相关论文: Edge Effects on Local Statistics in Lattice Dimers…
In this paper, we consider the direct and inverse problems of the description of lattice positive random fields by various systems of finite-dimensional (as well as one-point) probability distributions parameterized by boundary conditions.…
The honeycomb lattice in the cylinder geometry with zigzag edges, bearded edges, zigzag and bearded edges (zigzag-bearded), and armchair edges are studied. The tight-binding model with nearest-neighbor hoppings is used. Edge states are…
In this paper we determine the interaction of diagonal defect clusters in regions of an Aztec rectangle that scale to arbitrary points on its symmetry axis (in earlier work we treated the case when this point was the center of the scaled…
In this work, the tridiagonal method is used to distinguish between edges modes and area modes to study the edge sites properties effect on edge localized states of semi-infinite zigzag 2D honeycomb graphene sheet. The results show a…
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…
A unifying description of lattice potentials generated by aperiodic one-dimensional sequences is proposed in terms of their local reflection or parity symmetry properties. We demonstrate that the ranges and axes of local reflection symmetry…
The spectral properties of the Laplacian on a class of quantum graphs with random metric structure are studied. Namely, we consider quantum graphs spanned by the simple $\ZZ^d$-lattice with $\delta$-type boundary conditions at the vertices,…
We investigate the influence of the granularity of the lattice on the potential between monopoles. Using the flux definition of monopoles we introduce their centers of mass and are able to realize continuous shifts of the monopole…
We applied finite difference time domain (FDTD) algorithm to the study of field and intensity correlations in random media. Close to the onset of Anderson localization, we observe deviations of the correlation functions, in both shape and…
We present an experimental study of a four beam optical lattice using the light scattered by the atoms in the lattice. We use both intensity correlations and observations of the transient behavior of the scattering when the lattice is…
We use methods from algebra and discrete geometry to study the irreducibility of the dispersion polynomial of a discrete periodic operator associated to a periodic graph after changing the period lattice. We provide numerous applications of…
In this paper we present a theoretical analysis of the effect of local geometrical structure of the Fermi surface on the surface impedance of a metal at the anomalous skin effect. We show that when the Fermi surface includes nearly…
A celebrated result of Legendre and Gauss determines which integers can be represented as a sum of three squares, and for those it is typically the case that there are many ways of doing so. These different representations give collections…
We study the effects of finite size and of vacancies on the photonic band gap recently predicted for an atomic diamond lattice. Close to a $J_g=0\to J_e=1$ atomic transition, and for atomic lattices containing up to $N\approx 3\times10^4$…
This is a contribution to the number theory of the dimer problem. The number of dimer coverings (i.e., perfect matchings) of a square lattice graph is discussed modulo powers of 2.
We study the entropy of a set of identical hard objects, of general shape, with each object pivoted on the vertices of a d-dimensional regular lattice of lattice spacing a, but can have arbitrary orientations. When the pivoting point is…
We study the dimer model on special subgraphs of the square hexagon lattice called "tower graphs" of size $N$. Using integrable probability techniques, we confirm that as $N \rightarrow \infty$, the local statistics are translation…
In this paper we consider sparsely random potentials in 5 or more dimensional cubic lattice and exhibit localized and extended states. We identify also the mobility edge for a class of potentials going to infinity at infinity. Our treatment…
Motivated by recent progress on quantum engineered Kondo lattices, we numerically investigated the local magnetic properties of a hexagonal Anderson droplet consisting of multiple rings of magnetic atoms periodically arrayed on a triangular…
The effects of periodic and aperiodic distortions on the structure factor and radial distribution function of single-component lattices are investigated. To this end, different kinds of distortions are applied to the otherwise perfect…