Exact Kohn-Sham eigenstates versus quasiparticles in simple models of strongly correlated electrons

We present analytic expressions for the exact density functional and Kohn-Sham Hamiltonian of simple tight-binding models of correlated electrons. These are the single- and double-site versions of the Anderson, Hubbard and spinless fermion models. The exact exchange and correlation potentials are fully non-local. The analytic expressions allow to compare the Kohn-Sham eigenstates of exact density functional theory with the many-body quasi-particle states of these correlated-electron systems. The exact Kohn-Sham spectrum describes correctly many of the non-trivial features of the many-body quasi-particle spectrum, as for example the precursors of the Kondo peak. However, we find that some pieces of the quasi-particle spectrum are missing because the many-body phase-space for electron and hole excitations is richer

Can simple models explain Zipf’s law for all exponents?

H. Simon proposed a simple stochastic process for explaining Zipf’s law for word frequencies. Here we introduce two similar generalizations of Simon’s model that cover the same range of exponents as the standard Simon model. The mathematical approach followed minimizes the amount of mathematical background needed for deriving the exponent, compared to previous approaches to the standard Simon’s model. Reviewing what is known from other simple explanations of Zipf’s law, we conclude there is no single radically simple explanation covering the whole range of variation of the exponent of Zipf’s law in humans. The meaningfulness of Zipf’s law for word frequencies remains an open question.Peer ReviewedPostprint (published version

Universality in the transport response of molecular wires physisorbed onto graphene electrodes

We analyze the low-voltage transport response of large molecular wires bridging graphene electrodes, where the molecules are physisorbed onto the graphene sheets by planar anchor groups. In our study, the sheets are pulled away to vary the gap length and the relative atomic positions. The molecular wires are also translated in directions parallel and perpendicular to the sheets. We show that the energy position of the Breit-Wigner molecular resonances is universal for a given molecule, in the sense that it is independent of the details of the graphene edges, gaps lengths or of the molecule positions. We discuss the need to converge carefully the k-sampling to provide reasonable values of the conductance.Comment: 6 pages, 6 figure

Research on WASH sector, environment and water resources in the Central Rift Valley of Ethiopia

Peer ReviewedPostprint (published version

Impact of edge shape on the functionalities of graphene-based single-molecule electronics devices

We present an ab-initio analysis of the impact of edge shape and graphene-molecule anchor coupling on the electronic and transport functionalities of graphene-based molecular electronics devices. We analyze how Fano-like resonances, spin filtering and negative differential resistance effects may or may not arise by modifying suitably the edge shapes and the terminating groups of simple organic molecules. We show that the spin filtering effect is a consequence of the magnetic behavior of zigzag-terminated edges, which is enhanced by furnishing these with a wedge shape. The negative differential resistance effect is originated by the presence of two degenerate electronic states localized at each of the atoms coupling the molecule to graphene which are strongly affected by a bias voltage. The effect could thus be tailored by a suitable choice of the molecule and contact atoms if edge shape could be controlled with atomic precision.Comment: 11 pages, 20 figure

Beyond-Constant-Mass-Approximation Magnetic Catalysis in the Gauge Higgs-Yukawa Model

Beyond-constant-mass approximation solutions for magnetically catalyzed fermion and scalar masses are found in a gauge Higgs-Yukawa theory in the presence of a constant magnetic field. The obtained fermion masses are several orders of magnitude larger than those found in the absence of Yukawa interactions. The masses obtained within the beyond-constant-mass approximation exactly reduce to the results within the constant-mass approach when the condition $\nu \ln (\frac{1}{\hat{m}^{2}})\ll 1$ is satisfied. Possible applications to early universe physics and condensed matter are discussed.Comment: Revised numerical results. New figures. Several sections rewritte