Related papers: Green's functions and DOS for some 2D lattices
We examine the formation of bound states on a generalized nonlinear impurity located at or near the beginning (surface) of a linear, tight-binding semi-infinite lattice. Using the formalism of lattice Green functions, we obtain in closed…
Two-dimensional lattices provide the arena for many physics problems of essential importance, a non-trivial symmetry in such lattices will help to reveal the underlying physics. Whether there is a directional scaling for the 2D lattices is…
By a 1997 result of R. Freese, an $n$-element lattice has at most $2^{n-1}$ congruences. This motivates us to define the congruence density cd$(L)$ of a finite $n$-element lattice as $|$Con$(L)|/2^{n-1}$, where $|$Con$(L)|$ is the number of…
We construct the Green function for second order elliptic equations in non-divergence form when the mean oscillations of the coefficients satisfy the Dini condition and the domain has $C^{1,1}$ boundary. We also obtain pointwise bounds for…
In this work we develop an algebraic theory of linear recurrence equations and systems with constant coefficients and reflection. We obtain explicit solutions and the Green's functions associated to different problems under general linear…
We consider a model for 2D electrons in a very strong magnetic field (i.e. projected onto a single Landau level) and a random potential $V$. The computation of the averaged Green function for this system reduces to calculating the averaged…
A wide range of analytical and numerical methods are available to study quantum spin systems. However, the complexity of spin correlations and interactions limits their applicability to specific temperature ranges. The analytical approach…
The pointwise space-time behavior of the Green's function of the three-dimensional relativistic Boltzmann equation is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive waves and…
1-Dimensional (1D) photonics crystals with and without defects have been numerically studied using efficient Transfer Matrix Method (TMM). Detailed numerical recipe of the TMM has been laid out. Dispersion relation is verified for the…
We map certain highly correlated electron systems on lattices with geometrical frustration in the motion of added particles or holes to the spatial defect-defect correlations of dimer models in different geometries. These models are studied…
We verify a conjecture proposed by X. Chen and Y. Shi, which arises from their study of the Green function on spheres in Euclidean space. More precisely, let $M\subset \mathbb{R}^3$ be a closed $C^{2}$ embedded surface and suppose that…
The Coulomb Green's function (GF) for non-relativistic charged particle in field of attractive Coulomb force is extended to describe the interaction of two non-relativistic electrons through repulsive Coulomb forces. Closed-form expressions…
We propose a fast and versatile algorithm to calculate local and transport properties such as conductance, shot noise, local density of state or local currents in mesoscopic quantum systems. Within the non equilibrium Green function…
The reasoning is a slight extension of that employed in my article [1] and its further development [2]. A formal solution to the title problem is presented for a general periodic laminate and its application for the construction of…
Stieltjes boundary problems generalize the customary class of well-posed two-point boundary value problems in three independent directions, regarding the specification of the boundary conditions: (1) They allow more than two evaluation…
Hybrid spectral-spatial representations are introduced to rapidly calculate periodic scalar and dyadic Green's functions of the Helmholtz equation for 2D and 3D configurations with a 1D (linear) periodicity. The presented schemes work…
Two-dimensional honeycomb lattices, characterized by their low coordination numbers, provide a fertile platform for exploring various quantum phenomena due to the intricate interplay between competing magnetic interactions, spin-orbit…
We present a spin-rotation-invariant Green-function theory for the dynamic spin susceptibility in the spin-1/2 antiferromagnetic Heisenberg model on a stacked honeycomb lattice. Employing a generalized mean-field approximation for arbitrary…
We study the Laplacian on Stenzel spaces (generalized deformed conifolds), which are tangent bundles of spheres endowed with Ricci flat metrics. The (2d-2)-dimensional Stenzel space has SO(d) symmetry and can be embedded in C^d through the…
Motivated by the discovery of superconductivity in beta-pyrochlore oxides, we study property of rattling motion coupled with conduction electrons. We derive the general expression of the Green's function of fully anharmonic lattice…