Physics
  • Advanced Mathematical Modeling in Engineering
  • Numerical methods in inverse problems
  • Quantum chaos and dynamical systems
  • Geometric Analysis and Curvature Flows
  • Nonlinear Partial Differential Equations
  • Stability and Controllability of Differential Equations

They have published extensively, with a total of 116 publications in Mathematics and 40 in Computer Science. Their frequent publication venues include:

  • arXiv (Cornell University)
  • Integral Equations and Operator Theory
  • Pure and Applied Analysis
  • Journal de l'École polytechnique - Mathématiques
  • Asymptotic Analysis

Bernard Helffer has contributed to book publications as well, including a work published by Memoirs of the European Mathematical Society titled On the Stability of Symmetric Flows in a Two-Dimensional Channel, set for 2025.

Recent papers authored by Bernard Helffer include:

  • Improving Semigroup Bounds with Resolvent Estimates (2021), published in Integral Equations and Operator Theory
  • Semi-classical edge states for the Robin Laplacian (2022), published in Mathematika
  • Quantum tunneling in deep potential wells and strong magnetic field revisited (2024), published in Pure and Applied Analysis
  • Thin domain limit and counterexamples to strong diamagnetism (2020), published in Reviews in Mathematical Physics

Frequent co-authors collaborating with Bernard Helffer include:

  • Pierre Bérard
  • Ayman Kachmar
  • François Nicoleau
  • Mikael Persson Sundqvist
  • Rola Kiwan

Best Publications

  • Multiple wells in the semi-classical limit I

    B. Helffer;J. Sjostrand

  • Semi-Classical Analysis for the Schrödinger Operator and Applications

    Bernard Helffer

  • Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians

    Bernard Helffer;Francis Nier

  • Equation de Schrödinger avec champ magnétique et équation de Harper

    Bernard Helffer;Johannes Sjöstrand

  • Spectral Methods in Surface Superconductivity

    Søren Fournais;Bernard Helffer

  • Résonances en limite semi-classique

    B. Helffer;J. Sjöstrand

  • Magnetic Bottles in Connection with Superconductivity

    Bernard Helffer;Abderemane Morame

  • Ergodicité et limite semi-classique

    B. Helffer;A. Martinez;D. Robert

  • Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles

    B Helffer;B Helffer;D Robert

  • Puits multiples en mecanique semi-classique iv etude du complexe de witten

    B. Helffer;J. Sjöstrand

  • Eigenvalues Variation. I.: Neumann Problem for Sturm-Liouville Operators

    M. Dauge;B. Helffer

  • On the correlation for Kac-like models in the convex case

    Bernard Helffer;Johannes Sjöstrand

  • Théorie spectrale pour des opérateurs globalement elliptiques

    Bernard Helffer

  • Nodal Domains and Spectral Minimal Partitions

    B. Helffer;T. Hoffmann-Ostenhof;T. Hoffmann-Ostenhof;S. Terracini

  • Semiclassical Analysis for the Ground State Energy of a Schrödinger Operator with Magnetic Wells

    Bernard Helffer;Abderemane Mohamed

  • Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs

    Bernard Helffer;Jean Nourrigat

  • Spectral Theory and its Applications

    Bernard Helffer

  • Caracterisation des operateurs hypoelliptiques homogenes

    B. Helffer;J. Nourrigat

  • Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach

    Bernard Helffer;Markus Klein;Francis Nier

  • Analyse semi-classique pour l'équation de Harper (avec application à l'équation de Schrödinger avec champ magnétique)

    B. Helffer;J. Sjöstrand

  • Quantitative Analysis of Metastability in Reversible Diffusion Processes Via a Witten Complex Approach: The Case With Boundary

    Bernard Helffer;Francis Nier

Frequent Co-Authors

Johannes Sjöstrand
Johannes Sjöstrand University of Burgundy
Denis S. Grebenkov
Denis S. Grebenkov École Polytechnique
Susanna Terracini
Susanna Terracini University of Turin
Rupert L. Frank
Rupert L. Frank California Institute of Technology
Monique Dauge
Monique Dauge University of Rennes
Laurent Veron
Laurent Veron François Rabelais University
Fred B. Weissler
Fred B. Weissler Université Paris Cité

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