Localization properties of the nonbonding pi states at the Fermi level in amorphous carbon

Polycyclic aromatic hydrocarbons, carbon nanoparticles and the diffuse interstellar bands

Observational data on the appearance and properties of the diffuse interstellar bands (DIBs) are reviewed in the context of a model in which the proposed carriers of these bands are large carbon molecules and carbon nanoparticles containing between 30 and several hundred carbon atoms. The abundance of these carriers, as estimated from the observed strengths of the DIBs, place strong constraints on their rates of formation and destruction, and suggest that the strongest bands, including that at 4428 A, could be produced via the decomposition of larger carbon particles, possibly those particles that have been postulated to be the source of the 2175 A extinction feature. Such particles are of mixed sp2 and sp3 carbon composition, with sizes between that of large molecules and small macroscopic solids. Any description of their characteristics must combine aspects of molecular and condensed matter physics, and this is incorporated in the present discussion. I discuss recent experimental and theoretical data related to these matters.

Rényi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems

We discuss some properties of the generalized entropies, called Rényi entropies, and their application to the case of continuous distributions. In particular, it is shown that these measures of complexity can be divergent; however, their differences are free from these divergences, thus enabling them to be good candidates for the description of the extension and the shape of continuous distributions. We apply this formalism to the projection of wave functions onto the coherent state basis, i.e., to the Husimi representation. We also show how the localization properties of the Husimi distribution on average can be reconstructed from its marginal distributions that are calculated in position and momentum space in the case when the phase space has no structure, i.e., no classical limit can be defined. Numerical simulations on a one-dimensional disordered system corroborate our expectations.