The Quasicrystal conductivity conundrum: spectral theory and optical experiments
Mikael Rechtsman, CIMS


Quasicrystals are solid materials (typically metal alloys) whose atoms are not arranged periodically but have long-range order and rotational symmetries that are disallowed in  periodic systems.  Among the fascinating paradoxes that have emerged from experiments on quasicrystals is the conductivity problem: quasicrystal conductivity increases with  temperature, in direct opposition to crystalline materials. To date, there is no  definitive theoretical explanation for this effect with experimental corroboration.  I  describe an optical experiment in which this question can be resolved and explain how by  use of simulations.  Initial experimental results agree with the numerics.  The key mathematics here is the spectral theory of Schrodinger operators with quasiperiodic and disordered potentials.  This project is in collaboration with Liad Levi and Moti Segev of the Technion.