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- W4223511819 abstract "Shannon quantum-information entropies $$S_{rho ,gamma }(phi _{AB},r_0)$$ , Fisher informations $$I_{rho ,gamma }(phi _{AB},r_0)$$ , Onicescu energies $$O_{rho ,gamma }(phi _{AB},r_0)$$ and Rényi entropies $$R_{rho ,gamma }(phi _{AB},r_0;alpha )$$ 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 $$phi _{AB}$$ . Small (huge) values of $$r_0$$ correspond to the thick (thin) rings with extreme of $$r_0=0$$ describing the dot. Discussion is based on the analysis of the corresponding position $$varPsi _{nm}(phi _{AB},r_0;mathbf{r})$$ and momentum $$varPhi _{nm}(phi _{AB},r_0;mathbf{k})$$ waveforms, with n and m being principal and magnetic quantum indices, respectively: the former allows an analytic expression at any AB field whereas for the latter it is true at the flux-free configuration, $$phi _{AB}=0$$ , only. It is shown, in particular, that the position Shannon entropy $$S_{rho _{nm}}(phi _{AB},r_0)$$ [Onicescu energy $$O_{rho _{nm}}(phi _{AB},r_0)$$ ] grows logarithmically [decreases as $$1/r_0$$ ] with large $$r_0$$ tending to the same asymptote $$S_rho ^{mathrm{asym}}=ln (4pi r_0)-1$$ [ $$O_rho ^{mathrm{asym}}=3/(4pi r_0)$$ ] 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 $$varPhi _{nm}(phi _{AB},r_0;mathbf{k})$$ increases with the inner radius what results in the identical $$r_0gg 1$$ 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 $$r_0$$ . Based on these calculations, properties of the complexities $$e^SO$$ are addressed too. Among many findings on the Rényi entropy, 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 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 unable to change $$alpha _{TH}=2/5$$ . AB field influence on the measures is calculated too. Parallels are drawn to the geometry with volcano-shape confining potential and similarities and differences between them are discussed." @default.
- W4223511819 created "2022-04-15" @default.
- W4223511819 creator A5025509849 @default.
- W4223511819 date "2022-04-01" @default.
- W4223511819 modified "2023-10-16" @default.
- W4223511819 title "Quantum-information theory of a Dirichlet ring with Aharonov–Bohm field" @default.
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- W4223511819 doi "https://doi.org/10.1140/epjp/s13360-022-02627-5" @default.
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