论文标题
变形的中心对称网络中的运输
Transport in deformed centrosymmetric networks
论文作者
论文摘要
中心对称通常会介导从量子线到光合网络的各种复杂系统中的完美状态转移（PST）。我们介绍了随机矩阵的变形中心对称集合（DCE），$ h（λ）\ equiv h_++λh_- $，其中$ h _+ $是centrosymmmetric，而$ h _- $ h- $ as askew-centrosmmetricric。 $ h_ \ pm $的相对强度提示控制参数的系统大小缩放为$λ= n^{ - \fracγ{2}} $。我们提出了两次数量，分别是$ \ Mathcal {p} $和$ \ Mathcal {C} $，分别量化Centro-和skewcentro-Memmetry，在$γ_\ text {p} \ equiv 1 $和$γ_\ equiv-equiv -1 $ 1 $ 1 $ quartiv {p} \ equiv 1 $和$γ_\ equiv 1 $和$γ_\ equiv-equiv -1 $ 1中表现出二阶阶段过渡。此外，DCE在$γ_\ text {e} \ equiv 0 $下都具有恒星过渡。因此，我们精确地控制了DCE中的中心对称程度，我们研究了$γ$在复杂网络的运输特性上的表现。我们建议可以使用$ h（λ）$的特征向量构建此类随机网络，并确定最大传输保真度（$ f_t $）等于Centrosymmetry，$ \ Mathcal {p} $。
Centrosymmetry often mediates Perfect State Transfer (PST) in various complex systems ranging from quantum wires to photosynthetic networks. We introduce the Deformed Centrosymmetric Ensemble (DCE) of random matrices, $H(λ) \equiv H_+ + λH_-$, where $H_+$ is centrosymmetric while $H_-$ is skew-centrosymmetric. The relative strength of the $H_\pm$ prompts the system size scaling of the control parameter as $λ= N^{-\fracγ{2}}$. We propose two quantities, $\mathcal{P}$ and $\mathcal{C}$, quantifying centro- and skewcentro-symmetry, respectively, exhibiting second order phase transitions at $γ_\text{P}\equiv 1$ and $γ_\text{C}\equiv -1$. In addition, DCE posses an ergodic transition at $γ_\text{E} \equiv 0$. Thus equipped with a precise control of the extent of centrosymmetry in DCE, we study the manifestation of $γ$ on the transport properties of complex networks. We propose that such random networks can be constructed using the eigenvectors of $H(λ)$ and establish that the maximum transfer fidelity, $F_T$, is equivalent to the degree of centrosymmetry, $\mathcal{P}$.
