We use quantum billiard with many scattering centers to describe conducting electrons properties in A_{n}C_{60} crystals, where A denotes alkali metal. We focus our attention on the A_{3}C_{60} crystal, for which we calculate the band structure, density of states, and conductivity for normal electrons. Conductivity shows linear dependence on temperature in this model, which agrees well with experimental data. We also discuss consequences of our results for superconductivity mechanism in A_{3}C_{60} and possibilities of analogous approach to describe electron properties in fused fullerenes and multiply connected carbon clusters.
We show that band electrons in A_{n}C_{60} crystal (C_{60} fullerene doped with alkali ions A) are in highly chaotic quantum state. We describe intensity of the chaos by means of the Shannon information entropy, which we calculate using single particle Bloch functions. The entropy provides a quantitative measure of scars as well as degree of electrons delocalization in gaps between C_{60} molecules. Implications of our results for conductivity in A_{3}C_{60} are discussed.
Gutzwiller variational ground states |Φ^{G}⟩ of π electrons, described by single-band half-filling Hubbard model, were determined for the molecules C_{60} and C_{70} and their energies and magnetic properties investigated. To construct these states two types of trial functions were used: generalized spin-density wave |Φ_{SD}⟩ and tight-binding wave |Φ_{ΤΒ}⟩. Our results evidently show that the Gutzwiller state |Φ^{G}_{TΒ}⟩ determined by means of function |Φ_{ΤΒ}⟩ has lower energy than the other investigated variational states |Φ^{G}_{SD}⟩. Mean values of the operators in the Gutzwiller states were calculated using Monte Carlo method.
It is shown that mean values of electron operators in variational Gutzwiller state are equal to mean values of corresponding classical quantities calculated by means of a hermitian matrix model. In cases with small number of electrons in the system this property enables exact calculation of the mean values. In case of large number of electrons a simple and effective Monte Carlo method is formulated (within matrix model).