Anomalous thermal conductivity and local temperature distribution on harmonic Fibonacci chains

The harmonic Fibonacci chain, which is one of a quasiperiodic chain constructed with a recursion relation, has a singular continuous frequency-spectrum and critical eigenstates. The validity of the Fourier law is examined for the harmonic Fibonacci chain with stochastic heat baths at both ends by investigating the system size N dependence of the heat current J and the local temperature distribution. It is shown that J asymptotically behaves as (ln N)^{-1} and the local temperature strongly oscillates along the chain. These results indicate that the Fourier law does not hold on the harmonic Fibonacci chain. Furthermore the local temperature exhibits two different distribution according to the generation of the Fibonacci chain, i.e., the local temperature distribution does not have a definite form in the thermodynamic limit. The relations between N-dependence of J and the frequency-spectrum, and between the local temperature and critical eigenstates are discussed.Comment: 10 pages, 4 figures, submitted to J. Phys.: Cond. Ma

Exact Eigenstates of Tight-Binding Hamiltonians on the Penrose Tiling

We investigate exact eigenstates of tight-binding models on the planar rhombic Penrose tiling. We consider a vertex model with hopping along the edges and the diagonals of the rhombi. For the wave functions, we employ an ansatz, first introduced by Sutherland, which is based on the arrow decoration that encodes the matching rules of the tiling. Exact eigenstates are constructed for particular values of the hopping parameters and the eigenenergy. By a generalized ansatz that exploits the inflation symmetry of the tiling, we show that the corresponding eigenenergies are infinitely degenerate. Generalizations and applications to other systems are outlined.Comment: 24 pages, REVTeX, 13 PostScript figures include

Fragile-glass behavior of a short range pp-spin model

In this paper we propose a short range generalization of the $p$-spin interaction spin-glass model. The model is well suited to test the idea that an entropy collapse is at the bottom-line of the dynamical singularity encountered in structural glasses. The model is studied in three dimensions through Monte Carlo simulations, which put in evidence fragile glass behavior with stretched exponential relaxation and super-Arrhenius behavior of the relaxation time. Our data are in favor of a Vogel-Fulcher behavior of the relaxation time, related to an entropy collapse at the Kauzmann temperature. We however encounter difficulties analogous to those found in experimental systems when extrapolating thermodynamical data at low temperatures. We study the spin glass susceptibility investigating the behavior of the correlation length in the system. We find that the the increase of the relaxation time is not accompanied by any growth of the correlation length. We discuss the scaling properties of off-equilibrium dynamics in the glassy regime, finding qualitative agreement with the mean-field theory.Comment: 8 pages, LaTeX, 8 postscript figure

Binary self-similar one-dimensional quasilattices: Mutual local-derivability classification and substitution rules

Self-similar binary one-dimensional (1D) quasilattices (QLs) are classified into mutual local-derivability (MLD) classes. It is shown that the MLD classification is closely related to the number-theoretical classification of parameters which specify the self-similar binary 1D QLs. An algorithm to derive an explicit substitution rule, which prescribes the transformation of a QL into another QL in the same MLD class, is presented. An explicit inflation rule, which prescribes the transformation of the self-similar 1D QL into itself, is obtained as a composition of the explicit substitution rules. Symmetric substitution rules and symmetric inflation rules are extensively discussed.Comment: 24 pages, 4 figures, submitted to PR

Three-Dimensional Quantum Percolation Studied by Level Statistics

Three-dimensional quantum percolation problems are studied by analyzing energy level statistics of electrons on maximally connected percolating clusters. The quantum percolation threshold \pq, which is larger than the classical percolation threshold \pc, becomes smaller when magnetic fields are applied, i.e., \pq(B=0)>\pq(B\ne 0)>\pc. The critical exponents are found to be consistent with the recently obtained values of the Anderson model, supporting the conjecture that the quantum percolation is classified onto the same universality classes of the Anderson transition. Novel critical level statistics at the percolation threshold is also reported.Comment: to appear in the May issue of J. Phys. Soc. Jp

Survival and residence times in disordered chains with bias

We present a unified framework for first-passage time and residence time of random walks in finite one-dimensional disordered biased systems. The derivation is based on exact expansion of the backward master equation in cumulants. The dependence on initial condition, system size, and bias strength is explicitly studied for models with weak and strong disorder. Application to thermally activated processes is also developed.Comment: 13 pages with 2 figures, RevTeX4; v2:minor grammatical changes, typos correcte

