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Register a new userScattering lengths and universality in superdiffusive Levy materials
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We study the effects of scattering lengths on Levy walks in quenched one-dimensional random and fractal quasi-lattices, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling properties of the random-walk probability distribution, we show that the effect of the varying scattering length can be reabsorbed in the multiplicative coefficient of the scaling length. This leads to a superscaling behavior, where the dynamical exponents and also the scaling functions do not depend on the value of the scattering length. Within the scaling framework, we obtain an exact expression for the multiplicative coefficient as a function of the scattering length both in the annealed and in the quenched random and fractal cases. Our analytic results are compared with numerical simulations, with excellent agreement, and are supposed to hold also in higher dimensions
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Thermal conductivities are routinely calculated in molecular dynamics simulations by keeping the boundaries at different temperatures and measuring the slope of the temperature profile in the bulk of the material, explicitly using Fouriers law of heat conduction. Substantiated by the observation of a distinct linear profile at the center of the material, this approach has also been frequently used in superdiffusive materials, such as nanotubes or polymer chains, which do not satisfy Fouriers law at the system sizes considered. It has been recently argued that this temperature gradient procedure yields worse results when compared with a method based on the temperature difference at the boundaries -- thus taking into account the regions near the boundaries where the temperature profile is not linear. We study a realistic example, nanocomposites formed by adding boron nitride nanotubes to a polymer matrix of amorphous polyethylene, to show that in superdiffusive materials, despite the appearance of a central region with a linear profile, the temperature gradient method is actually inconsistent with a conductivity that depends on the system size, and, thus, it should be only used in normal diffusive systems.
We consider a random walk on one-dimensional inhomogeneous graphs built from Cantor fractals. Our study is motivated by recent experiments that demonstrated superdiffusion of light in complex disordered materials, thereby termed Levy glasses. We introduce a geometric parameter $alpha$ which plays a role analogous to the exponent characterizing the step length distribution in random systems. We study the large-time behavior of both local and average observables; for the latter case, we distinguish two different types of averages, respectively over the set of all initial sites and over the scattering sites only. The single long jump approximation is applied to analytically determine the different asymptotic behaviours as a function of $alpha$ and to understand their origin. We also discuss the possibility that the root of the mean square displacement and the characteristic length of the walker distribution may grow according to different power laws; this anomalous behaviour is typical of processes characterized by Levy statistics and here, in particular, it is shown to influence average quantities.
We study the collisional properties of an ultracold mixture of cesium atoms and dimers close to a Feshbach resonance near 550G in the regime of positive $s$-wave scattering lengths. We observe an atom-dimer loss resonance that is related to Efimovs scenario of trimer states. The resonance is found at a value of the scattering length that is different from a previous observation at low magnetic fields. This indicates non-universal behavior of the Efimov spectrum for positive scattering lengths. We compare our observations with predictions from effective field theory and with a recent model based on the van der Waals interaction. We present additional measurements on pure atomic samples in order to check for the presence of a resonant loss feature related to an avalanche effect as suggested by observations in other atomic species. We could not confirm the presence of such a feature.
We study Levy walks in quenched disordered one-dimensional media, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling relations for the random-walk probability and for the resistivity in the equivalent electric problem, we obtain the asymptotic behavior of the mean square displacement as a function of the exponent characterizing the scatterers distribution. We demonstrate that in quenched media different average procedures can display different asymptotic behavior. In particular, we estimate the moments of the displacement averaged over processes starting from scattering sites, in analogy with recent experiments. Our results are compared with numerical simulations, with excellent agreement.
Kinetic facilitated models and the Mode Coupling Theory (MCT) model B are within those systems known to exhibit a discontinuous dynamical transition with a two step relaxation. We consider a general scaling approach, within mean field theory, for such systems by considering the behavior of the density correlator <q(t)> and the dynamical susceptibility <q^2(t)> -<q(t)>^2. Focusing on the Fredrickson and Andersen (FA) facilitated spin model on the Bethe lattice, we extend a cluster approach that was previously developed for continuous glass transitions by Arenzon et al (Phys. Rev. E 90, 020301(R) (2014)) to describe the decay to the plateau, and consider a damage spreading mechanism to describe the departure from the plateau. We predict scaling laws, which relate dynamical exponents to the static exponents of mean field bootstrap percolation. The dynamical behavior and the scaling laws for both density correlator and dynamical susceptibility coincide with those predicted by MCT. These results explain the origin of scaling laws and the universal behavior associated with the glass transition in mean field, which is characterized by the divergence of the static length of the bootstrap percolation model with an upper critical dimension d_c=8.
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