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arXiv 2202.04692cond-mat.mes-hallmath-phmath.MPquant-ph
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具有Aharonov-Bohm场的Dirichlet环的量子信息理论

Quantum-information theory of a Dirichlet ring with Aharonov-Bohm field

O. Olendski

备注：
40 pages, 14 figures
发表信息：
Eur. Phys. J. Plus 137, 451 (2022)
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摘要：

在位置（下标$ρ$）和动量（$γ$）空间中计算了Aharonov-Bohm（AB）通量$ϕ_{AB}$穿过的二维Dirichlet单位宽度环的Shannon量子信息熵$S_{ρ,γ}$、Fisher量子信息熵$I_{ρ,γ}$、Onicescu能量$O_{ρ,γ}$和Rényi熵$R_{ρ,γ}(α)$，它们都是内半径$r_0$的函数.讨论是基于相应的位置和动量波形的分析。位置香农熵（Onicescu能量）随大的$r_0$呈指数增长（随$1/r_0$减小），对于所有轨道，大的$r_0$趋向于相同的渐近线$S_ρ^{asym}=\ln(4πr_0)-1$ [ $O_ρ^{asym}=3/(4πr_0)$ ]，而它们的Fisher对应物（$I_{ρ_{nm}}(ϕ_{AB},r_0$）在相同的状态下接近$m$独立极限，以这种方式模拟$r_0$的能谱变化，对于薄的结构，$r_0$表现出对主指数的二次依赖性。波矢函数的径向部分的衰减振荡的频率随着内半径的增加而增加，这导致对于具有相同的$n$和不同的$m$的所有动量香农熵$S_{γ_{nm}}(ϕ_{AB};r_0)$，具有相同的$r_0\gg1$渐近线。相同的限制导致Fisher动量分量$I_γ(ϕ_{AB},r_0)$随$r_0$呈指数增长。证明了无量纲系数$α$的半无限范围的下限$α_{TH}$，其中存在该单参数熵的动量分量，是受半径影响的\textit{not};特别地，拓扑从简单的$r_0=0$到双重的$r_0>0$，连通域的变化是\textit{un}能够改变$α_{TH}=2/5$ .计算了AB场对测量结果的影响。

英文摘要：

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.

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