Null-eigenvalue localization of quantum walks on real-world complex
networks
- URL: http://arxiv.org/abs/2007.00129v1
- Date: Tue, 30 Jun 2020 22:05:16 GMT
- Title: Null-eigenvalue localization of quantum walks on real-world complex
networks
- Authors: Ruben Bueno and Naomichi Hatano
- Abstract summary: We show that complex networks have null eigenspaces with higher dimensions than that of random networks.
These null eigenvalues are caused by duplication mechanisms leading to structures with local symmetries.
We then evaluate these microstructures in the context of quantum mechanics.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: First we report that the adjacency matrices of real-world complex networks
systematically have null eigenspaces with much higher dimensions than that of
random networks. These null eigenvalues are caused by duplication mechanisms
leading to structures with local symmetries which should be more present in
complex organizations. The associated eigenvectors of these states are strongly
localized. We then evaluate these microstructures in the context of quantum
mechanics, demonstrating the previously mentioned localization by studying the
spread of continuous-time quantum walks. This null-eigenvalue localization is
essentially different from the Anderson localization in the following points:
first, the eigenvalues do not lie on the edges of the density of states but at
its center; second, the eigenstates do not decay exponentially and do not leak
out of the symmetric structures. In this sense, it is closer to the bound state
in continuum.
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