## Contact

Swiss National Science Foundation (SNSF)

Wildhainweg 3P.O. Box

CH-3001 Bern

Phone +41 31 308 22 22

Applicant | Saffirio Chiara |
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Number | 161287 |

Funding scheme | Ambizione |

Research institution | Institut für Mathematik Universität Zürich |

Institution of higher education | University of Zurich - ZH |

Main discipline | Mathematics |

Start/End | 01.08.2016 - 31.07.2019 |

Approved amount | 379'388.00 |

Quantum dynamics; Effective evolution equations; Scaling limits; Landau equation; Boltzmann equation; Hartree-Fock equation

Lead |
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Tipici sistemi di interesse in fisica, biologia e scienze applicate possono essere descritti da modelli a un gran numero di componenti. A causa dell'elevato numero di particelle, il loro comportamento microscopico è molto complicato. D'altra parte, l'osservatore è interessato al comportamento collettivo del sistema, emergente su una scala spazio-temporale più grande di quella caratterizzante la dinamica microscopica. Su questa scala macroscopica, il sistema appare più semplice e può essere descritto da equazioni alle derivate parziali. |

Lay summary |

L'obiettivo principale di questo progetto è studiare matematicamente l'emergere di una dinamica macroscopica effettiva da una microscopica. |

Direct link to Lay Summary | Last update: 18.05.2016 |

Lead |
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Typical systems if interest in physics, biology and applied science can be described by models with a large number of components. Because of the huge number of particles, the microscopic behavior is very complicated. On the other hand, observers are interested in the collective behaviour of the system, arising on space and time scales which are much larger than the ones characterizing the microscopic dynamics. On such macroscopic scales, the systems appear much simpler, and can be described by partial differential equations. |

Lay summary |

The goal of this project is to study the effective |

Direct link to Lay Summary | Last update: 18.05.2016 |

Publication |
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Semiclassical limit to the Vlasov equation with inverse power law potentials |

Lagrangian solutions to the Vlasov-Poisson system with a point charge |

Mean-field evolution of fermions with singular interaction |

Group / person | Country |
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Types of collaboration |
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Scuola Normale Superiore di Pisa | Italy (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Exchange of personnel |

Rutgers University | United States of America (North America) |

- in-depth/constructive exchanges on approaches, methods or results |

Institute of Mathematics, University of Zurich | Switzerland (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

ENS Paris | France (Europe) |

- in-depth/constructive exchanges on approaches, methods or results |

Lyon ENS | France (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

Dundee University | Great Britain and Northern Ireland (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

Università di Torino | Italy (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

Univeristy of Bonn | Germany (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

Paris 7 | France (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

University of Copenaghen | Denmark (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

Title | Type of contribution | Title of article or contribution | Date | Place | Persons involved |
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Workshop "Analytical and Computational Problems for Mixtures and Plasma Dynamics" | Talk given at a conference | From the many-body quantum dynamics to the Vlasov equation | 17.06.2019 | HCM Bonn, Germany | Saffirio Chiara; |

Seminar in Mathematical Physics | Individual talk | From the many-body quantum dynamics to the Vlasov equation | 28.05.2019 | Heidelberg, Germany | Saffirio Chiara; |

Seminar in Analysis | Individual talk | From the many-body quantum dynamics to the Vlasov equation | 04.02.2019 | Dundee, Great Britain and Northern Ireland | Saffirio Chiara; |

Nonlinear phenomena in Stockholm | Talk given at a conference | From the many-body quantum dynamics to the Vlasov equation | 19.11.2018 | KTH Stockholm, Sweden | Saffirio Chiara; |

Young Women in Mathematical Physics | Talk given at a conference | From the many-body quantum dynamics to the Vlasov equation | 24.09.2018 | Bonn, Germany | Saffirio Chiara; |

La mécanique quantique à N corps | Talk given at a conference | From many-body quantum dynamics to the Vlasov equation | 10.09.2018 | Montreal, Canada | Saffirio Chiara; |

