1. From local to latent symmetries and hidden degeneracies in wave mechanical systems

Peter Schmelcher

University of Hamburg, Germany

2 February 2021 Tue 4 pm

                                      IBS Center for Theoretical Physics of Complex Systems (PCS), Administrative Office (B349), Theory Wing, 3rd floor

                                      Expo-ro 55, Yuseong-gu, Daejeon, South Korea, 34126 Tel: +82-42-878-8633                     

We will use the concept of local symmetries in combination with recent graph theoretical results in order to explore and obtain desired wave mechanical properties. In a first step we will discuss the symmetry-induced emergence of compact localized states and flat band structures. The latter allows to design bound states in the continuum which are of immediate relevance for lasers and sensors. An application to an array of dipolar nanoparticles as an open scattering medium will be discussed. Compact localized states are then used to obtain high fidelity quantum state transfer in a corresponding network. Free time evolution and optimal control techniques are employed here to store and transfer quantum states. Finally, we exploit isospectral reduction schemes to predict so-called latent symmetries of effective Hamiltonians by subsystem partitioning. We relate latent to local symmetries and explain otherwise seemingly accidental degeneracies.