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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

Coordinator

BCAM - BASQUE CENTER FOR APPLIED MATHEMATICS
Net EU contribution
€ 158 121,60
Address
AL MAZARREDO 14
48009 Bilbao
Spain

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Region
Noreste País Vasco Bizkaia
Activity type
Research Organisations
Links
Total cost
€ 158 121,60