Energy spectra, wavefunctions and quantum diffusion for quasiperiodic systems

We study energy spectra, eigenstates and quantum diffusion for one- and two-dimensional quasiperiodic tight-binding models. As our one-dimensional model system we choose the silver mean or `octonacci' chain. The two-dimensional labyrinth tiling, which is related to the octagonal tiling, is derived from a product of two octonacci chains. This makes it possible to treat rather large systems numerically. For the octonacci chain, one finds singular continuous energy spectra and critical eigenstates which is the typical behaviour for one-dimensional Schr"odinger operators based on substitution sequences. The energy spectra for the labyrinth tiling can, depending on the strength of the quasiperiodic modulation, be either band-like or fractal-like. However, the eigenstates are multifractal. The temporal spreading of a wavepacket is described in terms of the autocorrelation function C(t) and the mean square displacement d(t). In all cases, we observe power laws for C(t) and d(t) with exponents -delta and beta, respectively. For the octonacci chain, 0<delta<1, whereas for the labyrinth tiling a crossover is observed from delta=1 to 0<delta<1 with increasing modulation strength. Corresponding to the multifractal eigenstates, we obtain anomalous diffusion with 0<beta<1 for both systems. Moreover, we find that the behaviour of C(t) and d(t) is independent of the shape and the location of the initial wavepacket. We use our results to check several relations between the diffusion exponent beta and the fractal dimensions of energy spectra and eigenstates that were proposed in the literature.Comment: 24 pages, REVTeX, 10 PostScript figures included, major revision, new results adde

Clusters in Simple Fluids

This article concerns the correspondence between thermodynamics and the morphology of simple fluids in terms of clusters. Definitions of clusters providing a geometric interpretation of the liquid-gas phase transition are reviewed with an eye to establishing their physical relevance. The author emphasizes their main features and basic hypotheses, and shows how these definitions lead to a recent approach based on self-bound clusters. Although theoretical, this tutorial review is also addressed to readers interested in experimental aspects of clustering in simple fluids.Comment: 48 pages, 12 figures included, to be published in Physics Report

Trazodone regulates neurotrophic/growth factors, mitogen-activated protein kinases and lactate release in human primary astrocytes

Background: In the central nervous system, glial cells provide metabolic and trophic support to neurons and respond to protracted stress and insults by up-regulating inflammatory processes. Reactive astrocytes and microglia are associated with the pathophysiology of neuronal injury, neurodegenerative diseases and major depression, in both animal models and human brains. Several studies have reported clear anti-inflammatory effects of anti-depressant treatment on astrocytes, especially in models of neurological disorders. Trazodone (TDZ) is a triazolopyridine derivative that is structurally unrelated to other major classes of antidepressants. Although the molecular mechanisms of TDZ in neurons have been investigated, it is unclear whether astrocytes are also a TDZ target. Methods: The effects of TDZ on human astrocytes were investigated in physiological conditions and following inflammatory insult with lipopolysaccharide (LPS) and tumour necrosis factor-aα (TNF-aα). Astrocytes were assessed for their responses to pro-inflammatory mediators and cytokines, and the receptors and signalling pathways involved in TDZ-mediated effects were evaluated. Results: TDZ had no effect on cell proliferation, but it decreased pro-inflammatory mediator release and modulated trophic and transcription factor mRNA expression. Following TDZ treatment, the AKT pathway was activated, whereas extracellular signal-regulated kinase and c-Jun NH2-terminal kinase were inhibited. Most importantly, a 72-h TDZ pre-treatment before inflammatory insult completely reversed the anti-proliferative effects induced by LPS-TNF-aα. The expression or the activity of inflammatory mediators, including interleukin-6, c-Jun NH2-terminal kinase and nuclear factor ΚB, were also reduced. Furthermore, TDZ affected astrocyte metabolic support to neurons by counteracting the inflammation-mediated lactate decrease. Finally, TDZ protected neuronal-like cells against neurotoxicity mediated by activated astrocytes. These effects mainly involved an activation of 5-HT1A and an antagonism at 5-HT2A/C serotonin receptors. Fluoxetine, used in parallel, showed similar final effects nevertheless it activates different receptors/intracellular pathways. Conclusions: Altogether, our results demonstrated that TDZ directly acts on astrocytes by regulating intracellular signalling pathways and increasing specific astrocyte-derived neurotrophic factor expression and lactate release. TDZ may contribute to neuronal support by normalizing trophic and metabolic support during neuroinflammation, which is associated with neurological diseases, including major depression