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

Influence of the transverse uniform magnetic field B on position (subscript ρ) and momentum (γ) Shannon quantum-information entropies S_ρ,γ, Fisher informations I_ρ,γ and Onicescu energies O_ρ,γ is studied theoretically for the 2D circular quantum dots whose circumference supports homogeneous either Dirichlet or Neumann boundary condition. Comparative analysis reveals similarities and differences of the surface influence on the properties of the structure. A conspicuous distinction between the two spectra are crossings of the Neumann energies with the same radial quantum number n and adjacent non-positive angular indices m. At the growing B, either system undergoes Landau condensation when its characteristics turn into their uniform field counterparts. It is shown that for the Dirichlet system this takes place at the smaller magnetic intensities; e.g., the n=m=0 Dirichlet sum S_ρ+S_γ on its approach to the fundamental limit 2(1+ln π) is at any B smaller than the corresponding Neumann sum what physically means that the former geometry provides more total information about the position and the motion of the particle. Comparison with electrostatic harmonic confinement is performed. Physical interpretation is based on the different roles of the two BCs and their interplay with the field: Dirichlet (Neumann) surface is a repulsive (attractive) interface.