Seminar in Mathematical Physics | Individual talk | Derivation of the Vlasov-Boltzmann equation | 13.12.2017 | Politecnico di Milano, Italy | Saffirio Chiara; |

Classical and Quantum Mechanical Models of Many-Particle Systems | Talk given at a conference | From the Hartree-Fock dynamics to the Vlasov equation with singular interactions | 03.12.2017 | MFO Oberwolfach, Germany | Saffirio Chiara; |

Particle systems and PDEs VI | Talk given at a conference | From the Hartree-Fock dynamics to the Vlasov Equation | 27.11.2017 | Nice, France | Saffirio Chiara; |

Collisionless Boltzmann (Vlasov) equation and modeling of self-gravitating systems and plasmas | Talk given at a conference | Lagrangian solutions to the Vlasov-Poisson system with a point charge | 30.10.2017 | CIRM Luminy, France | Saffirio Chiara; |

Workshop on the Analysis of Effective One-Particle Equations and their Derivation | Talk given at a conference | Derivation of the linear Bolzmann-Vlasov equation from particle system | 31.07.2017 | LMU Munich, Germany | Saffirio Chiara; |

7TH INTERNATIONAL WORKSHOP ON KINETIC THEORY & APPLICATIONS | Talk given at a conference | Derivation of the linear Bolzmann-Vlasov equation from particle system | 19.06.2017 | University of Karlstad, Sweden | Saffirio Chiara; |

Macroscopic Limits of Quantum Systems | Talk given at a conference | Mean Field Evolution of Fermions with Coulomb Interaction | 30.03.2017 | TU Munich, Germany | Saffirio Chiara; |

Seminar in Statistical Mechanics | Individual talk | Mean Field Evolution of Fermions with Coulomb Interaction | 09.03.2017 | University of Warwick , Great Britain and Northern Ireland | Saffirio Chiara; |

Seminar in Mathematical Physics | Individual talk | Mean Field Evolution of Fermions with Coulomb Interaction | 02.02.2017 | SISSA Trieste, Italy | Saffirio Chiara; |

Mean-field dynamics of many particle systems | Talk given at a conference | Mean Field Evolution of Fermions with Coulomb Interaction | 14.12.2016 | Pauli Institut, Vienna , Austria | Saffirio Chiara; |

Mathematical Physics | Talk given at a conference | Mean Field Evolution of Fermions with Coulomb Interaction | 28.11.2016 | ETH Zürich, Switzerland | Saffirio Chiara; |

Kinetic Theory and its neighbours | Talk given at a conference | Mean field evolution of fermions with Coulomb interaction | 19.10.2016 | L'Aquila, Italy | Saffirio Chiara; |

Weakly seminar | Individual talk | Derivation of effective equations from many body dynamics | 11.10.2016 | Politecnico Torino, Italy | Saffirio Chiara; |

Title | Date | Place |
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Workshop "Effective equations: frontiers in classical and quantum systems" | 24.06.2019 | HCM Bonn, Germany |

Oberwolfach mini-workshop "Lorentz gas dynamics: particle systems and scaling limits" | 04.03.2019 | MFO Oberwolfach, Germany |

Communication | Title | Media | Place | Year |
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Talks/events/exhibitions | What is... the arrow of time? | German-speaking Switzerland | 2018 |

Title | Year |
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SNSF Eccellenza Professorial Fellow | 2018 |

Number | Title | Start | Funding scheme |
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181153 | From Newton and Schrödinger many-body dynamics to the Boltzmann equation | 01.08.2019 | Eccellenza |

The subject of this project is the rigorous derivation of effective macroscopic equations starting from the fundamental laws of classical and quantum physics. This is a central question in non-equilibrium statistical mechanics. In particular, we are interested in the Boltzmann equation arising from classical Hamiltonian mechanics for long range potentials and in the emergence of the Hartree-Fock equation and of the quantum Boltzmann equation from the many body Schroedinger evolution.

Swiss National Science Foundation (SNSF)

Wildhainweg 3P.O. Box

CH-3001 Bern

Phone +41 31 308 22 22

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