Mesoscopic superconductors under irradiation: Microwave spectroscopy of Andreev states

We show that irradiation of a voltage-biased superconducting quantum point contact at frequencies of the order of the gap energy can remove the suppression of subgap dc transport through Andreev levels. Quantum interference among resonant scattering events involving photon absorption is furthermore shown to make microwave spectroscopy of the Andreev levels feasible. We also discuss how the same interference effect can be applied for detecting weak electromagnetic signals up to the gap frequency, and how it is affected by dephasing and relaxation.Comment: Submitted to a special volume of "Superlattices and Microstructures" on Mesoscopic Superconductivit

On a generic Verma module at the critical level over affine Lie superalgebras

We describe the structure of a Verma module with a generic highest weight at the critical level over a symmetrizable affine Lie superalgebra not of the type A(2k,2l)^{(4)}. We obtain the character formula for a simple module with a generic highest weight at the critical level conjectured by V. G. Kac and D. A. Kazhdan.Comment: considerably revised text, including the title; 33 page

MICROWAVE-INDUCED RESONANT REFLECTION AND LOCALIZATION OF BALLISTIC ELECTRONS IN QUANTUM MICROCHANNELS

We show that electron transport in a ballistic microchannel supporting both propagating and reflected modes can be completely blocked by applying a microwave electromagnetic field. The effect is due to resonant reflection caused by multiple coherent electron-photon scattering involving at least two spatially localized scattering centers in the channel. With many such scattering centers present the conductance is shown to have an irregular dependence on bias voltage, gate voltage and frequency with irregularily spaced dips corresponding to resonant reflection. When averaged over bias, gate voltage or frequency the conductance will decay exponentially with channel length in full analogy with the localization of 1D electrons caused by impurity scattering.Comment: 4 pages, latex, 1 figure available on reques