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 insight into 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, similar to the weak localisation correction of the magneto-resistance in chaotic mesoscopic systems. The semiclassical theory is shown to be in good agreement with quantum mechanical calculations.

We demonstrate that recent experiments for positron impact ionization of He and H 2 can be interpreted by extending Wannier theory to higher energies. Anharmonicities in the expansion of the three-particle potential around the Wannier configuration give rise to corrections in the threshold behavior of the breakup cross section. These corrections are taken into account perturbatively by employing the hidden crossing theory. The resulting threshold law is s͑E͒~E 2.640 exp͓20.73 p E ͔. The actual energy range for which the Wannier law is valid is found to be smaller for positron impact ionization than for electron impact ionization. [S0031-9007(97)03161-X]

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We derive an expression for the total photodissociation cross section of a molecule incorporating both indirect processes that proceed through excited resonances, and direct processes. We show that this cross section exhibits generalized Beutler-Fano line shapes in the limit of isolated resonances. Assuming that the closed system can be modeled by random matrix theory, we derive the statistical properties of the photodissociation cross section and find that they are significantly affected by the direct processes. We identify a unique signature of the direct processes in the cross-section distribution in the limit of isolated resonances.

The decay of photoexcited quantum systems (examples are photodissociation of molecules and autoionization of atoms) can be viewed as a half-collision process (an incoming photon excites the system which subsequently decays by dissociation or autoionization).For this reason, the standard statistical approach to quantum scattering, originally developed to describe nuclear compound reactions, is not directly applicable. Using an alternative approach, correlations and fluctuations of observables characterizing this process were first derived in [Fyodorov YV and Alhassid Y 1998 Phys. RevHere we show how the results cited above, and more recent results incorporating direct decay processes, can be obtained from the standard statistical scattering approach by introducing one additional channel.