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BCAMSevero Ochoa Award

basque center for applied mathematics

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Breteaux, Sébastien

Marie Skłodowska-Curie Fellow (H2020-MSCA-IF-2014)

Quantum Mechanics
Address

Mazarredo, 14. 48009 Bilbao Basque Country - Spain

Contact


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 effectively those physical systems 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.



I am currently supported by a the European Unions's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 660021.



In my post-doctorat at the BCAM (Basque Country, Spain) in the group of Jean-Bernard Bru:

  • With V. Bach, T. Chen, J. Fröhlich and I.M. Sigal we started a collaboration on the Hartree-Fock-Bogolubov equation, already resulting in one article.
  • With V. Bach, P. Pickl and S. Petrat we continue a collaboration on a derivation of the time dependent Hartree-Fock equation.
  • With Z. Ammari and F. Nier we work on the relations between quantum mean field asymptotics and multiscale analysis.

During my post-doctorat at the TU Braunschweig (Germany) in the group of Volker Bach:

  • I worked in collaboration with V. Bach, S. Petrat, P. Pickl and T. Tzaneteas on the accuracy of the time-dependent Hartree-Fock approximation, that is a method to approximate the dynamics of electron in a molecule.
  • 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, P. Pickl and S. Petrat and T. Tzaneteas on a derivation of the time dependent Hartree-Fock equation.

During my PhD at the university of Rennes 1 (France) under the supervision 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.







Some interesting links:

Eusko Jaurlaritza - Gobierno Vasco ikerbasque - Basque Foundation for Science Bizkaia xede. Bizkaiko Foru Aldundia innobasque - Agencia vasca de la innovación Universidad del PaÌs Vasco (UPV/EHU)