Related papers: Localization in random fractal lattices

We demonstrate that all of the salient features of the Harper-Hofstadter model can be implemented with ultracold atoms trapped in a bichromatic ring-shaped lattice. Using realistic sinusoidal lattice potentials rather than assume the…

Artificial defects embedded in periodic structures are important foundation for creating localized states with vast range of applications in condensed matter physics, photonics and acoustics. In photonics, localized states are extensively…

We experimentally investigate the evolution of linear and nonlinear waves in a realization of the Anderson model using disordered one dimensional waveguide lattices. Two types of localized eigenmodes, flat-phased and staggered, are directly…

We investigate the statistical properties of translation invariant random fields (including point processes) on Euclidean spaces (or lattices) under constraints on their spectrum or structure function. An important class of models that…

The presence of flat bands is a source of localization in lattice systems. While flat bands are often unstable with respect to interactions between the particles, they can persist in certain cases. We consider a diamond ladder with…

We consider two bidimensional random models characterised by the following features: a) their Hamiltonians are separable in polar coordinates and b) the random part of the potential depends either on the angular coordinate or on the radial…

In this paper, we study non-interacting bosons in a disordered one-dimensional optical lattice in a harmonic potential. We consider the case of deterministic disorder produced by an Aubry-Andr\'{e} potential. Using exact diagonalization, we…

Two-dimensional non-Hermitian photonic lattices with asymmetric couplings offer rich possibilities for controlling wave localization, through the emergence of the non-Hermitian skin effect at lattice corners or sides. Incorporating optical…

We investigate the localization of waves in aperiodic structures that manifest the characteristic multiscale complexity of certain arithmetic functions with a central role in number theory. In particular, we study the eigenspectra and wave…

Exploring the deep insights into localization, disorder, and wave transport in non-Hermitian systems is an emergent area of research of relevance in different areas of physics. Engineered photonic lattices, with spatial regions of optical…

We study how the influence of structural correlations in disordered systems manifests itself in experimentally measurable magnitudes, focusing on dc conductance of semiconductor superlattices with general potential profiles. We show that…

We discuss the role of rare fluctuation effects in quantum condensed matter systems. In particular, we present recent numerical results of the effect of resonant states in Anderson's original model of electron localization. We find that…

Photonic lattices facilitate band structure engineering, supporting both localized and extended modes through their geometric design. However, greater control over these modes can be achieved by taking advantage of the interference effect…

An analysis of the electron localization properties in doped graphene is performed by doing a numerical multifractal analysis. By obtaining the singularity spectrum of a tight-binding model, it is found that the electron wave functions…

We study a two-dimensional tight-binding lattice for excitons with on-site disorder, coupled to a thermal environment at infinite temperature. The disorder acts to localise an exciton spatially, while the environment generates dynamics…

We study excitations of the local field (locsitons) in nanoscale two-dimensional (2D) lattices of strongly interacting resonant atoms and various unusual effects associated with them. Locsitons in low-dimensional systems and the resulting…

We study the spectral statistics of interacting spinless fermions in a two-dimensional disordered lattice. Within a full quantum treatment for small few-particle-systems, we compute the low-energy many-body states numerically. While at weak…

Electrons moving through a spatially periodic lattice potential develop a quantized energy spectrum consisting of discrete Bloch bands. In two dimensions, electrons moving through a magnetic field also develop a quantized energy spectrum,…

We establish strong dynamical localization for a class of multi-particle Anderson models in a Euclidean space with an alloy-type random potential and a sub-exponentially decaying interaction of infinite range. For the first time in the…

Emerging experimental platforms use amorphousness, a constrained form of disorder, to tailor meta-material properties. We study localization under this type of disorder in a family of 2D models generalizing recent experiments on photonic…