Localization–delocalization of a particle in a quantum corral in presence of a constant magnetic field

We obtained the energy and wave functions of a particle in a quantum corral subjected to a constant magnetic field, as a function of the radius of the quantum corral R c and the intensity of the magnetic field b 2 . We also computed the standard deviation and the Shannon information entropies as a function of R c and b 2 , which in turn are compared to determine their effectiveness in measuring particle (de)localization. For a fixed magnitude of the magnetic field b 2 , the Shannon entropy of all states diminishes as the confinement radius R c decreases revealing an extensive localization. For a fixed value of R c , the Shannon entropy of the states (0, 0) and (0, 1) decreases monotonically as the magnetic field b 2 grows, whereas for the states (1, 0), (2, 0), (1, 1) and (2, 1), the Shannon entropy grows slowly, reaching a maximum (delocalization), and then diminishes as b 2 increases. The expectation value of r for a fixed value R c , for the states (0, 0) and (0, 1), decreases monotonically as b 2 increases, whereas for the states (1, 0), (2, 0), (1, 1) and (2, 1) increases and after reaching a maximum, it decreases as b 2 grows. This behavior is counter-intuitive because the particle is forecasted to be closer to the origin as the magnetic field grows. Graphic abstract The Shannon entropy of few low lying states of a quantum corral as a function of magnetic field.