https://doi.org/10.1140/epjd/s10053-021-00119-2
Regular Article - Quantum Information
Localization–delocalization of a particle in a quantum corral in presence of a constant magnetic field
1
Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, C.P. 09340, Iztapalapa, México, D.F., Mexico
2
Department of Physics, Swami Shraddhanand College, University of Delhi, New Delhi, India
Received:
16
November
2020
Accepted:
17
February
2021
Published online:
22
March
2021
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 
and the intensity of the magnetic field 
. We also computed the standard deviation and the Shannon information entropies as a function of and , which in turn are compared to determine their effectiveness in measuring particle (de)localization. For a fixed magnitude of the magnetic field , the Shannon entropy of all states diminishes as the confinement radius decreases revealing an extensive localization. For a fixed value of , the Shannon entropy of the states (0, 0) and (0, 1) decreases monotonically as the magnetic field 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 increases. The expectation value of 
for a fixed value , for the states (0, 0) and (0, 1), decreases monotonically as increases, whereas for the states (1, 0), (2, 0), (1, 1) and (2, 1) increases and after reaching a maximum, it decreases as grows. This behavior is counter-intuitive because the particle is forecasted to be closer to the origin as the magnetic field grows.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2021
