论文标题
带有aharonov-bohm领域的dirichlet环的量子信息理论
Quantum-information theory of a Dirichlet ring with Aharonov-Bohm field
论文作者
论文摘要
Shannon量子信息熵$ s_ {ρ，γ} $，Fisher Infors $ i_ {ρ，γ} $，Onicescu Energies $ o_ o_ o_ {ρ，γ} $和Rényi熵$ r_ {ρ，γ} $均在site $ $ $ $ $ r_ r_ {ρ，γ} $ comption $ promition $ pertion $ pertion $ ploct（and）$ pection $ pertion（半径$ r_0 $用于二维dirichlet单位宽度环，由Aharonov-bohm（AB）Flux $ ϕ__ {ab} $螺纹。讨论基于对相应位置和动量波形的分析。 Shannon熵（Onicescu Energy）的位置以对数增长（减少为$ 1/R_0 $），大$ R_0 $倾向于同一渐近$S_ρ^{asym} = \ ln（4πr_0）-1 $ [$ o_p p^{asmym} = 3/（4πr_0）-1 $ [aSym} = 3/（4πr_0）$] $ i_ {ρ_{nm}}（ϕ_ {ab}，r_0 $）在同一制度中接近$ m $的限制，以这种方式模仿$ r_0 $的能量谱变化，对于薄结构而言，薄结构对主要索引表现出二次依赖性。波动矢量函数的径向部分的褪色振荡的频率随着内部半径的增加而增加，这导致了所有动量Shannon Entropies $ s_ {γ_{γ_{nm}}（ϕ__ {ab}; r_0）$与Allike $ n $和不同的$ M的相同动量Shannon Entropies $ S_ {γ_{nm}} $ s_ {γ_{nm}} $ S_ {γ_{nm}} $。相同的限制导致Fisher动量组件$I_γ（ϕ_ {AB}，R_0）$用$ R_0 $成倍增长。事实证明，无尺寸系数$α$的半限制范围的下限$α_{th} $，其中存在此单参数熵的动量成分，是受半径影响的\ textIt {not}；特别是，拓扑从简单的变化$ r_0 = 0 $，$ r_0> 0 $，连接域是\ textit {un}能够更改$α__{th} = 2/5 $。 AB场对措施的影响也是计算的。
Shannon quantum information entropies $S_{ρ,γ}$, Fisher informations $I_{ρ,γ}$, Onicescu energies $O_{ρ,γ}$ and Rényi entropies $R_{ρ,γ}(α)$ are calculated both in the position (subscript $ρ$) and momentum ($γ$) spaces as functions of the inner radius $r_0$ for the two-dimensional Dirichlet unit-width annulus threaded by the Aharonov-Bohm (AB) flux $ϕ_{AB}$. 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 $S_ρ^{asym}=\ln(4πr_0)-1$ [$O_ρ^{asym}=3/(4πr_0)$] for all orbitals whereas their Fisher counterpart $I_{ρ_{nm}}(ϕ_{AB},r_0$) 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 $S_{γ_{nm}}(ϕ_{AB};r_0)$ with the alike $n$ and different $m$. The same limit causes the Fisher momentum components $I_γ(ϕ_{AB},r_0)$ to grow exponentially with $r_0$. It is proved that the lower limit $α_{TH}$ of the semi-infinite range of the dimensionless coefficient $α$, 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 $α_{TH}=2/5$. AB field influence on the measures is calculated too.
