Topological Dynamics of Self-Coupling Resonators

ABSTRACT

Atoms, quantum dots, quantum wells can be thought of as quantum resonators trapping electrons which self-interact via Coulomb potential. As a result, the dynamics of the electrons is completely determined by the type and position of the quantum resonators. In a similar way, the dynamics of the classical degrees of freedom of self-coupling classical resonators, such as acoustic or photonic cavities, is entirely determined by the position and orientation of the resonators. Topological classification tries to determin which patterns of resonators are equivalent from the dynamical point of view. In this talk I will introduce the notion of phason, known from quasicrystals, but generalized to any point patern. I will show how the topology and other properties of phason spaces separate the patterns in dynamical classes. I will back up the predictions with numerical simulations that exhibit perfect similarities of the resonant spectra for vastly different looking patterns. I will end with demonstrations of how these somewhat abstract theoretical ideas become a source of inspiration for many topological architected materials.

BIOGRAPHY

Dr. Emil Prodan received BS and MS degrees in theoretical and mathematical physics from University of Bucharest. His advisor for the MS degree was Gheorghe Nenciu. He received another MS degree in theoretical physics from University of Houston and then he graduated with a PhD from Rice University in theoretical physics. His advisor at Rice University was Peter Nordlander. Dr. Prodan received further postdoctoral training at University of California Santa Barbara under the direction of Walter Kohn, a Nobel Laureate in theoretical chemistry. He was a fellow of the Princeton Center for Complex Materials at Princeton University, where he was sponsored by Roberto Car and Nobel Laureate Duncan Haldane. Dr. Prodan joined the Physics Department of Yeshiva University in 2007 and now he is a full professor of physics.