In this paper we study research trends in condensed matter physics. Trends are analyzed by means of the the number of publications in the different sub-fields as function of the years. We found that many research topics have a similar behavior with a
n initial fast growth and a next slower exponential decay. We derived a simple model to describe this behavior and built up some predictions for future trends.
We present an emph{ab-initio} study of the graphene quasi-particle band structure as function of the doping in G_0 W_0 approximation. We show that the LDA Fermi velocity is substantially renormalized and this renormalization rapidly decreases as func
tion of the doping. We found, in agreement with previous papers, that close to the Dirac point the linear dispersion of the bands is broken but this behaviour disappears with a small doping. We discuss our results in the light of recent experiments on graphene and intercalate graphite.
