Appalachia

published or submitted for publicatio

Spontaneous and stimulated emission tuning characteristics of a Josephson junction in a microcavity

We have investigated theoretically the tuning characteristics of a Josephson junction within a microcavity for one-photon spontaneous emission and for one-photon and two-photon stimulated emission. For spontaneous emission, we have established the linear relationship between the magnetic induction and the voltage needed to tune the system to emit at resonant frequencies. For stimulated emission, we have found an oscillatory dependence of the emission rate on the initial Cooper pair phase difference and the phase of the applied field. Under specific conditions, we have also calculated the values of the applied radiation amplitude for the first few emission maxima of the system and for the first five junction-cavity resonances for each process. Since the emission of photons can be controlled, it may be possible to use such a system to produce photons on demand. Such sources will have applications in the fields of quantum cryptography, communications and computation

The Stepanov differentiability theorem in metric measure spaces

We extend Cheeger's theorem on differentiability of Lipschitz functions in metric measure spaces to the class of functions satisfying Stepanov's condition. As a consequence, we obtain the analogue of Calderon's differentiability theorem of Sobolev functions in metric measure spaces satisfying a Poincaré inequalit

Absolute Continuity of Quasiconformal Mappings on Curves

Abstract.: We show that a quasiconformal mapping between two proper, locally Ahlfors Q-regular metric spaces, Q > 1, is absolutely continuous on almost every curve. We further relax the limes superior in the definition of quasiconformality to a limes inferior and verify that exceptional sets analogous to the Euclidean setting can be allowe