Classical-quantum Correspondence in Two-dimensional Nanomaterials

Two-dimensional nanomaterials are becoming the focus of intensive research due to their novel physical properties and the potential applications in nanodevices. We define a quantum spectrum function using the eigenvalues and the eigenfunctions in the system of two-dimensional nanomaterials. We find that the Fourier transform of the quantum spectrum function reveals a lot of information of the classical orbits from one point to another for a particle in the two-dimensional nanomaterials. These results give new evidence about the classical-quantum correspondence. All the methods and results can be used in a lot of other systems, including some one-dimensional and three-dimensional systems. The researches about these systems are very important in the field of applied science.