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EFFECT

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Effective Equations for Fermionic Systems

The goal of this project is to substantially improve the understanding of the non-equilibrium dynamics of large fermionic systems and their interaction with the quantized electromagnetic field. Fermionic systems play a significant... ver más

15/11/2023

UNIVERSITAT BASEL

191K€

Presupuesto del proyecto: 191K€

Líder del proyecto

UNIVERSITAT BASEL No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2023-11-15

MSCA-IF-2020: Individual Fellowships

I+D

Cerrada hace 4 años

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1 Participantes

UNIVERSITAT BASEL

191.15K€ | Lider

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Duración del proyecto: 32 meses Fecha Inicio: 2021-03-04
Fecha Fin: 2023-11-15

Líder del proyecto

UNIVERSITAT BASEL No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 191K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto The goal of this project is to substantially improve the understanding of the non-equilibrium dynamics of large fermionic systems and their interaction with the quantized electromagnetic field. Fermionic systems play a significant role in the description of molecules and condensed matter. Their time evolution is determined by the Schrödinger equation which, however, is very challenging to analyze for large systems with many particles. For this reason simpler effective equations are used to approximately predict the time evolution. These are easier to investigate but less exact. In physics, effective equations are derived by heuristic arguments. Beyond that, a mathematical analysis is essential to prove the range of validity of the applied approximation. In the scope of this project new mathematical tools will be developed to rigorously derive effective evolution equations for fermionic systems at zero and finite temperature. The Hartree-Fock equation with Coulomb potential will be derived from the Schrödinger equation in a many-fermion mean-field limit which is coupled to a semiclassical limit. In the same scaling limit the use of the (fermionic) Maxwell-Schrödinger equations as approximate time evolution of the Pauli-Fierz Hamiltonian will be justified. Moreover, it will be proven that the quantum fluctuations around the effective equations are described by Bogoliubov theory. Explicit estimates for the error caused by the approximation will be provided. In total, this will enhance the understanding about the creation of correlations among fermions and the emergence of classical field theories from quantum field theories. The derivations are long outstanding and there is an extensive need for new mathematical methods in semiclassical analysis and many-body quantum mechanics. It is expected that the new techniques will also have a strong impact on studies about dilute Bose gases at positive temperature and fermionic systems in the kinetic regime.

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