Dr. Sébastien Breteaux

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Telefon: (++49 531) 391-7433

E-Mail: s.breteaux@tu-bs.de



Research themes

I am a mathematician interested in quantum systems with a large number of particles. For such systems the microscopic dynamics is often complicated and the important information on the macroscopic scale is not directly appearing. I work on the derivation, in some particular cases, of the equations describing those physical systems at the macroscopic scale starting from the equation at the microscopic scale.

In particular I use the mathematical framework of quantum field theory, pseudo-differential calculus (in finite and infinite dimension) and semiclassical measures to derive those equations.

More precisely, during my PhD under the direction of Francis Nier:

  • I worked in collaboration with Z. Ammari on a derivation of the cubic non-linear Schrödinger equation for particles interacting through a point pair interaction (in one dimension).
  • I studied the derivation of the linear Boltzmann equation using a quantic microscopic model of a particle interacting with a gaussian random field.

And in my post-doctorat under the supervision of Volker Bach:

  • I worked in collaboration with V. Bach and T. Tzaneteas on getting some estimates of ground state energies using quasifree states for the non-relativistic Pauli-Fierz model with one electron.
  • I worked in collaboration with V. Bach, H. Knörr and E. Menge on a generalization of Lieb's variational principle.
  • I am working in collaboration with V. Bach and T. Tzaneteas on a derivation of the time dependent Hartree-Fock equation.

Curriculum Vitæ of Sébastien Breteaux

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PDF Research Statement (In English)

PDF Teaching Statement (In English)

Online Version below (In English)


2011-2013  Post Doctorat, in the group of Volker Bach, Technical University of Braunschweig, Germany.
2010-2011 ATER Plein, Antenne de Bretagne de l'ENS de Cachan, Rennes.
2010 Work under the direction of Volker Bach, Gutenberg University, Mainz, Germany.
On the minimization of an energy functional.
2007-2011 PhD in mathematics, under the direction of Francis Nier, University of Rennes1.
An approach of the derivation of kinetic equations using quantum field theory.
June 2005 Work under the direction of Fabio Benatti, International Center for Theoretical Physics, Trieste, Italy.
Study of a case of quantum entanglement. 


•   Submitted

Kinetic Energy Estimates for the Accuracy of the Time-Dependent Hartree-Fock Approximation with Coulomb Potential. With Volker Bach and Tim Tzaneteas.

•   Published or Accepted

Generalization of Lieb's variational principle to Bogoliubov-Hartree-Fock theory. With Volker Bach, Hans Knörr and Edmund Menge. Journal of Mathematical Physics.


Asymptotic analysis of a non-linear non-local integro-differential equation arising from bosonic quantum field dynamics. Nonlinear Differential Equations and Applications.


Minimization of the energy of the non-relativistic one electron Pauli-Fierz model on quasifree states. With Volker Bach and Tim Tzaneteas. Documenta Mathematica.


A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field. Accepted, Annales de l'Institut Fourier.


Higher order terms for the quantum evolution of an observable within the Hepp method. Cubo, A mathematical Journal.


Propagation of chaos for many-bosons systems in one dimension with a point pair-interaction. With Zied Ammari. Asymptotic analysis.


Slipped nonpositive reduced dynamics and entanglement. With Fabio Benatti and Roberto Floreanini. Laser Physics.

  Freely available prepublication version on arXiv.org.
 My thesis
 2011 Quantum field theory approach to the derivation of kinetic equations (Approche QFT de la dérivation d'équations cinétiques) 


2007-2010 "Monitorat", Antenne de Bretagne de l'ENS de Cachan, Rennes.
2007 Master 2 of Mathematics, Scuola Normale Superiore di Pisa, Italy. Grade TB.
One year of Erasmus exchange with the SNS.
2007 Magistère of Mathematics, Rennes. Grade TB.
For the four year of formation at the ENS.
2006 "Agrégation" of Mathematics, Rennes. Rank 91.
Specialized in Scientific Calculus.
2005 Maîtrise of Mathematics, Rennes. Grade B.
2005 Maîtrise of Physics, Rennes. Grade AB.
June 2004

Work at the Polytechnique school laboratory of astrophysics, Palaiseau.

Study of an algorithm on the numerical resolution of the Fokker-Planck equation.

2004 "Travail Encadré de Recherche", University of Rennes1.
Resolution of the Gross-Pitaevskii equation by several numerical methods.
2004 Bachelor in Mathematics, Rennes. Grade TB.
Bachelor in Physics, Rennes. Grade B.
2003 Admitted in the Antenne de Bretagne de l'Ecole normale supérieure de Cachan. Rennes. 

Invited Talks in International Conferences

2013 Haagen, (Germany) "Walkshop" of Mathematical physics.
Paris, Variational and spectral methods in quantum field theory.
Cergy, Day on quantum field theory.
Lille, 5th Meeting of the GDR Quantum Dynamics.

Talks in Seminars

2013 Grenoble, Seminar of mathematical physics.
Aarhus (Denmark), Analysis seminar.
Montpellier, Seminar of the ACSIOM team.
2012 Rennes, Seminar of the PDE team.
         Toulouse, Seminar of the MIP team.
Cergy, Seminar of geometry, PDE and mathematical physics.
Bordeaux, Seminar of mathematical physics.
Grenoble, Seminar of mathematical physics.
2011 Braunschweig (Germany), Seminar of the analysis and algebra institut.
Rennes, Summer school: Spectral analysis of non self-adjoint operators.
Rennes, Seminar of partial differential equations.
2010 Mainz (Germany), Seminar of partial differential equations.
2009 Rennes, Work group on the mean field limit.
Rennes, PhD students seminar in mathematics.
2008 Brest, PhD students seminar in mathematics.


  • At the Technical University of Braunschweig (teachings in German):
2013-2014 Course of partial differential equations 2.
Exercises of Analysis for 2nd year students.
2012-2013 Exercises  of Mathematics for 1st year electrotechnics students, and  
     in charge of the organisation of the different exercises groups.
Exercises of Functional Analysis in 3rd year.
2011-2012 Exercises of Analysis in 1srt year.
 • Analysis (informatics and telecommunications students).
  • At the Antenne de Bretagne de l'ENS de Cachan (Monitorat et ATER plein):
2007-2011 Preparation to the competitve exam for mathematics teachers "agrégation".
 • Mock oral exams in Analysis and Modelisation.
 • Corrections of mock exams.
 • Exercises on computers for the modelisation speciality.
2007-2011 Exercises (with and without computers) to 1st years at the antenne de Bretagne de l'ENS Cachan.
 • Numerical linear algebra (mathematics students).
 • Analysis (informatics and telecommunications students).
  • Other
2005-2006 Mathematics summer courses to teachers of the normal school and of high school in Pakse. Laos.


French  Native language
English  Fluent
Italian  Fluent
German  Fluent

 Other charges

Referee for reviews in mathematical physics.
2008-2011 Council member of the mathematical research institut of Rennes.

  aktualisiert am 24.10.2014
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