Quantum information measures of the Aharonov-Bohm ring in uniform magnetic fields

Shannon quantum information entropies S-rho,S-gamma,S- Fisher informations I-rho,I-gamma,I- Onicescu energies O-rho,O-gamma and complexities e(s)O are calculated both in the position (subscript rho) and momentum (gamma) spaces for the azimuthally symmetric two-dimensional nanoring that is placed into the combination of the transverse uniform magnetic field B and the Aharonov-Bohm (AB) flux phi(AB) and whose potential profile is modelled by the superposition of the quadratic and inverse quadratic dependencies on the radius r. The increasing intensity B flattens momentum waveforms Phi(nm)(k) and in the limit of the infinitely large fields they turn to zero: Phi(nm)(k) -> 0 at B -> infinity, what means that the position wave functions psi(nm)(r), which are their Fourier counterparts, tend in this limit to the delta-functions. Position (momentum) Shannon entropy depends on the field B as a negative (positive) logarithm of omega(eff) equivalent to (omega(2)(0) + omega(2)(c)/4 )(1/2), where omega(0) determines the quadratic steepness of the confining potential and we is a cyclotron frequency. This makes the sum S-rho nm + S-gamma nm a field-independent quantity that increases with the principal n and azimuthal m quantum numbers and does satisfy entropic uncertainty relation. Position Fisher information does not depend on m, linearly increases with n and varies as weft whereas its n and m dependent Onicescu counterpart O-rho nm changes as omega(-1)(eff). The products I rho nmI gamma nm and O-rho nm O-gamma nm are B-independent quantities. A dependence of the measures on the ring geometry is discussed. It is argued that a variation of the position Shannon entropy or Onicescu energy with the AB field uniquely determines an associated persistent current as a function of phi(AB) at B = 0. An inverse statement is correct too. (C) 2019 Elsevier B.V. All rights reserved.