Related papers: Localization transition on complex networks via sp…
We study phenomena where some eigenvectors of a graph Laplacian are largely confined in small subsets of the graph. These localization phenomena are similar to those generally termed Anderson Localization in the Physics literature, and are…
We seek the possibility of a disorder driven transition in a tight-binding lattice with a flat band using complexity parameter approach. Our results indicate the existence of a localized to extended states transition with increasing…
In the modeling, monitoring, and control of complex networks, a fundamental problem concerns the comprehensive determination of the state of the system from limited measurements. Using power grids as example networks, we show that this…
We review the time evolution of wavepackets at the metal-insulator transition in two- and three-dimensional disordered systems. The importance of scale invariance and multifractal eigenfunction fluctuations is stressed. The implications of…
We numerically show that very small magnetic flux can significantly shift the metal-insulator transition point in a disordered electronic system. The shift we observe for the 3d Anderson model obeys a power law as predicted by Larkin and…
Using Ioffe-Regel-Mott (IRM) criterion for strong localization crossover in disordered doped 2D electron systems, we theoretically study the relationships among the three key experimentally determined localization quantities: critical…
The distribution of energy level separations for lattices of sizes up to 28$\times$28$\times$28 sites is numerically calculated for the Anderson model. The results show one-parameter scaling. The size-independent universality of the…
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…
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 theoretically consider the problem of doping induced insulator to metal transition in bulk semiconductors by obtaining the transition density as a function of compensation, assuming that the transition is an Anderson localization…
The insulating state of matter can be probed by means of a ground state geometrical marker, which is closely related to the modern theory of polarization (based on a Berry phase). In the present work we show that this marker can be applied…
Localization phenomena permeate many branches of physics playing a fundamental role on dynamical processes evolving on heterogeneous networks. These localization analyses are frequently grounded, for example, on eigenvectors of adjacency or…
The interplay between local, repulsive interactions and disorder acting only on one spin orientation of lattice fermions ("spin-dependent disorder") is investigated. The nonmagnetic disorder vs. interaction phase diagram is computed using…
The Anderson model for independent electrons in a disordered potential is transformed analytically and exactly to a basis of random extended states leading to a variant of augmented space. In addition to the widely-accepted phase diagrams…
We undertake an exact numerical study of the effects of disorder on the Anderson localization of electronic states in graphene. Analyzing the scaling behaviors of inverse participation ratio and geometrically averaged density of states, we…
We study the Anderson transition in lattices with the connectivity of a random-regular graph. Our results indicate that fractal dimensions are continuous across the transition, but a discontinuity occurs in their derivatives, implying the…
Anderson localization has been a subject of intense studies for many years. In this context, we study numerically the influence of long-range correlated disorder on the localization behavior in one dimensional systems. We investigate the…
We present a review of theoretical and experimental works on the problem of mutual interplay of Anderson localization and superconductivity in strongly disordered systems. We start with brief discussion of modern aspects of localization…
The percolation phase transition in complex network systems attracts much attention and has numerous applications in various research fields. Finite size effects smooth the transition and make it difficult to predict the critical point of…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…