Related papers: Disordered statistical physics in low dimensions: …
When $d\ge 3$, the directed polymer a in random environment on $\mathbb Z^d$ is known to display a phase transition from a diffusive phase, known as \textit{weak disorder} to a localized phase, referred to as \textit{strong disorder}. This…
One dimensional pinning models have been widely studied in the physical and mathematical literature, also in presence of disorder. Roughly speaking, they undergo a transition between a delocalized phase and a localized one. In mathematical…
This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic…
We study numerically and analytically the moments of the dimensionless level curvature for one-dimensional disordered rings of the circumference L pierced by a magnetic flux. The negative moments of the curvature distribution can be…
We consider random walk on a mildly random environment on finite transitive d- regular graphs of increasing girth. After scaling and centering, the analytic spectrum of the transition matrix converges in distribution to a Gaussian noise. An…
We study a one-dimensional model of disordered electrons (also relevant for random spin chains), which exhibits a delocalisation transition at half-filling. Exact probability distribution functions for the Wigner time and transmission…
Besides the dynamical slowing down signaled by an enormous increase of the viscosity approaching the glass transition, structural glasses show interesting anomalous thermodynamic features at low temperatures that hint at peculiar deviations…
We study the statistical mechanics of a one-dimensional log gas with general potential and arbitrary beta, the inverse of temperature, according to the method we introduced for two-dimensional Coulomb gases in [SS2]. Such ensembles…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
A mode-coupling theory for the slow single-particle dynamics in fluids adsorbed in disordered porous media is derived, which complements previous work on the collective dynamics [V. Krakoviack, Phys. Rev. E 75, 031503 (2007)]. Its…
We investigate the localization transition of interacting particles in a one-dimensional correlated disorder system. The disorder which we investigate allows for vanishing backwards scattering processes. We derive by two renormalization…
We study slow dynamics of particles moving in a matrix of immobile obstacles using molecular dynamics simulations. The glass transition point decreases drastically as the obstacle density increases. At higher obstacle densities, the…
In many interesting physical settings, such as the vulcanization of rubber, the introduction of permanent random constraints between the constituents of a homogeneous fluid can cause a phase transition to a random solid state. In this…
The statistical properties of the dynamics of energy levels are investigated in the case of two two-dimensional disordered quantum dot models with nearest neighbor hopping subjected to external time-dependent perturbations. While in the…
The power-law random banded matrix (PLRBM) is a paradigmatic ensemble to study the Anderson localization transition (AT). In $d$-dimension the PLRBM are random matrices with algebraic decaying off-diagonal elements $H_{\vec{n}\vec{m}}\sim…
We study the statistical and dynamic properties of the systems characterized by an ultrametric space of states and translationary non-invariant symmetric transition matrices of the Parisi type subjected to "locally constant" randomization.…
We investigate the localization of stiff directed lines with bending energy by a short-range random potential. We apply perturbative arguments, Flory scaling arguments, a variational replica calculation, and functional renormalization to…
Level statistics of systems that undergo many--body localization transition are studied. An analysis of the gap ratio statistics from the perspective of inter- and intra-sample randomness allows us to pin point differences between…
We study the nature and mechanisms of broken ergodicity (BE) in specific random walk models corresponding to diffusion on random potential surfaces, in both one and high dimension. Using both rigorous results and nonrigorous methods, we…
We consider quantum interferences of classically allowed or forbidden electronic trajectories in disordered dielectrics. Without assuming a directed path approximation, we represent a strongly disordered elastic scatterer by its…