Modified newtonian dynamics and non-relativistic ChSAS gravity

In the context of the non-relativistic theories, a generalization of the Chern--Weil-theorem allows us to show that extended Chern--Simons actions for gravity in d=4 invariant under some specific non-relativistic groups lead to modified Poisson equations. In some particular cases, these modified equations have the form of the so-called MOND approach to gravity. The modifications could be understood as due to the effects of dark matter. This result could leads us to think that dark matter can be interpreted as a non-relativistic limit of dark energy

On Nilcompactifications of Prime Spectra of Commutative Rings

Given a ring R and S one of its ideals, we obtain a compactification of the prime spectrum of S through a mainly algebraic process. We name it the R-nilcompactification of SpecS. We study some categorical properties of this construction.Comment: 12 pages, 8 Tikz figure

Benchmarking Nonequilibrium Green's Functions against Configuration Interaction for time-dependent Auger decay processes

We have recently proposed a Nonequilibrium Green's Function (NEGF) approach to include Auger decay processes in the ultrafast charge dynamics of photoionized molecules. Within the so called Generalized Kadanoff-Baym Ansatz the fundamental unknowns of the NEGF equations are the reduced one-particle density matrix of bound electrons and the occupations of the continuum states. Both unknowns are one-time functions like the density in Time-Dependent Functional Theory (TDDFT). In this work we assess the accuracy of the approach against Configuration Interaction (CI) calculations in one-dimensional model systems. Our results show that NEGF correctly captures qualitative and quantitative features of the relaxation dynamics provided that the energy of the Auger electron is much larger than the Coulomb repulsion between two holes in the valence shells. For the accuracy of the results dynamical electron-electron correlations or, equivalently, memory effects play a pivotal role. The combination of our NEGF approach with the Sham-Schl\"uter equation may provide useful insights for the development of TDDFT exchange-correlation potentials with a history dependence.Comment: 7 pages, 3 figure

Sodium: a charge-transfer insulator at high pressures

By means of first-principles methods we analyze the optical response of transparent dense sodium as a function of applied pressure. We discover an unusual kind of charge-transfer exciton that proceeds from the interstitial distribution of valence electrons repelled away from the ionic cores by the Coulomb interaction and the Pauli repulsion. The predicted absorption spectrum shows a strong anisotropy with light polarization that just at pressures above the metal-insulator transition manifests as sodium being optically transparent in one direction but reflective in the other. This result provides a key information about the crystal structure of transparent sodium, a new unconventional inorganic electride.Comment: revtex4, 5+8 page