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

Abstract

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 Rc and the intensity of the magnetic field b 2 . We also computed the standard deviation and the Shannon information entropies as a function of Rc 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 Rc decreases revealing an extensive localization. For a fixed value of Rc, 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 Rc, 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.

Quantum-information theory of magnetic field influence on circular dots with different boundary conditions

“…Influence of the magnetic intensity B, Aharonov-Bohm flux and the topological defect on the position and momentum Shannon functionals was theoretically analyzed for the ring with Yukawa interaction in curved space with disclination [44]. Concerning our geometry, an attempt has been made to calculate the influence of the homogeneous field B on the Shannon entropies of the Dirichlet dot [45].…”

“…Figure 1 exhibits both Dirichlet (upper plots) and Neumann (lower panels) spectra where, in addition to the functions E B nm ( ), the dependencies E B nm ( )are also shown for better clarity. Despite the fact that the former curves are quite well known [45,[49][50][51][52][53][54][55][56][57][58], they are included here for completeness since a comparative analysis of the two geometries will point out to some important properties not discussed before. First, for either BC, the zero-field degeneracy of the m ≠ 0 states is lifted by the intensity B: as it follows from equations (21), the difference E nm − E n,−m is just the m multiple of the cyclotron energy:…”

The Shape Complexity of a Particle in the Circular Quantum Well with Homogeneous Perpendicular Magnetic Field

“…The Wave Function for a Particle Confined in the Magnetic Circular Quantum Well (MCQW) Suppose the particle is confined in a circular quantum well with impenetrable walls, the radius of the well is R. The circular quantum well is placed in the x-y plane, and the external homogeneous magnetic field points along the z axis with the magnitude B 0 , ⃑ B ¼ B 0 ⃑ k. For simplicity, we take the particle as an electron, with charge q = Àe and mass m e . Using atomic units, the Hamiltonian for the electron confined in the MCQW can be described as [32] H…”

“…Cruz and colleagues recently studied the localization–delocalization behavior of a particle in a quantum corral under the influence of a constant magnetic field. [ 32 ] The quantum corral in the magnetic field can be considered as a type of MCQW. They discussed the influence of magnetic field on the localization and delocalization of this system.…”

“…For simplicity, we take the particle as an electron, with charge q = − e and mass m e . Using atomic units, the Hamiltonian for the electron confined in the MCQW can be described as [ 32 ] where is the vector potential.…”