Spectral and eigenfunction properties of a model based in random networks

5:45 pm - 6:10 pm 24 Thursday

Track

Theory

Based in the Erdos-Renyi [1] model for random networks, we construct a model that describes systems in the transition from regular to chaotic dynamics analyzed in the Random Matrix Theory context [2].We study statistical properties for spectral and eigenfunction using extensive numerical simulations inwhich we nd universal properties for xed average degree E= aN(a and N being the average network connectivity and the network size, respectively). Finally, we demonstrate that the distribution for nearest-neightbor energy-level spacing is well describe by Brody distribution[3].

References

[1] P. Erdos and A. Renyi. The Evolution of Random Graphs.Publ. Math. Inst. Hung. Acad. Sci., 5: 17,1960.

[2] M. L. Metha. Random Matrices.Phys. Rep., 299: 189, 1998.

[3] T. A. Brody. A Statistical Measure for the Repulsion of Energy Levels.Lettere Al Nouvo Cimento, 7:482, 1973.