Related papers: Observation of surface states with algebraic local…

The capability to temporarily arrest the propagation of optical signals is one of the main challenges hampering the ever more widespread use of light in rapid long-distance transmission as well as all-optical on-chip signal processing or…

Anderson localization is a fundamental phenomenon in disordered quantum systems, where transport is suppressed by wave interference from extensive randomness. Moving beyond traditional multi-impurity scenarios, we investigate…

In this letter, we report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen stringnet model. The full Hamiltonian in our…

We prove that Archimedean sharply dominating atomic lattice effect algebras can be characterized by property called basic decomposition of elements. As an application we prove the state smearing theorem for these effect algebras.

We construct finite-dimensional projective representations of the mapping class groups of compact connected oriented surfaces having one boundary component using stated skein algebras.

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…

We study ultracold fermionic atoms trapped in an optical lattice with harmonic confinement by means of the dynamical mean-field approximation. It is demonstrated that a supersolid state, where an s-wave superfluid coexists with a…

Inspired by the growing interest in probing many-body phases in novel two-dimensional lattice geometries we investigate the properties of cold atoms as they could be observed in an optical Lieb lattice. We begin by computing Wannier…

We report the first experimental observation of vector surface solitons, which form at the edge and in the corner of two-dimensional laser-written waveguide arrays. These elliptically polarized vector states are composed of two orthogonally…

We present the results of detailed theoretical investigations of changes in local density of total electronic surface states in 2D anisotropic atomic semiconductor lattice in vicinity of impurity atom for a wide range of applied bias…

We study quantum dots defined by external potentials within finite flakes of bilayer graphene using the tight-binding approach. We find that in the limit of large flakes containing zigzag edges the dot-localized energy levels appear within…

One-dimensional superlattices with periodic spatial modulations of onsite potentials or tunneling coefficients can exhibit a variety of properties associated with topology or symmetry. Recent developments of ring-shaped optical lattices…

In this paper, we investigate the ground state properties of a mixture of two species of fermionic atoms in one-dimensional optical lattice, as described by the asymmetric Hubbard model. The quantum phase transition from density wave to…

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…

We present the first experimental demonstration of a new type of bound states in the continuum, namely, compacton-like linear states in flat bands lattices. To this end, photonic Lieb lattices are employed, which exhibit three tight-binding…

We study the spectrum of the Helmholtz equation in a two-dimensional infinite waveguide, containing a weak heterogeneity localized at an internal point, and obeying Dirichlet boundary conditions at its border. We prove that, when the…

We address edge states and rich localization regimes available in the one-dimensional (1D) dynamically modulated superlattices, both theoretically and numerically. In contrast to conventional lattices with straight waveguides, the…

We consider the fate of the Dirac points in the spectrum of a honeycomb optical lattice in the presence of a harmonic confining potential. By numerically solving the tight binding model we calculate the density of states, and find that the…

We present algebraic techniques to analyze state space models in the areas of structural identifiability, observability, and indistinguishability. While the emphasis is on surveying existing algebraic tools for studying ODE systems, we also…

In the present work, we study coherent structures in a one-dimensional discrete nonlinear Schr\"odinger lattice in which the coupling between waveguides is periodically modulated. Numerical experiments with single-site initial conditions…