Related papers: Localization in random fractal lattices
The localisation of electrons in a lattice potential is an quantum-mechanical phenomenon and is often associated with remarkable physical properties of solids involving electron spins, electric polarisations and topological effects. In…
The paper investigates localized deformation patterns resulting from the onset of instabilities in lattice structures. The study is motivated by previous observations on discrete hexagonal lattices, where the onset of non-uniform,…
We theoretically investigate the effects of atomic defect related short-range disorders and electron-electron interactions on Anderson type localization and the magnetic properties of hexagonal armchair graphene quantum dots using an…
We study spectra and localization properties of Euclidean random matrices. The problem is approximately mapped onto that of a matrix defined on a random graph. We introduce a powerful method to find the density of states and the…
Solitons in the fractional space, supported by lattice potentials, have recently attracted much interest. We consider the limit of deep one- and two-dimensional (1D and 2D) lattices in this system, featuring finite bandgaps separated by…
The present paper deals with the wave propagation in a particular two dimensional structure, obtained from a localized perturbation of a reference periodic medium. This reference medium is a ladder like domain, namely a thin periodic…
The two-dimensional Hubbard model on the square lattice is studied in the presence of lattice distortions in the adiabatic approximation. The self energy is computed within perturbation theory up to second order, which provides a way for…
We demonstrate that a weak disorder in atomic positions introduces spatially localized optical modes in a dense three-dimensional ensemble of immobile two-level atoms arranged in a diamond lattice and coupled by the electromagnetic field.…
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…
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 phenomenon of Anderson localization of waves in elastic systems is studied. We analyze this phenomenon in two different set of systems: disordered linear chains of harmonic oscillators and disordered rods which oscillate with torsional…
We investigate the impact of harmonic confinement in a finite optical superlattice and reveal the different mechanisms that can lead to the emergence of localized states. The optical superlattice, with odd or even number of unit cells, can…
We study localization properties of electronic states in one-dimensional lattices with nearest-neighbour interaction. Both the site energies and the hopping amplitudes are supposed to be of arbitrary form. A few cases are considered in…
We study charge transport in one-dimensional graphene superlattices created by applying layered periodic and disordered potentials. It is shown that the transport and spectral properties of such structures are strongly anisotropic. In the…
Multifractal dimensions allow for characterizing the localization properties of states in complex quantum systems. For ergodic states the finite-size versions of fractal dimensions converge to unity in the limit of large system size.…
The spectral approach to infinite disordered crystals is applied to an Anderson-type Hamiltonian to demonstrate the existence of extended states for nonzero disorder in 2D lattices of different geometries. The numerical simulations shown…
Wave localization is a fundamental phenomenon that appears universally in both natural materials and artificial structures and plays a crucial role in understanding the various physical properties of a system. Usually, a localized state has…
Localization of coherent propagating waves has been extensively studied over the years, primarily in homogeneous random media. However, significantly less attention has been given to wave localization in inhomogeneous systems, where the…
An application of an effective numerical algorithm for solving eigenvalue problems which arise in modelling electronic properties of quantum disordered systems is considered. We study the electron states at the localization-delocalization…
Higher dimensions provide fertile ground for diverse topological phases and their associated localization phenomena, thanks to the rich geometric features of boundaries and defects. In this paper, we investigate non-Hermitian lattices with…