Investigating Quantum Chaos in the (10,0) @ (18,0) Double-walled Carbon Nanotubes Using the Gaussian Unitary Ensemble and Some Distributions

In this paper, we used random matrix theory to investigate quantum chaos in the (10,0) @ (18,0) doublewalled carbon nanotubes.Also, Tracy-Widom Distribution, the level density and largest eigenvalues of the Gaussian unitary ensemble are calculated.Our results are based on random matrix theory of the (10,0) @ (18,0) double-walled carbon nanotubes using a tightbinding model which show that there is a transition of Gaussian orthogonal ensemble to Gaussian unitary ensemble.The results are different in both ensembles which indicate that quantum chaos depends on the geometry of the system.Double-walled carbon nanotubes are attractive which show the simplest system for investigating the effect of the interwall coupling on the physical properties of multi-walled carbon nanotubes.