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We study two coupled 3D lattices, one of them featuring uncorrelated on-site disorder and the other one being fully ordered, and analyze how the interlattice hopping affects the localization-delocalization transition of the former and how the latter responds to it. We find that moderate hopping pushes down the critical disorder strength for the disordered channel throughout the entire spectrum compared to the usual phase diagram for the 3D Anderson model. In that case, the ordered channel begins to feature an effective disorder also leading to the emergence of mobility edges but with higher associated critical disorder values. Both channels become pretty much alike as their hopping strength is further increased, as expected. We also consider the case of two disordered components and show that in the presence of certain correlations among the parameters of both lattices, one obtains a disorder-free channel decoupled from the rest of the system.
We study quantum transport in anisotropic 3D disorder and show that non rotation invariant correlations can induce rich diffusion and localization properties. For instance, structured finite-range correlations can lead to the inversion of the transpo
We present a full description of the nonergodic properties of wavefunctions on random graphs without boundary in the localized and critical regimes of the Anderson transition. We find that they are characterized by two critical localization lengths:
The localization of one-electron states in the large (but finite) disorder limit is investigated. The inverse participation number shows a non--monotonic behavior as a function of energy owing to anomalous behavior of few-site localization. The two-s
The disordered many-body systems can undergo a transition from the extended ensemble to a localized ensemble, known as many-body localization (MBL), which has been intensively explored in recent years. Nevertheless, the relation between Anderson loca
We establish a phase diagram of a model in which scalar waves are scattered by resonant point scatterers pinned at random positions in the free three-dimensional (3D) space. A transition to Anderson localization takes place in a narrow frequency band