Adiabatic quantization of Andreev levels

We identify the time $T$ between Andreev reflections as a classical adiabatic invariant in a ballistic chaotic cavity (Lyapunov exponent $\lambda$), coupled to a superconductor by an $N$-mode point contact. Quantization of the adiabatically invariant torus in phase space gives a discrete set of periods $T_{n}$, which in turn generate a ladder of excited states $\epsilon_{nm}=(m+1/2)\pi\hbar/T_{n}$. The largest quantized period is the Ehrenfest time $T_{0}=\lambda^{-1}\ln N$. Projection of the invariant torus onto the coordinate plane shows that the wave functions inside the cavity are squeezed to a transverse dimension $W/\sqrt{N}$, much below the width $W$ of the point contact.Comment: 4 pages, 3 figure

Fano Lineshapes Revisited: Symmetric Photoionization Peaks from Pure Continuum Excitation

In a photoionization spectrum in which there is no excitation of the discrete states, but only the underlying continuum, we have observed resonances which appear as symmetric peaks, not the commonly expected window resonances. Furthermore, since the excitation to the unperturbed continuum vanishes, the cross section expected from Fano's configuration interaction theory is identically zero. This shortcoming is removed by the explicit introduction of the phase shifted continuum, which demonstrates that the shape of a resonance, by itself, provides no information about the relative excitation amplitudes to the discrete state and the continuum.Comment: 4 pages, 3 figure

Fano interference and cross-section fluctuations in molecular photodissociation

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.Comment: 4 pages, 4 figure

Semiclassical threshold law when the Wannier exponent diverges

Using semiclassical methods we investigate the threshold behavior for three-particle breakup of a system with one particle of charge Z and two other particles of charge -q. For the particular case where the ratio of the charges of the third particle to the wing particles is Z/g = 1/4, the Wannier exponent for breakup diverges and the threshold law changes from a power law to an exponential law of the form exp(-lambda/root E). The threshold behavior is tested above the region of divergence and it is found that for Z/q < 0.3 a power law does not hold. Ionizing trajectories show that the dynamics within the near zone can become crucial to the energy dependence of the cross section. Cases are found to arise where more than one trajectory contributes to the same final state giving rise to semiclassical interference effects

The decay of photoexcited quantum systems: a description within the statistical scattering model

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. Rev. A 58, R3375]. Here 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.Comment: 7 pages, 2 figure

Commensurability effects in Andreev antidot billiards

An Andreev billiard was realized in an array of niobium filled antidots in a high-mobility InAs/AlGaSb heterostructure. Below the critical temperature T_C of the Nb dots we observe a strong reduction of the resistance around B=0 and a suppression of the commensurability peaks, which are usually found in antidot lattices. Both effects can be explained in a classical Kubo approach by considering the trajectories of charge carriers in the semiconductor, when Andreev reflection at the semiconductor-superconductor interface is included. For perfect Andreev reflection, we expect a complete suppression of the commensurability features, even though motion at finite B is chaotic.Comment: 4 pages, 4 figure

Random matrix description of decaying quantum systems

This contribution describes a statistical model for decaying quantum systems (e.g. photo-dissociation or -ionization). It takes the interference between direct and indirect decay processes explicitely into account. The resulting expressions for the partial decay amplitudes and the corresponding cross sections may be considered a many-channel many-resonance generalization of Fano's original work on resonance lineshapes [Phys. Rev 124, 1866 (1961)]. A statistical (random matrix) model is then introduced. It allows to describe chaotic scattering systems with tunable couplings to the decay channels. We focus on the autocorrelation function of the total (photo) cross section, and we find that it depends on the same combination of parameters, as the Fano-parameter distribution. These combinations are statistical variants of the one-channel Fano parameter. It is thus possible to study Fano interference (i.e. the interference between direct and indirect decay paths) on the basis of the autocorrelation function, and thereby in the regime of overlapping resonances. It allows us, to study the Fano interference in the limit of strongly overlapping resonances, where we find a persisting effect on the level of the weak localization correction.Comment: 16 pages, 2 figure

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