Homepage: Denis BERNARD

Département de Physique, Ecole Normale Supérieure de Paris.


  • Contact, CV.
  • Intérêts de recherche/Research Interests.
  • Publications.
  • Enseignement/Teaching.
  • Talks.
  • Balades quantiques & Forum de physique statistique.
  • Stage/Internship: Thesis, Post-docs...
  • Open Position: Ph.D. starting Fall 2020...

    Contact & CV:

    E-mail: prenom.nom AT ens.fr
    Phone: (+33) 1 44 32 37 75
    Fax: (+33) 1 43 36 76 66

    Adresse postale/Postal address:
    Laboratoire de Physique de l'Ecole Normale Supérieure,
    24 rue Lhomond, 75005 Paris,

    Curriculum Vitae:
  • Directeur de recherche (DRCE) au C.N.R.S.
  • Professeur à temps partiel à l'Ecole Polytechnique (2002-2016).
    Un CV en francais en version courte ou longue.
    CV: an English version, short or long.
    Two press articles: in French (2006), in English (2016).
  • Here is another photo or one more.

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    Intérêts de recherche/Research Interests:

  • Random Geometry, Random Spatial Processes/ Géométrie aléatoire, processus spatiaux aléatoires.
    Understanding random fractal patterns is at the core of the comprehension of many physical phenomena or mathematical structures, and the Brownian motion is a historical example of such structures. I participated to the understanding of newly constructed planar random curves or interfaces (called SLE), a theme which fits into random geometry. In collaboration with M. Bauer, we developed bridges linking probabilistic approaches from mathematicians with those of physicists based on field theories.
  • Conformal Field Theory, Integrable Systems and Applications/ Théories conformes, systèmes intégrables et applications.
    Conformal field theories (CFT) and integrable systems find applications to 2d phase transitions, to critical quantum systems, and they are closely related to string theories. I have been involved in the development of the CFT methodological tools. Part of my work relies on deciphering and using quantum symmetries, others have a more mathematical flavour related either to algebraic structures of CFT and to geometrical aspects of Riemann surfaces.
  • Turbulent Systems, Turbulent Transports / Systèmes turbulents, transports turbulents.
    Turbulent phenomena are ubiquitous in many every day phenomena, but still lack a complete theoretical understanding. I participated to the physical and mathematical collective understanding of intermittence phenomena in the (up-to-now) unique solvable model of turbulent transport, and to enlighten traces of conformal invariance in two dimensional turbulence.
  • Quantum Noises, Open or Out-of-Equilibrium Quantum Systems / Bruits quantiques, systèmes quantiques ouverts ou hors d'équilibre.
    Experimental progresses in controlling quantum systems gave new impetus to study unexplored territory of quantum dynamics, and simultaneously to answer old questions of quantum mechanics. My recent research aims at studying quantum stochastic processes, their mathematical structures and their applications to the physics of monitored or open quantum systems, in or out of equilibrium. In particular, I analysed an iconic model of stochastic quantum many-body dynamics, the quantum symmetric simple exclusion process.
  • Motivated by curiosity, I also considered problems related to 2d disordered systems, to localisation phenomena, to topological matters, and to facets of semi-classical gravity or to random or genetic networks.

  • I am currently involved in two ANR research projects: one ESQuisses, on "Stochastic Quantum Evolutions" in connection with quantum information, quantum noises and open quantum systems, another Confica, on "conformal field theory, constructive aspects and integrability".

  • Here is a brief research summary.

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    Here is my arXiv list of publications (posterior to 1992, with abstracts and full texts but with one plus another one references missing).
    Here is a complete list of publications, (a pdf file but without abstracts).
    Here is my Google Scholar page.
    Here is my
    ORCID page.

