Coupled oscillator networks appear in a vast range of systems in nature and technology. While emergent global (complete) synchronization is paramount to the proper functioning of many technological networks such as power grids or communication networks, the ability to exhibit and maintain stable localized synchronization patterns is crucial to serve complex higher order functions in the brain such as information processing (or in future technological oscillator arrays). In this talk, I consider simple phase oscillator models for community networks and provide analytic results on the structure of the phase space for two (and more) communities. Finally, I discuss and outline open challenges regarding mean field descriptions of complex networks with community structures, and hope to inspire an open discussion.
This seminar shows that entangled state tunneling under bias can properly explain tunneling conductance line shapes of correlated systems such as cuprate and iron-based superconductors  as well as mesoscopic Kondo systems . In the former, the density of states (DOS) is an important quantity unlike the latter. We obtain the DOS in the fitting process of theoretical tunneling conductance to the experimental data. The obtained density of states is consistent with the spectral function given by angle-resolved photoemission spectroscopy (ARPES). It has been known that an inconsistency for the superconducting gap always exists in comparison between ARPES and scanning tunneling spectroscopy. Removing the inconsistency is a long standing task in condensed matter physics. I show that entangled state tunneling may resolve this problem. In addition, the origin of two side peaks appearing in tunneling conductance of all correlated systems is clarified. I will show that the appearance of two side peaks is a generic feature of non-equilibrium coherent tunneling in strongly correlated systems. We use the Green’s function technique in operator space (Liouvillian approach) instead of Hamiltonian approach because the latter has difficulties in determining basis vectors.
We explore the feasibility of realizing repulsive Casimir-Polder (CP) forces for a magnetic particle near a surface. Considering the toy model of an atom with an electric-dipole transition and an arbitrarily large magnetic spin, we analyze the interplay between the repulsive magnetic-dipole and the attractive electric-dipole contributions to the total CP force. Particularly noting that the magnetic CP interaction is relatively longer-ranged than the electric CP interaction due to the difference in their respective characteristic transition frequencies, we find a regime where the repulsive magnetic contribution to the total force can potentially exceed the attractive electric part in magnitude, thus making the overall force repulsive. We discuss some fundamental constraints and conditions necessary for achieving such a repulsion, identifying the magnetizability to polarizability ratio for the particle as a key figure of merit. We analyze ways to further enhance the magnitude of the repulsive magnetic CP force for an excited magnetic atom, such as, by preparing the atom in a "super-radiant" magnetic sub-level, and designing surface resonances close to the magnetic transition frequency. Our results could be instructive in identifying potential systems, mechanisms, and regimes where one could realize stable levitation via repulsive magnetic Casimir-Polder forces.