How the site degree influences quantum probability on inhomogeneous substrates

Abstract

We investigate the effect of the node degree and energy $E$ on the electronic wave function for regular and irregular structures, namely, regular lattices, disordered percolation clusters, and complex networks. We evaluate the dependence of the quantum probability for each site on its degree. For bi-regular structures, we prove analytically that the probability $P_k(E)$ of finding the particle on any site with $k$ neighbors is independent of $E$. For more general structures, the dependency of $P_k(E)$ on $E$ is discussed by taking into account exact results on a one-dimensional semi-regular chain: $P_k(E)$ is large for small values of $E$ when $k$ is also small, and its maximum values shift towards large values of $|E|$ with increasing $k$. Numerical evaluations of $P_k(E)$ for two different types of percolation clusters and the Apollonian network suggest that this feature might be generally valid

19 pages, 6 figures, original article

References in corpus (6)

• Anderson Transitions
• Explosive percolation via control of the largest cluster
• Coherent transport on Apollonian networks and continuous-time quantum walks
• Delocalization transition for the Google matrix
• Localization properties of a tight-binding electronic model on the Apollonian network
• Dynamical Aspects of 2D Quantum Percolation

Cited by in corpus (3)

• Flat-band quantum communication induced by disorder
• Binary Apollonian networks
• Random Apollonian networks with tailored clustering coefficient