47 research outputs found
Adiabatic quantization of Andreev levels
We identify the time between Andreev reflections as a classical adiabatic
invariant in a ballistic chaotic cavity (Lyapunov exponent ), coupled
to a superconductor by an -mode point contact. Quantization of the
adiabatically invariant torus in phase space gives a discrete set of periods
, which in turn generate a ladder of excited states
. The largest quantized period is the
Ehrenfest time . Projection of the invariant torus
onto the coordinate plane shows that the wave functions inside the cavity are
squeezed to a transverse dimension , much below the width 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