PDEA Seminar: A nonlinear and nonlocal Schrödinger functional theory for magnetic self-interaction

Abstract: In the development of our understanding of interacting quantum systems, a crucial role has been played by effective functionals and corresponding PDEs which extend the famous Schrödinger theory of quantum mechanics to incorporate self-interaction, such as the nonlinear Schrödinger (NLS) and Gross-Pitaevskii (GP) theories. In this seminar I plan to introduce and discuss an effective functional in the plane (2D) which describes magnetic self-interaction, thus replacing the scalar nonlinearity of NLS and GP by a nonlocal vector nonlinearity. Models of this kind appear in the effective description of many-body systems with intermediate quantum statistics (termed "anyons"), and they have been studied analytically and numerically in joint works together with Michele Correggi, Romain Duboscq and Nicolas Rougerie.

This is a seminar in the PDEs and Applications seminar series