论文标题
Dirichlet和Neumann一维量子井的Rényi和Tsallis熵
Rényi and Tsallis entropies of the Dirichlet and Neumann one-dimensional quantum wells
论文作者
论文摘要
对这两种几何形状之间的rényi$ r（α）$以及tsallis $ t（α）$熵的一维（1d）量子井的差异和诺伊曼边界条件（BC）的比较分析。特别是，对于任何一个BC而言，Rényi位置组件对参数$α$的依赖性对于所有轨道都是相同的，但最低的Neumann依赖性相同，而Neumann的neumann则不受$α$的变化影响相应的功能$ r $。无量纲rényi/tsallis系数的半限制$α_{在接近此临界值的$α$时，相应的动量功能确实有分歧。两个bcs的阈值$α_{th}之间的差距导致rényi不确定性关系的不同行为作为$α$的函数。对于这两种配置，$α= 1/2 $的最低能量水平都使两种类型的熵不平等都饱和，从而证实了早期的推测。还可以猜想一半的阈值$α_{th} $是任何一维非迪里奇系统的特征。从数学和物理观点讨论和分析了其他属性。
A comparative analysis of the Dirichlet and Neumann boundary conditions (BCs) of the one-dimensional (1D) quantum well extracts similarities and differences of the Rényi $R(α)$ as well as Tsallis $T(α)$ entropies between these two geometries. It is shown, in particular, that for either BC the dependencies of the Rényi position components on the parameter $α$ are the same for all orbitals but the lowest Neumann one for which the corresponding functional $R$ is not influenced by the variation of $α$. Lower limit $α_{TH}$ of the semi infinite range of the dimensionless Rényi/Tsallis coefficient where {\em momentum} entropies exist crucially depends on the {\em position} BC and is equal to one quarter for the Dirichlet requirement and one half for the Neumann one. At $α$ approaching this critical value, the corresponding momentum functionals do diverge. The gap between the thresholds $α_{TH}$ of the two BCs causes different behavior of the Rényi uncertainty relations as functions of $α$. For both configurations, the lowest-energy level at $α=1/2$ does saturate either type of the entropic inequality thus confirming an earlier surmise about it. It is also conjectured that the threshold $α_{TH}$ of one half is characteristic of any 1D non-Dirichlet system. Other properties are discussed and analyzed from the mathematical and physical points of view.
