We explain the origin of the Kondo mirage seen in recent quantum corral Scanning Tunneling Microscope (STM) experiments with a scattering theory of electrons on the surfaces of metals. Our theory combined with experimental data provides the first direct observation of a single Kondo atom phase shift. The Kondo mirage observed at the empty focus of an elliptical quantum corral is shown to arise from multiple electron bounces off the corral wall adatoms in a manner analagous to the formation of a real image in optics. We demonstrate our theory with direct quantitive comparision to experimental data.PACS numbers: 73.20. At, 72.10.Fk, 72.15.Qm, 3.65.Nk The Kondo effect is a fascinating, many-body quantum phenomenon occuring at low temperatures, whereby a magnetic impurity in metallic bulk or on a metallic surface has its local moment screened by a cloud of conduction electrons, called the Kondo cloud, that 1

We demonstrate the existence and significance of diffractive orbits in an open microwave billiard, both experimentally and theoretically. Orbits that diffract off of a sharp edge strongly influence the conduction spectrum of this resonator, especially in the regime where there are no stable classical orbits. On resonance, the wavefunctions are influenced by both classical and diffractive orbits. Off resonance, the wavefunctions are determined by the constructive interference of multiple transient, nonperiodic orbits. Experimental, numerical, and semiclassical results are presented.Recently, Katine et al. studied the transmission behavior of an open quantum billiard in the context of a two dimensional electron gas (2DEG) in a GaAs/AlGaAs heterostructure [1]. Their resonator was formed by a wall with a small aperture, called a quantum point contact (QPC), and an arc-shaped reflector. A schematic of this resonator is shown in Fig. 1. The voltage on the reflector could be varied, effectively moving the reflector towards or away from the wall. Their measurements showed a series of conductance peaks, analogous to those seen in a Fabry-Perot, as the reflector position was varied.As we discuss below, the resonator considered here represents a new class of billiards, to our knowledge not previously studied in the literature. That is, the billiard is geometrically open, but in the stable regime, it is classically closed. In the unstable regime, the resonance properties of the billiard are determined in large part by diffraction.The resonator shown in Fig. 1 has two distinct modes of operation. When the center of curvature of the reflector is to the left of the wall (the regime studied in [1]), then all classical paths starting from the QPC that hit the reflector remain forever in the region between wall and the reflector: the dynamics is stable and the periodic orbits can be semiclassically quantized. Each quantized mode of the resonator can be characterized by two quantum numbers (n, m), which represent the number of radial and angular nodes respectively. As the reflectorwall separation is varied, the conductance exhibits a peak each time one of these quantized modes is allowed.

In this paper, we demonstrate the existence and significance of diffractive orbits in an open microwave billiard, both experimentally and theoretically. Orbits that diffract off of a sharp edge of the system are found to have a strong influence on the transmission spectrum of the system, especially in the regime where there are no stable classical orbits. On resonance, the wavefunctions are influenced by both classical and diffractive orbits. Off resonance, the wavefunctions are determined by the constructive interference of multiple transient, nonperiodic orbits. Experimental, numerical, and semiclassical results are presented.

Experiments with dielectric scatterers in a parallel-plate waveguide have verified for the first time the existence of proximity resonances in two dimensions. A numerical solution to the scattering problem supports the analysis of the experimental data.It has recently been shown that two resonant s-wave scatterers placed close together produce two resonances in the spectrum of the combined system [1]. The first, which remains s-wave in character, is shifted down in energy and broadened with respect to the original single scatterer resonance. The second resonance, which is p-wave in character, is shifted up an equal amount in energy and can have a very narrow width. In fact, the width of the p-wave resonance vanishes as the scatterers approach each other. This second resonance has been dubbed the proximity resonance.Proximity resonances are important in a number of physical contexts, including scattering of sound from small identical bubbles in liquids [2,3], and scattering and emission of light from nearby dipole scatterers [4,5] where a proximity resonance effect has long been known under the name of Dicke super-radiance and sub-radiance. In Ref.[1], the effect was discussed for particle scattering from two identical atoms (or other identical scatterers) for the first time. Here we discuss yet another context, the classical scattering of electromagnetic waves from dielectric discs. At the same time (however see the caveat below) the system we describe mimics quantum scattering from two adjacent potential wells in two dimensions [6,7].For the purposes of modeling the experiment, we developed a method of solving the scattering problem involving cylindrical basis functions centered on each disc. It turned out that the point scatterer model [8,9], which was used in the original discussion of proximity resonances [1], was not sufficient to accurately model the experiment. In order for the point scatterer model to be applicable, at least two conditions must be met: r ≪ λ, and r ≪ d, where r is the physical radius of each scatterer, λ the wavelength, and d the distance between the scatterers. In our experiments, the first condition was always met, but the second was not.Other work [10] indicates that there may be a similar effect present in the bound state spectrum of two nearby dielectric discs in a parallel-plate waveguide. Szmytkowski et al. [11] have found theoretically a similar resonance with fixed scattering length point interactions.The picture to keep in mind when thinking about the proximity resonance is the following: imagine two nearby point sources of unit amplitude, situated much closer together than a wavelength. When these sources are in phase, amplitude will add up nearly in phase everywhere in space, and the amplitude far from the sources will be appreciable. The far field intensity clearly will be s-wave in character. When the sources are out of phase, amplitude will interfere destructively everywhere, and the far field intensity will be much reduced compared to the in-phase case. Now, for a scatter...

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