Random walks and the electronic structure of grapheneBašić, Nino (Avtor) Fowler, Patrick W. (Avtor) Pickup, Barry T. (Avtor) Potočnik, Primož (Avtor) graph theoryrandom walksgraphenebond numberResults from the mathematical literature on random walks reveal a closed-form analytical expression for the $\pi$-energy and bond number of graphene in the simplest tight-binding model and its Hartree-Fock Hubbard extension. Closed-form expressions follow for all $\pi$ spectral moments of graphene. Bond numbers of carbon and boron nitride (BN) zigzag nanotubes are found as finite sums, with graphene and hexagonal boron nitride sheets as asymptotes.20262026-03-10 09:33:13Neznano28097sl