Special Lectures “Mean-field limits of quantum many-body dynamics I and II”

0830

WED 2023

Place: Room A(East), 1st Floor, Building 62W, Waseda University, Nishi-Waseda Campus
Time: 10:00 - 15:30
Posted: 2023年7月29日(土)

The Multiscale Analysis, Modelling and Simulation Unit will hold the following special lectures as part of its international educational activities. In this lecture, we will explain the basics of how to derive continuous macro models from discrete micro models, including recent research results.

Dates

August 30, 2023

10:00 – 11:30　 Lecture I
14:00 – 15:30　 Lecture II

Venue

Room A(East), 1st Floor, Building 62W, Waseda University, Nishi-Waseda Campus

Title/Abstract

Mean-field limits of quantum many-body dynamics I and II

Abstract:
The rigorous justification of mean-field type equations (Boltzmann, Vlasov-Poisson, nonlinear Schrödinger…) from the many-body systems they are supposed to describe is a vast and fundamental subject. In these two lectures, we survey the mathematical achievements in the quantum aspect of the area, mainly regarding the nonlinear Schrödinger equation (NLS). Since the Nobel Prize winning first observation of Bose-Einstein condensation (BEC), the investigation of the new state of matter and thus NLS has become a research hot spot and seen vast developments in recent years. At the same time, the study of many-body dynamics feeds back into the study of the corresponding mean-field equations. We discuss such a derivation in the energy-critical setting which also yields a solution to a problem raised by T. Kato.