We consider the Schrödinger operator with a periodic potential on quasi-1D models of zigzag single-wall carbon nanotubes. The spectrum of this operator consists of an absolutely continuous part (intervals separated by gaps) plus an infinite number of eigenvalues with infinite multiplicity. We describe all compactly supported eigenfunctions with the same eigenvalue. We define a Lyapunov function, w...... hiện toàn bộ
We consider a quantum system constituted by N identical particles interacting by means of a mean-field Hamiltonian. It is well known that, in the limit N → ∞, the one-particle state obeys to the Hartree equation. Moreover, propagation of chaos holds. In this paper, we take care of the
$$\bar {h}$$
depend...... hiện toàn bộ