A new correlation measure, the product of the Shannon entropy power and the Fisher information of the electron density, is introduced by analyzing the Fisher-Shannon information plane of some two-electron systems (He-like ions, Hooke's atoms). The uncertainty and scaling properties of this information product are pointed out. In addition, the Fisher and Shannon measures of a finite many-electron system are shown to be bounded by the corresponding single-electron measures and the number of electrons of the system.

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An uncertainty Fisher information relation in quantum mechanics is derived for multidimensional single-particle systems with central potentials. It is based on the concept of Fisher information in the two complementary position and momentum spaces, which is a gradient functional of the corresponding probability distributions. The lower bound of the product of position and momentum Fisher informations is shown to depend on the orbital and magnetic quantum numbers of the physical state and the space dimensionality. Applications to various elementary systems is discussed.

The Husimi distribution is proposed for a phase space analysis of quantum phase transitions in the Dicke model of spin-boson interactions. We show that the inverse participation ratio and Wehrl entropy of the Husimi distribution give sharp signatures of the quantum phase transition. The analysis has been done using two frameworks: a numerical treatment and an analytical variational approximation. Additionally we have proposed a new characterization of the Dicke model quantum phase transition by means of the zeros of the Husimi distribution in the variational approach.

Revivals of electric current in graphene in the presence of an external magnetic field are described. It is shown that when the electrons are prepared in the form of wave packets assuming a Gaussian population of only positive (or negative) energy Landau levels, the presence of the magnetic field induce revivals of the electron currents, besides the classical cyclotron motion. When the population comprises both positive and negative energy Landau levels, revivals of the electric current manifest simultaneously with zitterbewegung and the classical cyclotron motion. We relate the temporal scales of these three effects and discuss to what extent these results hold for real graphene samples.