Thermal conductivity of the Toda lattice with conservative noise

We study the thermal conductivity of the one dimensional Toda lattice perturbed by a stochastic dynamics preserving energy and momentum. The strength of the stochastic noise is controlled by a parameter $\gamma$. We show that heat transport is anomalous, and that the thermal conductivity diverges with the length $n$ of the chain according to $\kappa(n) \sim n^\alpha$, with $0 < \alpha \leq 1/2$. In particular, the ballistic heat conduction of the unperturbed Toda chain is destroyed. Besides, the exponent $\alpha$ of the divergence depends on $\gamma$

Reconstructing Fourier's law from disorder in quantum wires

The theory of open quantum systems is used to study the local temperature and heat currents in metallic nanowires connected to leads at different temperatures. We show that for ballistic wires the local temperature is almost uniform along the wire and Fourier's law is invalid. By gradually increasing disorder, a uniform temperature gradient ensues inside the wire and the thermal current linearly relates to this local temperature gradient, in agreement with Fourier's law. Finally, we demonstrate that while disorder is responsible for the onset of Fourier's law, the non-equilibrium energy distribution function is determined solely by the heat baths

Third Order Renormalization Group applied to the attractive one-dimensional Fermi Gas

We consider a Callan-Symanzik and a Wilson Renormalization Group approach to the infrared problem for interacting fermions in one dimension with backscattering. We compute the third order (two-loop) approximation of the beta function using both methods and compare it with the well known multiplicative Gell-Mann Low approach. We point out a previously unnoticed qualitative dependence of the third order fixed point on an arbitrary dimensionless parameter, which strongly suggest the spurious nature of the fixed point.Comment: 16 pages, Revised version, added comment

Long time, large scale limit of the Wigner transform for a system of linear oscillators in one dimension

We consider the long time, large scale behavior of the Wigner transform W_\eps(t,x,k) of the wave function corresponding to a discrete wave equation on a 1-d integer lattice, with a weak multiplicative noise. This model has been introduced in Basile, Bernardin, and Olla to describe a system of interacting linear oscillators with a weak noise that conserves locally the kinetic energy and the momentum. The kinetic limit for the Wigner transform has been shown in Basile, Olla, and Spohn. In the present paper we prove that in the unpinned case there exists $\gamma_0>0$ such that for any $\gamma\in(0,\gamma_0]$ the weak limit of W_\eps(t/\eps^{3/2\gamma},x/\eps^{\gamma},k), as \eps\ll1, satisfies a one dimensional fractional heat equation $\partial_t W(t,x)=-\hat c(-\partial_x^2)^{3/4}W(t,x)$ with $\hat c>0$. In the pinned case an analogous result can be claimed for W_\eps(t/\eps^{2\gamma},x/\eps^{\gamma},k) but the limit satisfies then the usual heat equation

Analyticity of the SRB measure of a lattice of coupled Anosov diffeomorphisms of the torus

We consider the "thermodynamic limit"of a d-dimensional lattice of hyperbolic dynamical systems on the 2-torus, interacting via weak and nearest neighbor coupling. We prove that the SRB measure is analytic in the strength of the coupling. The proof is based on symbolic dynamics techniques that allow us to map the SRB measure into a Gibbs measure for a spin system on a (d+1)-dimensional lattice. This Gibbs measure can be studied by an extension (decimation) of the usual "cluster expansion" techniques.Comment: 28 pages, 2 figure

Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions

We study the thermal conductivity, at fixed positive temperature, of a disordered lattice of harmonic oscillators, weakly coupled to each other through anharmonic potentials. The interaction is controlled by a small parameter $\epsilon > 0$. We rigorously show, in two slightly different setups, that the conductivity has a non-perturbative origin. This means that it decays to zero faster than any polynomial in $\epsilon$ as $\epsilon\rightarrow 0$. It is then argued that this result extends to a disordered chain studied by Dhar and Lebowitz, and to a classical spins chain recently investigated by Oganesyan, Pal and Huse.Comment: 21 page

Eurocode 7 and rock engineering design: The case of rockfall protection barriers

The Eurocode 7 or EC7 is the Reference Design Code (RDC) for geotechnical design including rock engineering design within the European Union (EU). Moreover, its principles have also been adopted by several other countries, becoming a key design standard for geotechnical engineering worldwide. It is founded on limit state design (LSD) concepts, and the reliability of design is provided mainly by a semi-probabilistic method based on partial factors. The use of partial factors is currently an advantage, mainly for the simplicity in its applicability, and a limitation, especially concerning geotechnical designs. In fact, the application of partial factors to geotechnical design has proven to be difficult. In this paper, the authors focus on the way to apply EC7 principles to rock engineering design by analyzing the design of rockfall protection structures as an example. A real case of slope subjected to rockfall is reported to outline the peculiarity connected to rock engineering. The main findings are related to the complementarity of the reliability-based design (RBD) approach within EC7 principles and the possibility of overcoming the limitations of a partial factor approach to this type of engineering problem

Eurocode 7 and rock engineering design: The case of rockfall protection barriers

The Eurocode 7 or EC7 is the Reference Design Code (RDC) for geotechnical design including rock engineering design within the European Union (EU). Moreover, its principles have also been adopted by several other countries, becoming a key design standard for geotechnical engineering worldwide. It is founded on limit state design (LSD) concepts, and the reliability of design is provided mainly by a semi-probabilistic method based on partial factors. The use of partial factors is currently an advantage, mainly for the simplicity in its applicability, and a limitation, especially concerning geotechnical designs. In fact, the application of partial factors to geotechnical design has proven to be difficult. In this paper, the authors focus on the way to apply EC7 principles to rock engineering design by analyzing the design of rockfall protection structures as an example. A real case of slope subjected to rockfall is reported to outline the peculiarity connected to rock engineering. The main findings are related to the complementarity of the reliability-based design (RBD) approach within EC7 principles and the possibility of overcoming the limitations of a partial factor approach to this type of engineering problem