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We characterize the avoided crossings in a two-parameter, time-periodic system which has been the basis for a wide variety of experiments. By studying these avoided crossings in the near-integrable regime, we are able to determine scaling laws for the dependence of their characteristic features on the non-integrability parameter. As an application of these results, the influence of avoided crossings on dynamical tunneling is described and applied to the recent realization of multiple-state tunneling in an experimental system.
We study time-optimal protocols for controlling quantum systems which show several avoided level crossings in their energy spectrum. The structure of the spectrum allows us to generate a robust guess which is time-optimal at each crossing. We correct
Axion haloscope detectors require high-$Q$ cavities with tunable TM$_{010}$ modes whose resonant electric field occupies as much of the full volume of the cavity as possible. An analytical study of the effects of longitudinal symmetry breaking within
Cavity optomechanics offers powerful methods for controlling optical fields and mechanical motion. A number of proposals have predicted that this control can be extended considerably in devices where multiple cavity modes couple to each other via the
Optically addressable paramagnetic defects in wide-band-gap semiconductors are promising platforms for quantum communications and sensing. The presence of avoided crossings between the electronic levels of these defects can substantially alter their
The relation between the Shannon entropy and avoided crossings is investigated in dielectric microcavities. The Shannon entropy of probability density for eigenfunctions in an open elliptic billiard as well as a closed quadrupole billiard increases a