Related papers: Disorder effects in the two-dimensional Lieb latti…
We study Anderson localization in disordered tight-binding models on hyperbolic lattices. Such lattices are geometries intermediate between ordinary two-dimensional crystalline lattices, which localize at infinitesimal disorder, and Bethe…
The stability of the magnetization in Lieb graphene quantum dots (GQD) against disorder is studied. Such systems exhibit the degenerate shell of edge states in the middle of the energy gap occupied by spin polarized electrons. Disorder…
We study numerically the effects of nonlinearity on the Anderson localization in lattices with disorder in one and two dimensions. The obtained results show that at moderate strength of nonlinearity an unlimited spreading over the lattice…
We examine how disordering joint position influences the linear elastic behavior of lattice materials via numerical simulations in two-dimensional beam networks. Three distinct initial crystalline geometries are selected as representative…
We study the mean-field phase diagram of the two-dimensional (2D) Hubbard model in the Lieb lattice allowing for spin and charge density waves. Previous studies of this diagram have shown that the mean-field magnetization surprisingly…
Recently, waveguide lattices with non-uniform tunneling amplitudes have been explored due to their myriad tunable properties, many of which arise from the extended nature of their eigenstates in the absence of disorder. Here, we investigate…
Flat-band systems are highly sensitive to external perturbations, providing a route to study unconventional localization, transport, and spin physics. Lieb lattice, a two-dimensional geometry with an inherent flat band, exemplifies this…
We investigate the dispersion relations of strained as well as complex Lieb lattices systematically based on the tight-binding method when the nearest-neighbor approximation is adopted. We find that edge states will no appear for strained…
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 theoretically investigate light propagation and Anderson localization in one-dimensional disordered superlattices composed of dielectric stacks with graphene sheets in between. Disorder is introduced either on graphene material…
We investigate experimentally the light evolution inside a two-dimensional finite periodic array of weakly- coupled optical waveguides with a disordered boundary. For a completely localized initial condition away from the surface, we find…
We study site- and bond-percolation on a class of lattices referred to as Lieb lattices. In two dimensions the Lieb lattice (LL) is also known as the decorated square lattice, or as the CuO$_2$ lattice; in three dimensions it can be…
The transfer matrix method is applied to quasi one-dimensional and one-dimensional disordered systems with long-range interactions, described by band random matrices. We investigate the convergence properties of the whole Lyapunov spectra…
We present a numerical study of the transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations. The model is characterized by the modulation period $\kappa$ and the disorder…
We investigate numerically the statistical properties of spectra of two-dimensional disordered systems by using the exact diagonalization and decimation method applied to the Anderson model. Statistics of spacings calculated for system…
We theoretically study magnetic properties of two-component cold fermions in half-filled multilayer Lieb optical lattices, i.e., two, three, and several layers, using the dynamical mean-field theory. We clarify that the magnetic properties…
Steady-state and transient antiplane dynamic processes in a structured solids consisting of uniform periodic square-cell lattices connected by a lattice layer of different bond stiffnesses and point masses are analyzed. A semi-infinite…
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…
We analyze the origin and features of localized excitations in a discrete two-dimensional Hamiltonian lattice. The lattice obeys discrete translational symmetry, and the localized excitations exist because of the presence of nonlinearities.…
A survey is given on asymptotic diffusion coefficients of particles in lattices with random transition rates. Exact and approximate results for single particles are reviewed. A recent exact expression in $d = 1$ which includes occupation…