Supramolecular interactions in clusters of polar and polarizable molecules

We present a model for molecular materials made up of polar and polarizable molecular units. A simple two state model is adopted for each molecular site and only classical intermolecular interactions are accounted for, neglecting any intermolecular overlap. The complex and interesting physics driven by interactions among polar and polarizable molecules becomes fairly transparent in the adopted model. Collective effects are recognized in the large variation of the molecular polarity with supramolecular interactions, and cooperative behavior shows up with the appearance, in attractive lattices, of discontinuous charge crossovers. The mean-field approximation proves fairly accurate in the description of the gs properties of MM, including static linear and non-linear optical susceptibilities, apart from the region in the close proximity of the discontinuous charge crossover. Sizeable deviations from the excitonic description are recognized both in the excitation spectrum and in linear and non-linear optical responses. New and interesting phenomena are recognized near the discontinuous charge crossover for non-centrosymmetric clusters, where the primary photoexcitation event corresponds to a multielectron transfer.Comment: 14 pages, including 11 figure

On the Proximity Factors of Lattice Reduction-Aided Decoding

Lattice reduction-aided decoding features reduced decoding complexity and near-optimum performance in multi-input multi-output communications. In this paper, a quantitative analysis of lattice reduction-aided decoding is presented. To this aim, the proximity factors are defined to measure the worst-case losses in distances relative to closest point search (in an infinite lattice). Upper bounds on the proximity factors are derived, which are functions of the dimension $n$ of the lattice alone. The study is then extended to the dual-basis reduction. It is found that the bounds for dual basis reduction may be smaller. Reasonably good bounds are derived in many cases. The constant bounds on proximity factors not only imply the same diversity order in fading channels, but also relate the error probabilities of (infinite) lattice decoding and lattice reduction-aided decoding.Comment: remove redundant figure

Multifractal analysis of electronic states on random Voronoi-Delaunay lattices

We consider the transport of non-interacting electrons on two- and three-dimensional random Voronoi-Delaunay lattices. It was recently shown that these topologically disordered lattices feature strong disorder anticorrelations between the coordination numbers that qualitatively change the properties of continuous and first-order phase transitions. To determine whether or not these unusual features also influence Anderson localization, we study the electronic wave functions by multifractal analysis and finite-size scaling. We observe only localized states for all energies in the two-dimensional system. In three dimensions, we find two Anderson transitions between localized and extended states very close to the band edges. The critical exponent of the localization length is about 1.6. All these results agree with the usual orthogonal universality class. Additional generic energetic randomness introduced via random potentials does not lead to qualitative changes but allows us to obtain a phase diagram by varying the strength of these potentials

Approximation of small-amplitude weakly coupled oscillators with discrete nonlinear Schrodinger equations

Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are approximated by equations of the discrete nonlinear Schrodinger type. We show how to justify this approximation by two methods, which have been very popular in the recent literature. The first method relies on a priori energy estimates and multi-scale decompositions. The second method is based on a resonant normal form theorem. We show that although the two methods are different in the implementation, they produce equivalent results as the end product. We also discuss applications of the discrete nonlinear Schrodinger equation in the context of existence and stability of breathers of the Klein--Gordon lattice