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Derivation of Effective Dynamics from Microscopic Evolution Equations

Objective

The derivation of macroscopic (effective) equations from microscopic considerations is a long-standing challenge of the mathematical analysis of many-body problems. In this research proposal, we focus on the derivation of (linear or non-linear) kinetic and Hartree-type equations from microscopic quantum models.
The innovative and creative potential of the project relies on the combination of rigorous methods of Quantum Field Theory (QFT) and Quantum Statistical Mechanics (QSM).
Particular attention will indeed be paid to the macroscopic properties of interacting quantum systems governed by a microscopic dynamics. The latter is a notoriously difficult mathematical problem for which only few rigorous results exist. The proposed research will yield significant outcomes in this field, while developing important knowledge transfers, locally between the researchers Sébastien Breteaux, Jean-Bernard Bru and Miguel Escobedo, and globally between BCAM and TU Braunschweig, the University of Paris Nord, ETH Zürich and the University of São Paulo

Field of science

  • /natural sciences/physical sciences/quantum physics/quantum field theory
  • /natural sciences/physical sciences/classical mechanics/statistical mechanics
  • /natural sciences/mathematics/pure mathematics/mathematical analysis

Call for proposal

H2020-MSCA-IF-2014
See other projects for this call

Funding Scheme

MSCA-IF-EF-ST - Standard EF

Coordinator

BCAM - BASQUE CENTER FOR APPLIED MATHEMATICS
Address
Al Mazarredo 14
48009 Bilbao
Spain
Activity type
Research Organisations
EU contribution
€ 158 121,60