Quantum-information theory of a Dirichlet ring with Aharonov-Bohm field
- URL: http://arxiv.org/abs/2202.04692v3
- Date: Mon, 11 Apr 2022 03:45:46 GMT
- Title: Quantum-information theory of a Dirichlet ring with Aharonov-Bohm field
- Authors: O. Olendski
- Abstract summary: Shannon information entropies $S_rho,gamma$, Fisher informations $I_rho,gamma$, Onicescu energies $O_rho,gamma$ and R'enyi entropies $R_rho,gamma(alpha)$ are calculated.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Shannon quantum information entropies $S_{\rho,\gamma}$, Fisher informations
$I_{\rho,\gamma}$, Onicescu energies $O_{\rho,\gamma}$ and R\'{e}nyi entropies
$R_{\rho,\gamma}(\alpha)$ are calculated both in the position (subscript
$\rho$) and momentum ($\gamma$) spaces as functions of the inner radius $r_0$
for the two-dimensional Dirichlet unit-width annulus threaded by the
Aharonov-Bohm (AB) flux $\phi_{AB}$. Discussion is based on the analysis of the
corresponding position and momentum waveforms. Position Shannon entropy
(Onicescu energy) grows logarithmically (decreases as $1/r_0$) with large $r_0$
tending to the same asymptote $S_\rho^{asym}=\ln(4\pi r_0)-1$
[$O_\rho^{asym}=3/(4\pi r_0)$] for all orbitals whereas their Fisher
counterpart $I_{\rho_{nm}}(\phi_{AB},r_0$) approaches in the same regime the
$m$-independent limit mimicking in this way the energy spectrum variation with
$r_0$, which for the thin structures exhibits quadratic dependence on the
principal index. Frequency of the fading oscillations of the radial parts of
the wave vector functions increases with the inner radius what results in the
identical $r_0\gg1$ asymptote for all momentum Shannon entropies
$S_{\gamma_{nm}}(\phi_{AB};r_0)$ with the alike $n$ and different $m$. The same
limit causes the Fisher momentum components $I_\gamma(\phi_{AB},r_0)$ to grow
exponentially with $r_0$. It is proved that the lower limit $\alpha_{TH}$ of
the semi-infinite range of the dimensionless coefficient $\alpha$, where the
momentum component of this one-parameter entropy exists, is \textit{not}
influenced by the radius; in particular, the change of the topology from the
simply, $r_0=0$, to the doubly, $r_0>0$, connected domain is \textit{un}able to
change $\alpha_{TH}=2/5$. AB field influence on the measures is calculated too.
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