Related papers: On the uniform tiling with electrical resistors
Flexible boundary condition methods couple an isolated defect to a harmonically responding medium through the bulk lattice Green's function; in the case of an interface, interfacial lattice Green's functions. We present a method to compute…
Proctor's work on staircase plane partitions yields an enumeration of lozenge tilings of a halved hexagon on the triangular lattice. Rohatgi recently extended this tiling enumeration to a halved hexagon with a triangle removed from the…
We derive formulas for the matrix elements of the two dimensional square lattice Green function along the diagonal, and along the coordinate axes. We also give an asymptotic formula for the diagonal elements.
We report on a method for the realization of two-dimensional electrostatic lattices for excitons using patterned interdigitated electrodes. Lattice structure is set by the electrode pattern and depth of the lattice potential is controlled…
We show that the timed Dicke states of a collection of three-level atoms can form a tight-binding lattice in momentum space. This lattice, coined the superradiance lattice (SL), can be constructed based on electromagnetically induced…
Antilattices $(S;\lor, \land)$ for which the Green's equivalences $\mathcal L_{(\lor)}$, $\mathcal R_{(\lor)}$, $\mathcal L_{(\land)}$ and $\mathcal R_{(\land)}$ are all congruences of the entire antilattice are studied and enumerated.
The orbital angular momentum conservation of light reveals different diffraction patterns univocally dependent on the topological charge of the incident light beam when passing through a triangular aperture. It is demonstrated that these…
Sums of walks for charged particles (e.g. Hofstadter electrons) on a square lattice in the presence of a magnetic field are evaluated. Returning loops are systematically added to directed paths to obtain the unrestricted propagators.…
Proctor proved a formula for the number of lozenge tilings of a hexagon with side-lengths $a,b,c,a,b,c$ after removing a "maximal staircase." Ciucu then presented a weighted version of Proctor's result. Here we present weighted and…
We examine theoretically and experimentally the localized %and extended electrical modes existing in a bi-inductive electrical lattice containing a bulk or a surface capacitive impurity. By means of the formalism of lattice Green's…
We complete the proof started in "Universality of one-dimensional Fermi systems, I." of the universal Luttinger liquid relations for a general model of spinning fermions on a lattice, by making use of the Ward Identities due to…
A star-triangle mapping transformation is used to establish an exact correspondence between the spin-1/2 Ising model on the Shastry-Sutherland (orthogonal-dimer) lattice and respectively, the spin-1/2 Ising model on a bathroom tile (4-8)…
We propose a new algorithm of the finite lattice method to generate the high-temperature series for the Ising model in three dimensions. It enables us to extend the series for the free energy of the simple cubic lattice from the previous…
For a certain class of two-dimensional lattices, lattice-dual pairs are shown to have the same bond percolation critical exponents. A computational proof is given for the martini lattice and its dual to illustrate the method. The result is…
Geometrical arrangements of minimum energy of a system of identical repelling particles in two dimensions are studied for different forms of the interaction potential. Stability conditions for the triangular structure are derived, and some…
We discuss the properties of interacting electrons on a finite chain with open boundary conditions. We extend the Haldane Luttinger liquid description to these systems and study how the presence of the boundaries modifies various…
Lattice tilings of $\mathbb{Z}^n$ by limited-magnitude error balls correspond to linear perfect codes under such error models and play a crucial role in flash memory applications. In this work, we establish three main results. First, we…
We perform molecular dynamics simulations on an interacting electron gas confined to a cylindrical surface and subject to a radial magnetic field and the field of the positive background. In order to study the system at lowest energy states…
The concept of effective resistance, originally introduced in electrical circuit theory, has been extended to the setting of graphs by interpreting each edge as a resistor. In this context, the effective resistance between two vertices…
It is well-known that the question of whether a given finite region can be tiled with a given set of tiles is NP-complete. We show that the same is true for the right tromino and square tetromino on the square lattice, or for the right…