Guest Lecture: Constanza Rojas Molina

The Mathematics of Disordered Quantum Systems

Constanza Rojas-Molina is Associate Professor at the Department of Mathematics and Laboratoire AGM of CY Cergy Paris Université

Abstract: In 1958, physicist P.W. Anderson reported the absence of electron propagation in materials with impurities, a phenomenon known as Anderson localization, for which he won the Nobel Prize in Physics in 1977. In mathematics, Anderson's discovery sparked the search for a rigorous description of this phenomenon and the development of the theory of random Schrödinger operators. Since then, this theory has been improved and refined to consider a large class of quantum disordered systems. Despite the fact that by now it is well understood that Anderson localization is a consequence of the disorder present in the medium, some of the original questions remain open, such as the existence of phase transitions in disordered media. The search for a rigorous proof of this transition is a driving force behind much of the research done today in this field.

In this talk we will give an overview of the theory of random Schrödinger operators and the study of phase transitions in disordered systems. We will introduce an operator arising in a recent study of a class of random processes connected to statistical mechanics for which a phase transition is known. We will present some recent results on the Integrated Density of states, a function on the spectrum of the operator, which exhibits a phase transition in this model. This is based on joint work with M. Disertori (Bonn) and X. Zeng (Strasbourg).


Date: 13th December 2022 from 12:30 to 14:00

The hybrid guest lecture is organised in person at the Auditorium of MIR in Neuville-sur-Oise and remotely on Zoom.

To attend the remote guest lecture, please connect to Zoom:  https://cyu-fr.zoom.us/j/91374038485

ID meeting: 913 7403 8485

The video will be online on the CY AS YouTube channel