Shannon quantum information entropies $S_{ \rho,\gamma}$, Fisher informations $I_{ \rho,\gamma}$, Onicescu energies $O_{ \rho,\gamma}$ and complexities $e^SO$ are calculated both in position (subscript $\rho$) and momentum ($\gamma$) spaces for azimuthally symmetric 2D nanoring that is placed into combination of transverse uniform magnetic field $\bf B$ and Aharonov-Bohm (AB) flux $\phi_{ AB}$ and whose potential profile is modeled by superposition of quadratic and inverse quadratic dependencies on radius $r$. Increasing intensity $B$ flattens momentum waveforms $\Phi_{ nm}({ \bf k})$ and in the limit of infinitely large fields they turn to zero, what means that the position wave functions $\Psi_{ nm}({ \bf r})$, 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 $\omega_{ eff}\equiv\left(\omega_0^2+\omega_c^2/4\right)^{ 1/2}$, where $\omega_0$ determines the quadratic steepness of the confining potential and $\omega_c$ 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 $\omega_{ eff}$ whereas its $n$ and $m$ dependent Onicescu counterpart ${ O_\rho}_{ nm}$ changes as $\omega_{ eff}^{ -1}$. The products ${ I_\rho}_{ nm}{ I_\gamma}_{ nm}$ 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.
Categories: quant-ph cond-mat.mes-hall math-ph math.MP