    Lecture Notes (a sample):

  • "Can the macroscopic fluctuation theory be quantized?", (2021) by D.B., a brief review on the quantum symmetric simple exclusion process posing the problem of finding a quantum mesoscopic fluctuation theory (adapted to describing fluctuations of quantum mechanical effects in mesoscopic systems).
  • "Statistical Aspects of Quantum State Monitoring for (and by) Amateurs", (2016) by D.B., a series of lectures presented at the Artic School on quantum systems monitoring and on quantum trajectories, Finland, Dec. 2105.
  • "Conformal field thoery out of equilibrium: a review", (2016) by D.B. and B. Doyon, a review article for a special issue of JSTAT on non-equilibrium dynamics in integrable quantum systems.
  • "An Introduction to SLE for (and by) Amateurs", (2012) by D.B., Chern-Simons lecture series on Stochastic Schramm-Loewner Evolutions presented at UC Berkeley (Notes by J. Johnson-Freyd), and at few other places.
  • "2D Growth processes: SLE and Loewner Chains", (2006) by D.B. and M. Bauer, a review on 2D random spatial processes and Stochastic Schramm-Loewner Evolutions from a physicist point of view.
  • "Conformal Invariance in 2D Turbulence", (2006) by D.B., G. Boffetta, A. Celani and G. Falkovich, and a related "News and Views" by J. Cardy.
  • "Turbulence for (and by) Amateurs", (2000) by D.B., Lecture series at IPhT-Saclay.
  • "Some Simple (Integrable) Models of Fractional Statistics", (1994), Lectures presented at Les Houches Summer School on Fluctuating Geometries in Statistical Mechanics, France.
  • "Symétries quantiques des systèmes intégrables", (in French, 1993), un court texte écrit pour l'habilitation à diriger des recherches.
  • Original papers on the KZB equations on the torus or on Riemann surfaces, (1988).


  • "Eléments de théorie des groupes et symétries quantiques", (in French, 2012), de D. B., Y. Laszlo et D. Renard, Notes d'un cours d'approfondissement à l'Ecole Polytechnique.
  • "Introduction to Classical Integrable Systems", (2003), by O. Babelon, D. B. and M. Talon, Cambridge University Press.
  • "Statistical Field Theory and Applications: An Introduction for (and by) Amateurs", Lecture note (2018).

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    A l'Ecole Normale Supérieure:

  • M2-ICFP-Theoretical Physics: "Statistical Field Theories and Applications".
    Presentation: What are we aiming at describing?
    Plan of the lectures: "M2-SFT".
    Lecture notes: "Statistical Field Theory and Applications: An Introduction for (and by) Amateurs".
    Exercise booklet: "Statistical Field Theory Exercices". Idem "without corrections".
    Problem on the XY model: with the solution, without the solution.
    Notes (exercice plus correction) on the O(N) vector model.

    A l'Ecole Polytechnique:

  • MAT575, "Théorie des groupes et symétries quantiques / Group Theory and Quantum Symmetries".
    The lecture notes are in French: voir le polycopié.
  • PHY431, "Relativité et principe variationel": Texte des DM et des PC.
  • PHY311, "Mécanique quantique": Texte des DM et des PC.

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    Under construction.....

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    Balades Quantiques & Forum de Physique Statistique:

  • Le forum "Forum de physique statistique de l'ENS" se veut un espace d'échanges et de discussions. La programmation alterne les présentations informelles de membres du département ou de personnes extérieures sur des sujets en développement, sur des problèmes en cours d'étude, sur des thèmes plus anciens mais qui méritent un certain regard, etc. Ces rencontres ont lieu les mercredis à 12h00, toutes les deux semaines environ.
    The webpage of the Forum has been moved here.

  • We have initiated another seminar series at the LPENS, "Les Balades Quantiques", centred on quantum physics.
    The webpage of the Balades can be found here.

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  • Je propose régulièrement des sujets de stage ou de thèse en relation avec mes thèmes de recherche.
    Les étudiants intéréssés sont priés de me contacter par mail, et je ne manquerai pas de répondre rapidement.

  • Sujets de Thèse:
    Filled: New Opening: Ph.D. Staring Fall 2020.
    Here is a description of the subject: Quantum Stochastic Dynamics: from Qu-bits to Many-Body Physics .
    The followship will be financed via the Ecole Doctorale EDPIF (the student will have to apply for this fellowship).

  • Offre Postdoc:
    No new open post-doc position this year (2020).

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