Physikalisches Institut, Universität Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany.
Phys Rev Lett. 2015 Sep 18;115(12):120602. doi: 10.1103/PhysRevLett.115.120602. Epub 2015 Sep 17.
We consider single-particle quantum transport on parametrized complex networks. Based on general arguments regarding the spectrum of the corresponding Hamiltonian, we derive bounds for a measure of the global transport efficiency defined by the time-averaged return probability. For treelike networks, we show analytically that a transition from efficient to inefficient transport occurs depending on the (average) functionality of the nodes of the network. In the infinite system size limit, this transition can be characterized by an exponent which is universal for all treelike networks. Our findings are corroborated by analytic results for specific deterministic networks, dendrimers and Vicsek fractals, and by Monte Carlo simulations of iteratively built scale-free trees.
我们研究了参数化复杂网络上的单粒子量子输运。基于关于相应哈密顿量谱的一般论点，我们推导出了由时间平均返回概率定义的全局传输效率度量的界。对于树状网络，我们从分析上证明了取决于网络节点的（平均）功能，从有效输运到低效输运的转变会发生。在无限系统尺寸极限下，这个转变可以用一个对于所有树状网络都通用的指数来描述。我们的发现得到了特定确定性网络、树枝状大分子和 Vicsek 分形的分析结果以及迭代构建的无标度树的蒙特卡罗模拟的证实。
