Geometric Measure Theory (GMT) related to the localization of waves
This group investigates aspects of the Simons collaboration related to Geometric Measure Theory. This includes standard GMT issues such as the study of free boundary problems or regularity results for epiperimetric sets in convex domains, but also relations between elliptic measure and the regularity of PDE's in relation to the geometry of the domains where they are defined.
- Subgroup Leader: Guy David
- Subgroup Members: Zanbing Dai, Max Engelstein, Joseph Feneuil, David Jerison, Cole Jeznach, Polina Perstneva, Antoine Julia, Linhan Li, Svitlana Mayboroda, Tomas Merchán Rodríguez, Andrea Merlo, Bruno Poggi
Cold atoms in optical disorder: a simulator for quantum particles localization
In the spirit of Feynman's landmark paper, we use an ensemble of ultra-cold atoms in a laser speckle to study Anderson localization of quantum particles in a controlled disorder. We can vary dimensionality and control interactions between particles. The aim of the group is to compare the experimental findings and their standard theoretical interpretations with the landscape approach, and evaluate the new possibilities offered by the landscape theory.
- Subgroup Leader: Alain Aspect
- Subgroup Members: Douglas Arnold, Thomas Bourdel, Dominique Delande, Marcel Filoche, Yukun Guo, Vincent Josse, Lucas Lavoine, Svitlana Mayboroda, Pierre Pelletier, Azer Trimeche, Xudong Yu
Applying localization landscape theory to emerging optoelectronics (organics)
Emerging materials such as organics, perovskites and quantum dots are shaping the fields as diverse as solar cells, light-emitting diodes and lasers. Due to their facile solution-processed synthesis, they possess high degree of disorder which governs their fundamental optoelectronic properties. Here in the Organics subgroup, we are utilizing the state of the art localization landscape theory to determine how disorder in these materials are affecting their electronic, optical and transport properties, so as to design better devices based on improved understanding.
- Subgroup Leader: Richard Friend
- Subgroup Members: Yun Liu, Abel Thayil, Jean-Philippe Banon, Perceval Desforges, Douglas Arnold, Marcel Filoche, Arjun Ashoka
Static disorder in semiconductors
In disordered semiconductor alloys, localization of charge carriers at the nanoscale requires solving the Schrödinger equation to obtain the spatial electronic and hole densities. In addition, the electronic states, the hole states, and the charged impurities are coupled by the Coulomb interaction through the Poisson equation. The aim of this group is to investigate the role of quantum localization in this many-body interacting problem, and to determine how the localization landscape provides an efficient and accurate approach to computing the various properties of these materials (light absorption, emission, charge carrier transport).
- Subgroup Leader: Marcel Filoche
- Subgroup Members: Douglas Arnold, Jean-Philippe Banon, Li Chen, Guy David, Sir Richard Friend, Kaibo Hu, David Jerison, Guillaume Lheureux, Tyson Loudon, Cheyenne Lynsky, Svitlana Mayboroda, Camille Pivard, Clayton Qwah, Mylène Sauty, Jim Speck, Abel Thayil, Wei Wang, Claude Weisbuch, Shiwen Zhang
This subgroup investigates the deep connections between random media and waves localization. With the help of methods coming from probability theory (percolation, random walk in random environment, homogenization, spin systems, etc), it aims at improving our understanding of the landscape function and related central questions raised by the Simons Collaboration.
- Subgroup Leader: Hugo Duminil-Copin
- Subgroup Members: Svitlana Mayboroda, Guy David, David Jerison