DEDMEE | Derivation of Effective Dynamics from Microscopic Evolution Equations

Summary
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
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Web resources: https://cordis.europa.eu/project/id/660021
Start date: 01-06-2015
End date: 31-05-2017
Total budget - Public funding: 158 121,60 Euro - 158 121,00 Euro
Cordis data

Original description

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

Status

CLOSED

Call topic

MSCA-IF-2014-EF

Update Date

28-04-2024
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Horizon 2020
H2020-EU.1. EXCELLENT SCIENCE
H2020-EU.1.3. EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions (MSCA)
H2020-EU.1.3.2. Nurturing excellence by means of cross-border and cross-sector mobility
H2020-MSCA-IF-2014
MSCA-IF-2014-EF Marie Skłodowska-Curie Individual Fellowships (IF-EF)