Netons: Vibrations of Complex Networks

Details Netons: Vibrations of Complex Networks Netons: Vibrations of Complex Networks

2003-04-28

arxiv.org/abs/cond-mat/0304618v1

J. Phys. A: Math. Gen. 36, 6329 (2003)

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 pages, 6 figures, to appear in JPA

Scientific paper

10.1088/0305-4470/36/23/304

We consider atoms interacting each other through the topological structure of a complex network and investigate lattice vibrations of the system, the quanta of which we call {\em netons} for convenience. The density of neton levels, obtained numerically, reveals that unlike a local regular lattice, the system develops a gap of a finite width, manifesting extreme rigidity of the network structure at low energies. Two different network models, the small-world network and the scale-free network, are compared: The characteristic structure of the former is described by an additional peak in the level density whereas a power-law tail is observed in the latter, indicating excitability of netons at arbitrarily high energies. The gap width is also found to vanish in the small-world network when the connection range $r = 1$.

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