We show how frequency fluctuations of a vibrational mode can be separated from other sources of phase noise. The method is based on the analysis of the time dependence of the complex amplitude of forced vibrations. The moments of the complex amplitud
e sensitively depend on the frequency noise statistics and its power spectrum. The analysis applies to classical and to quantum vibrations.
We predict a novel nonlinear electromagnetic phenomenon in layered superconducting slabs irradiated from one side by an electromagnetic plane wave. We show that the reflectance and transmittance of the slab can vary over a wide range, from nearly zer
o to one, when changing the incident wave amplitude. Thus changing the amplitude of the incident wave can induce either the total transmission or reflection of the incident wave. In addition, the dependence of the superconductor transmittance on the incident wave amplitude has an unusual hysteretic behavior with jumps. This remarkable nonlinear effect (self-induced transparency) can be observed even at small amplitudes, when the wave frequency $omega$ is close to the Josephson plasma frequency $omega_J$.
Locally-gated single-layer graphene sheets have unusual discrete energy states inside the potential barrier induced by a finite-width gate. These states are localized outside the Dirac cone of continuum states and are responsible for novel quantum tr
ansport phenomena. Specifically, the longitudinal (along the barrier) conductance exhibits oscillations as a function of barrier height and/or width, which are both controlled by a nearby gate. The origin of these oscillations can be traced back to singularities in the density of localized states. These graphene conductance-oscillations resemble the Shubnikov-de-Haas (SdH) magneto-oscillations; however, here these are driven by an electric field instead of a magnetic field.
