Related papers: $f(\alpha)$ Multifractal spectrum at strong and we…
We study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path $\ell_{\rm opt}$ in a disordered Erd\H{o}s-R\'enyi (ER) random network and scale-free (SF) network. Each link $i$ is…
We consider the simplest instabilities involving multiple unstable electrostatic plasma waves corresponding to four-dimensional systems of mode amplitude equations. In each case the coupled amplitude equations are derived up to third order…
In quantum/wave systems with chaotic classical analogs, wavefunctions evolve in highly complex, yet deterministic ways. A slight perturbation of the system, though, will cause the evolution to diverge from its original behavior increasingly…
In this paper I have studied the fiber bundle model with a fraction {\alpha} of infinitely strong fibers. Inclusion of such unbreakable fraction has been proven to affect the failure process in early studies, especially around a critical…
In the one-dimensional quasiperiodic Aubry-Andr\'{e}-Harper Hamiltonian with nearest-neighbor hopping, all single-particle eigenstates undergo a phase transition from ergodic to localized states at a critical disorder strength $W_c/t =…
For the hopping dynamics in a one-dimensional model, containing energy and barrier disorder, we determine the linear and nonlinear response to an external field for arbitrary external frequencies. The calculation is performed in analytical…
The transmissivity of a one-dimensional random system that is periodic on average is studied. It is shown that the transmission coefficient for frequencies corresponding to a gap in the band structure of the average periodic system…
A theory for the effects of nonmagnetic disorder on the magnetic pair breaking rate $\alpha$ induced by paramagnetic impurities in quasi two-dimensional superconductors is presented. Within the framework of a strong-coupling theory for…
We study the large-order behavior of the functional renormalization group (FRG). For a model in dimension zero, we establish Borel-summability for a large class of microscopic couplings. Writing the derivatives of FRG as contour integrals,…
As a function of the disorder strength in a mesoscopic system, the electron dynamics crosses over from the ballistic through the diffusive towards the localized regime. The ballistic and the localized situation correspond to integrable or…
We study a partially disordered one-dimensional system with interacting particles. Concretely, we impose a disorder potential to only every other site, followed by a clean site. Our numerical analysis of eigenstate properties is based on…
An analysis of moments and spectra shows that, while the distribution of avalanche areas obeys finite size scaling, that of toppling numbers is universally characterized by a full, nonlinear multifractal spectrum. Rare, large avalanches…
The multifractal formalism characterizes the scaling properties of a physical density rho as a function of the distance L. To each singularity alpha of the field is attributed a fractal dimension for its support f(alpha). An alternative…
We study non-interacting systems with a power-law quasiparticle dispersion $\xi_{\bf k}\propto k^\alpha$ and a random short-range-correlated potential. We show that, unlike the case of lower dimensions, for $d>2\alpha$ there exists a…
Multifractal systems usually have singularity spectra defined on bounded sets of H\"older exponents. As a consequence, their associated multifractal scaling exponents are expected to depend linearly upon statistical moment orders at high…
We study the dynamics of the one dimensional disordered trap model presenting a broad distribution of trapping times $p(\tau) \sim 1/\tau^{1+\mu}$, when an external force is applied from the very beginning at $t=0$, or only after a waiting…
We study the effect of strong heterogeneities on the fracture of disordered materials using a fiber bundle model. The bundle is composed of two subsets of fibers, i.e. a fraction 0<\alpha<1 of fibers is unbreakable, while the remaining…
Using exact diagonalization technique, we investigate the many-body localization phenomenon in the 1D Heisenberg chain comparing several disorder models. In particular we consider a family of discrete distributions of disorder strengths and…
Dynamical conductivity in a disordered one-dimensional model of interacting fermions is studied numerically at high temperatures and in the weak-interaction regime in order to find a signature of many-body localization and vanishing d.c.…
We derive, from conformal invariance and quantum gravity, the multifractal spectrum f(alpha,c) of the harmonic measure (or electrostatic potential, or diffusion field) near any conformally invariant fractal in two dimensions, corresponding…