Related papers: Infinite Simple 3D Cubic Lattice of Identical Resi…
An exact method that analytically provides transfer matrices in finite networks of quasicrystalline approximants of any dimensionality is discussed. We use these matrices in two ways: a) to exactly determine the band structure of an…
The problem of characterizing the structure of an elastic network constrained to lie on a frozen curved surface appears in many areas of science and has been addressed by many different approaches, most notably, extending linear elasticity…
All indecomposable unimodular hermitian lattices in dimensions 14 and 15 over the ring of integers in $\mathbb{Q}(\sqrt{-3})$ are determined. Precisely one lattice in dimension 14 and two lattices in dimension 15 have minimal norm 3.
We examine the effect of adding PT-symmetric gain and loss terms to quasi 1D lattices (ribbons) that possess flat bands. We focus on three representative cases: (a) The Lieb ribbon, (b) The kagome ribbon, and (c) The stub Ribbon. In general…
This paper deals with synchronization of a class of infinite-dimensional systems. The considered network is described by a collection of semilinear Lipschitz boundary-actuated infinite-dimensional dynamics. For undirected connected graphs,…
A theoretical approach was developed for an exact numerical description of a pair of ultracold atoms interacting via a central potential that are trapped in a three-dimensional optical lattice. The coupling of center-of-mass and…
Simplifications of a result from a prior paper concerning the electric resistance between points in a distance-regular graph are given. In particular, we prove that the maximal resistance between points is bounded by twice the resistance…
We study asymptotic lower and upper bounds for the sizes of constant dimension codes with respect to the subspace or injection distance, which is used in random linear network coding. In this context we review known upper bounds and show…
In this work, we have employed Monte Carlo calculations to study the Ising model on a 2D additive small-world network with long-range interactions depending on the geometric distance between interacting sites. The network is initially…
The geometric properties of a lattice can have profound consequences on its band spectrum. For example, symmetry constraints and geometric frustration can give rise to topologicially nontrivial and dispersionless bands, respectively.…
Fundamental solitons pinned to the interface between two discrete lattices coupled at a single site are investigated. Serially and parallel-coupled identical chains (\textit{System 1} and \textit{System 2}), with the self-attractive on-site…
In a recent paper, we combined the technique of bosonization with the concept of a Rayleigh dissipation function to develop a model for resistances in one-dimensional systems of interacting spinless electrons [arXiv:1011.5058]. We also…
A periodic lattice in Euclidean space is the infinite set of all integer linear combinations of basis vectors. Any lattice can be generated by infinitely many different bases. This ambiguity was only partially resolved, but standard…
We measure the conductivity of neutral fermions in a cubic optical lattice. Using in-situ fluorescence microscopy, we observe the alternating current resultant from a single-frequency uniform force applied by displacement of a weak harmonic…
We analyse supersymmetric models that show supersymmetry breaking in one and two dimensions using lattice methods. Starting from supersymmetric quantum mechanics we explain the fundamental principles and problems that arise in putting…
The elementary 2-terminal network consisting of a resistively ($R-$) shunted inductance ($L$) in series with a capacitatively ($C-$) shunted resistance ($R$) with $R = \sqrt{L/C}$, is known for its non-dispersive dissipative response,…
Transport properties of the vortex lattice in high temperature superconductors are studied using numerical simulations in the case in which the non-local interactions between vortex lines are dismissed. The results obtained for the…
In this work, the origin of nonlocal effects is inspected and the contributions of nontrivial topological structures to physical properties are investigated in details for both the 3D Ising model and the Z2 lattice gauge model. Then the…
It is shown that a compound elastic structure, which displays a dynamic instability, may be designed as the union (or 'fusion') of two structures which are stable when separately analyzed. The compound elastic structure has two degrees of…
Double-exchange model in infinite dimension is studied as the strong Hund's coupling limit $J\to\infty$ of the Kondo lattice model. Several quantities such as Green's function and the d.c.\ conductivity are calculated in analytical forms.…