In this study, we investigate the effects of noncommutative Quantum Mechanics in three dimensions on the energy-levels of a charged isotropic harmonic oscillator in the presence of a uniform magnetic field in the z-direction. The extension of this problem to three dimensions proves to be non-trivial. We obtain the first-order corrections to the energy-levels in closed form in the low energy limit of weak noncommutativity. The most important result we can note is that all energy corrections due to noncommutativity are negative and their magnitude increase with increasing Quantum numbers and magnetic field.
We investigate the transition to synchronization in a two-layer network of oscillators with time-switching inter-layer links. We focus on the role of the number of inter-layer links and the timescale of topological changes. Initially, we observe a smooth transition to complete synchronization for the static inter-layer topology by increasing the number of inter-layer links. Next, for a dynamic topology with the existent inter-layer links randomly changing among identical oscillators in the layers, we observe a significant improvement in the system synchronizability; i.e., the layers synchronize with lower inter-layer connectivity. More interestingly, we find that, for a critical switching time, the transition from the network state of low inter-layer synchronization to high inter-layer synchronization occurs abruptly as the number of inter-layer links increases. We interpret this phenomenon as shrinking and ultimately the disappearance of the basin of attraction of a desynchronized network state.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.