Synthèse et caractérisation de systèmes conjugués hybrides thiophène-phénylene pour dispositifs électroniques

Date du colloque&nbsp;: 10/2009</p

On the existence of effective potentials in time-dependent density functional theory

We investigate the existence and properties of effective potentials in time-dependent density functional theory. We outline conditions for a general solution of the corresponding Sturm-Liouville boundary value problems. We define the set of potentials and v-representable densities, give a proof of existence of the effective potentials under certain restrictions, and show the set of v-representable densities to be independent of the interaction.Comment: 13 page

SCD Patterns Have Singular Diffraction

Among the many families of nonperiodic tilings known so far, SCD tilings are still a bit mysterious. Here, we determine the diffraction spectra of point sets derived from SCD tilings and show that they have no absolutely continuous part, that they have a uniformly discrete pure point part on the z-axis, and that they are otherwise supported on a set of concentric cylinder surfaces around this axis. For SCD tilings with additional properties, more detailed results are given.Comment: 11 pages, 2 figures; Accepted for Journal of Mathematical Physic

Random Walks Along the Streets and Canals in Compact Cities: Spectral analysis, Dynamical Modularity, Information, and Statistical Mechanics

Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random walkers is developed. The complexity of city modularity can be measured by an information-like parameter which plays the role of an individual fingerprint of {\it Genius loci}. Global structural properties of a city can be characterized by the thermodynamical parameters calculated in the random walks problem.Comment: 44 pages, 22 figures, 2 table

Mathematics and Morphogenesis of the City: A Geometrical Approach

Cities are living organisms. They are out of equilibrium, open systems that never stop developing and sometimes die. The local geography can be compared to a shell constraining its development. In brief, a city's current layout is a step in a running morphogenesis process. Thus cities display a huge diversity of shapes and none of traditional models from random graphs, complex networks theory or stochastic geometry takes into account geometrical, functional and dynamical aspects of a city in the same framework. We present here a global mathematical model dedicated to cities that permits describing, manipulating and explaining cities' overall shape and layout of their street systems. This street-based framework conciliates the topological and geometrical sides of the problem. From the static analysis of several French towns (topology of first and second order, anisotropy, streets scaling) we make the hypothesis that the development of a city follows a logic of division / extension of space. We propose a dynamical model that mimics this logic and which from simple general rules and a few parameters succeeds in generating a large diversity of cities and in reproducing the general features the static analysis has pointed out.Comment: 13 pages, 13 figure

Lyapunov exponents and transport in the Zhang model of Self-Organized Criticality

We discuss the role played by the Lyapunov exponents in the dynamics of Zhang's model of Self-Organized Criticality. We show that a large part of the spectrum (slowest modes) is associated with the energy transpor in the lattice. In particular, we give bounds on the first negative Lyapunov exponent in terms of the energy flux dissipated at the boundaries per unit of time. We then establish an explicit formula for the transport modes that appear as diffusion modes in a landscape where the metric is given by the density of active sites. We use a finite size scaling ansatz for the Lyapunov spectrum and relate the scaling exponent to the scaling of quantities like avalanche size, duration, density of active sites, etc ...Comment: 33 pages, 6 figures, 1 table (to appear

Numerical analysis of a spontaneous collapse model for a two-level system

We study a spontaneous collapse model for a two-level (spin) system, in which the Hamiltonian and the stochastic terms do not commute. The numerical solution of the equations of motions allows to give precise estimates on the regime at which the collapse of the state vector occurs, the reduction and delocalization times, and the reduction probabilities; it also allows to quantify the effect that an Hamiltonian which does not commute with the reducing terms has on the collapse mechanism. We also give a clear picture of the transition from the "microscopic" regime (when the noise terms are weak and the Hamiltonian prevents the state vector to collapse) to the "macroscopic" regime (when the noise terms are dominant and the collapse becomes effective for very long times). Finally, we clarify the distinction between decoherence and collapse.Comment: 7 pages, RevTeX. Significative improvements made. To appear on Phys. Rev.

Non-Markovian dynamics for bipartite systems

We analyze the appearance of non-Markovian effects in the dynamics of a bipartite system coupled to a reservoir, which can be described within a class of non-Markovian equations given by a generalized Lindblad structure. A novel master equation, which we term quantum Bloch-Boltzmann equation, is derived, describing both motional and internal states of a test particle in a quantum framework. When due to the preparation of the system or to decoherence effects one of the two degrees of freedom is amenable to a classical treatment and not resolved in the final measurement, though relevant for the interaction with the reservoir, non-Markovian behaviors such as stretched exponential or power law decay of coherences can be put into evidence.Comment: published version, 15 pages, revtex, no figure

Completeness in Photometric and Spectroscopic Searches for Clusters

We investigate, using simulated galaxy catalogues, the completeness of searches for massive clusters of galaxies in redshift surveys or imaging surveys with photometric redshift estimates, i.e. what fraction of clusters (M>10^14/h Msun) are found in such surveys. We demonstrate that the matched filter method provides an efficient and reliable means of identifying massive clusters even when the redshift estimates are crude. In true redshift surveys the method works extremely well. We demonstrate that it is possible to construct catalogues with high completeness, low contamination and both varying little with redshift.Comment: ApJ in press, 15 pages, 10 figure