Quantum Resonances and Trapped Trajectories

Ángel S. Sanz, Salvador Miret-Artés

The elastic resonant scattering of He atoms off the Cu(117) surface is fully described with the formalism of quantum trajectories provided by Bohmian mechanics. Within this theory of quantum motion, the concept of trapping is widely studied and discussed. Classically, atoms undergo impulsive collisions with the surface, and then the trapped motion takes place covering at least two consecutive unit cells. However, from a Bohmian viewpoint, atom trajectories can smoothly adjust to the equipotential energy surface profile in a sort of sliding motion; thus the trapping process could eventually occur within one single unit cell. In particular, both threshold and selective adsorption resonances are explained by means of this quantum trapping considering different space and time scales. Furthermore, a mapping between each region of the (initial) incoming plane wave and the different parts of the diffraction and resonance patterns can be easily established, an important issue only provided by a quantum trajectory formalism.

Hideo Tamura

We study the Aharonov-Bohm effect (the AB effect) in quantum resonances for scattering by three solenoids in two dimensions under the situation that the centers of the solenoids are placed almost in line.The resonances are shown to be generated near the real axis by the trapping trajectories when the centers are largely separated from one another.We analyze how the AB effect is reflected in the location of these resonances.The results are described by use of the backward scattering amplitude by one solenoid and depend on the ratio of the distances between the solenoids as well as on the magnetic fluxes.The method makes a full use of the information from the scattering system by one solenoid, which is known to be exactly solvable in quantum mechanics.We also discuss the case of four solenoids.

Jinshuang Jin, Jianhong Guo, JunYan Luo +2 more

A Monte Carlo simulation on the basis of quantum trajectory approach is carried out for the measurement dynamics of a single-electron spin resonance. The measured electron, which is confined in either a quantum dot or a defect trap, is tunnel coupled to a side reservoir and continuously monitored by a mesoscopic detector. The simulation not only recovers the observed telegraphic signal of detector current, but also predicts unique features in the output power spectrum which are associated with electron dynamics in different regimes.

Marco Merkli