Statistical Properties of Fano Resonances in Atomic and Molecular Photoabsorption

Statistical properties of Fano resonances occurring in photoabsorption to highly excited atomic or molecular states are derived. The situation with one open and one closed channel is analyzed when the classical motion of the excited complex in the closed channel is chaotic. The closed channel subspace is modeled by random matrix theory. The probability distribution of the Fano parameter is derived both for the case of time reversal symmetry (TRS) and broken time reversal symmetry. For the TRS case the area distribution under a resonance profile relevant for low resolution experiments is discussed in detail.Comment: 4 pages, 4 figure

Mesoscopic Fano Effect in a Quantum Dot Embedded in an Aharonov-Bohm Ring

The Fano effect, which occurs through the quantum-mechanical cooperation between resonance and interference, can be observed in electron transport through a hybrid system of a quantum dot and an Aharonov-Bohm ring. While a clear correlation appears between the height of the Coulomb peak and the real asymmetric parameter $q$ for the corresponding Fano lineshape, we need to introduce a complex $q$ to describe the variation of the lineshape by the magnetic and electrostatic fields. The present analysis demonstrates that the Fano effect with complex asymmetric parameters provides a good probe to detect a quantum-mechanical phase of traversing electrons.Comment: REVTEX, 9 pages including 8 figure

Non-universal features in the quasi-particle excitation spectra of Andreev billiards and wires

We study non-universal features of the quasi- particle excitation spectra of normal-conducting mesoscopic structures, whose classical dynamics are chaotic, and which are coupled to a superconducting lead. In the first part we demonstrate the importance of non-universal contributions in Andreev billiards when the ergodic time of the billiard is of the same order as the mean escape time. Non-universality introduces additional oscillations in the quasi- particle excitation spectrum which are related to the decaying modes of the classical evolution operator in the closed billiard. In the second part we demonstrate that in a long rough wire coupled to a superconductor classical anomalous diffusion modifies the energy scale below which universality holds as a function of the geometrical parameters in comparison to billiards with a narrow superconducting lead

Semiclassical theory of integrable and rough Andreev billiards

We study the effect on the density of states in mesoscopic ballistic billiards to which a superconducting lead is attached. The expression for the density of states is derived in the semiclassical S-matrix formalism shedding light onto the origin of the differences between the semiclassical theory and the corresponding result derived from random matrix models. Applications to a square billiard geometry and billiards with boundary roughness are discussed. The saturation of the quasiparticle excitation spectrum is related to the classical dynamics of the billiard. The influence of weak magnetic fields on the proximity effect in rough Andreev billiards is discussed and an analytical formula is derived. The semiclassical theory provides an interpretation for the suppression of the proximity effect in the presence of magnetic fields as a coherence effect of time reversed trajectories. It is shown to be in good agreement with quantum mechanical calculations