Session S30 - Mathematical Methods in Quantum Mechanics

Thursday, July 15, 19:00 ~ 19:25 UTC-3

Dirac Operators in a decaying random environment

Amal Taarabt

Pontificia Universidad Católica de Chile, Chile   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Electronic transport is a central object in the study of conduction in condensed matter. Recently, the development of new materials such as graphene has opened the doors to new technologies with applications in nano-engineering and telecommunications. From a mathematical point of view, the physics of these systems is encoded in the spectral and dynamic properties of random operators. The simplest model for charge carrier dynamics in a graphene-like structure is the discrete Laplacian on a hexagonal lattice, but at low excitation energies this dynamics is actually described by a massless two-dimensional Dirac operator. In this talk, we will introduce dynamical localization and we will present some recent results on the spectral and dynamic properties of random Dirac operators and notably in contexts where ergodicity is broken and where a transition phenomenon is observed between localization and delocalization regimes.

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