27. Jun 2025

Quantum Diffusion and Random Matrix Theory

Mathphys Analysis Seminar

Datum: 27. June 2025 | 10:00 – 11:30
Sprecher: Felipe Hernández, Eberly College of Science, Penn State University
Veranstaltungsort: Heinzel Seminar Room (I21.EG.101), Office Building West, ISTA
Sprache: Englisch

The random Schrödinger equation is a simple model of wave transport in random media. A fundamental problem in this setting is to establish diffusive behavior of waves at time scales that are much larger than the kinetic time. The traditional approach to understanding the behavior of solutions is to use perturbative series expansions and diagrammatic arguments. In this talk I will explain how simple ideas borrowed from random matrix theory can be used to derive "self-consistent equations" for the resolvent R(z) of the random Schrodinger operator, completely bypassing diagrammatic expansions. The error terms in the self-consistent equations are bounded using new dispersive-type estimates for the resolvent R(z). This is based on joint work with Adam Black and Reuben Drogin.