RESUMO
Solid state physics deals with systems composed of atoms with strongly bound electrons. The tunneling probability of each electron is determined by interactions that typically extend to neighboring sites, as their corresponding wave amplitudes decay rapidly away from an isolated atomic core. This kind of description is essential in condensed-matter physics, and it rules the electronic transport properties of metals, insulators and many other solid-state systems. The corresponding phenomenology is well captured by tight-binding models, where the electronic band structure emerges from atomic orbitals of isolated atoms plus their coupling to neighboring sites in a crystal. In this work, a mechanical system that emulates dynamically a quantum tightly bound electron is built. This is done by connecting mechanical resonators via locally periodic aluminum bars acting as couplers. When the frequency of a particular resonator lies within the frequency gap of a coupler, the vibrational wave amplitude imitates a bound electron orbital. The localization of the wave at the resonator site and its exponential decay along the coupler are experimentally verified. The quantum dynamical tight-binding model and frequency measurements in mechanical structures show an excellent agreement. Some applications in atomic and condensed matter physics are suggested.
RESUMO
Coherent transport phenomena are difficult to observe due to several sources of decoherence. For instance, in the electronic transport through quantum devices the thermal smearing and dephasing, the latter induced by inelastic scattering by phonons or impurities, destroy phase coherence. In other wave systems, the temperature and dephasing may not destroy the coherence and can then be used to observe the underlying wave behaviour of the coherent phenomena. Here, we observe coherent transmission of mechanical waves through a two-dimensional elastic Sinai billiard with two waveguides. The flexural-wave transmission, performed by non-contact means, shows the quantization when a new mode becomes open. These measurements agree with the theoretical predictions of the simplest model highlighting the universal character of the transmission fluctuations.