RESUMO
We present an in-depth study of the universal correlations of scattering-matrix entries required in the framework of nonstationary many-body scattering of noninteracting indistinguishable particles where the incoming states are localized wave packets. Contrary to the stationary case, the emergence of universal signatures of chaotic dynamics in dynamical observables manifests itself in the emergence of universal correlations of the scattering matrix at different energies. We use a semiclassical theory based on interfering paths, numerical wave function based simulations, and numerical averaging over random-matrix ensembles to calculate such correlations and compare with experimental measurements in microwave graphs, finding excellent agreement. Our calculations show that the universality of the correlators survives the extreme limit of few open channels relevant for electron quantum optics, albeit at the price of dealing with large-cancellation effects requiring the computation of a large class of semiclassical diagrams.
RESUMO
We explored the bonding properties of the quantum corral (a circle of 48 iron atoms placed on a copper surface) reported by Crommie et al. in 1993, along with variants, as an artificial atom using an atomic force microscope (AFM). The original corral geometry confines 102 electrons to 28 discrete energy states, and we found that these states can form a bond to the front atom of the AFM with an energy of about 5 millielectron volts. The measured forces are about 1/1000 of typical forces in atomically resolved AFM. The confined electrons showed covalent attraction to metal tips and Pauli repulsion to CO-terminated tips. The repulsion at close distance was evident from the response of corral states created by deliberately placing single iron atoms inside the corral. The forces scaled appropriately with a 24-atom corral.
