28 Settembre 2023 | Lezione Lagrangiana: Chiara Saffirio (University of Basel)
Weakly interacting fermions: mean-field and semiclassical regimes
University of Basel
Data e luogo:
28 settembre 2023 dalle 14.30 alle 15.30
in Aula De Filippi, Via Accademia Albertina, presso DBIOS, Torino
The derivation of effective macroscopic theories approximating microscopic systems of interacting particles is a major question in non-equilibrium statistical mechanics. For non-interacting particles this is a relatively easy task. However when particles interact among them, the many-body theory becomes very complicated and non-approachable from a computational viewpoint. In this lecture we will be concerned with the dynamics of systems made of many interacting fermions. We will focus on the mean-field regime, i.e. weakly interacting particles whose collective effect can be approximated by an averaged potential in convolution form, and review recent mean-field techniques based on second quantization approaches. As a first step we will obtain a reduced description given by the time-dependent Hartree-Fock equation. As a second step we will look at longer time scales where a semiclassical description starts to be relevant and approximate the many-body dynamics with the Vlasov equation, which describes the evolution of the effective probability density of particles on the one particle phase space and is largely used in plasma physics.
Chiara Saffirio received her PhD degree in Mathematics in 2012 from the University of Rome, La Sapienza. Afterwards she worked as postdoctoral researcher at the Hausdorff Center for Mathematics at the University of Bonn and as a SNF Ambizione fellow at the University of Zurich. Since 2019 she is SNF Eccellenza Assistant Professor at the University of Basel.
In 2021 she received the Young Scientist Award at the International Congress of Mathematical Physics in Geneva and in 2022 she was awarded an ERC Starting Grant.
Chiara's research focuses on kinetic theory, scaling limits in classical and quantum interacting particle systems, semiclassical analysis and theoretical aspects of partial differential equations.