Related papers: Multifractality and statistical localization in th…
Inspired by works on the Anderson model on sparse graphs, we devise a method to analyze the localization properties of sparse systems that may be solved using cavity theory. We apply this method to study the properties of the eigenvectors…
Trap models describe glassy dynamics as a stochastic process on a network of configurations representing local energy minima. We study within this class the paradigmatic Barrat-M\'ezard model, which has Glauber transition rates. Our focus…
We consider highly heterogeneous random networks with symmetric interactions in the limit of high connectivity. A key feature of this system is that the spectral density of the corresponding ensemble exhibits a divergence within the bulk.…
One of the simplest models for the slow relaxation and aging of glasses is the trap model by Bouchaud and others, which represents a system as a point in configuration-space hopping between local energy minima. The time evolution depends on…
The slow relaxation and aging of glassy systems can be modelled as a Markov process on a simplified rough energy landscape: energy minima where the system tends to get trapped are taken as nodes of a random network, and the dynamics are…
Understanding the dynamics of complex systems is a central task in many different areas ranging form biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even systems failure is sometimes difficult…
Multifractal properties of the distribution of topological invariants for a model of trajectories randomly entangled with a nonsymmetric lattice of obstacles are investigated. Using the equivalence of the model to random walks on a locally…
Multifractal properties of wave functions in a disordered system can be derived from self-consistent theory of localization by Vollhardt and Woelfle. A diagrammatic interpretation of results allows to obtain all scaling relations used in…
We study the correlation and response dynamics of trap models of glassy dynamics, considering observables that only partially decorrelate with every jump. This is inspired by recent work on a microscopic realization of such models, which…
We study the structural characteristics of complex networks using the representative eigenvectors of the adjacent matrix. The probability distribution function of the components of the representative eigenvectors are proposed to describe…
There have been some interesting recent advances in understanding the notion of mechanical disorder in structural glasses and the statistical mechanics of these systems' low-energy excitations. Here we contribute to these advances by…
We introduce a class of models containing robust and analytically demonstrable multifractality induced by disorder correlations. Specifically, we investigate the statistics of eigenstates of disordered tight-binding models on two classes of…
Random multifractals occur in particular at critical points of disordered systems. For Anderson localization transitions, Mirlin and Evers [PRB 62,7920 (2000)] have proposed the following scenario (a) the Inverse Participation Ratios…
In this paper, we study the dynamics of a random walker diffusing on a disordered one-dimensional lattice with random trappings. The distribution of escape probabilities is computed exactly for any strength of the disorder. These…
The scaling theory of Anderson localization is based on a global conductance $g_L$ that remains a random variable of order O(1) at criticality. One realization of such a conductance is the Landauer transmission for many transverse channels.…
Many real-world complex systems have small-world topology characterized by the high clustering of nodes and short path lengths.It is well-known that higher clustering drives localization while shorter path length supports delocalization of…
This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. We analyze several…
In this paper we study the structural, scattering, and wave localization properties of multifractal arrays of electric point dipoles generated from multiplicative random fields with different degrees of multiscale correlations.…
We study the spatio-temporal evolution of wave packets in one-dimensional quasiperiodic lattices which localize linear waves. Nonlinearity (related to two-body interactions) has destructive effect on localization, as recently observed for…
The spectral landscape and the transport property of a translationally invariant network with side-coupled quantum dots are demonstrated within the tight-binding framework. For periodic environment band structure is demonstrated…