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We present a complete analytical solution for the stress field inside a homogeneous, inside a homogeneous, linearly elastic solid sphere subjected to a concentrated normal load applied on its surface. Starting from the three-dimensional…
The effect of weak potential and bond disorder on the density of states of graphene is studied. By comparing the self-consistent non-crossing approximation on the honeycomb lattice with perturbation theory on the Dirac fermions, we…
Analytic results for the asymptotic decay of the electron density matrix in insulators have been obtained in all three dimensions ($D=1 - 3$) for a tight-binding model defined on a simple cubic lattice. The anisotropic decay length is shown…
Atomically thin sheets, such as graphene, are widely used in nanotechnology. Recently they have also been used in applications including kirigami and self-folding origami, where it becomes important to understand how they respond to…
A two-dimensional lattice gas model is proposed. The ground state of this model with a fixed density is neither periodic nor quasi-periodic. It also depends on system size in an irregular manner. On the other hand, it is ordered in the…
We address a problem of the upper critical field in a lattice described by a two-dimensional tight-binding model with the on-site pairing. We develop a finite-system-approach which enables investigation of magnetic and superconducting…
We consider a single atom in an optical lattice, subject to a harmonic trapping potential. The problem is treated in the tight-binding approximation, with an extra parameter \kappa denoting the strength of the harmonic trap. It is shown…
Interplay of superconductivity and density wave orders has been at the forefront of research of correlated electronic phases for a long time. 2H-NbSe$_2$ is considered to be a prototype system for studying this interplay, where the balance…
It is well known that the angles in a lattice acting on hyperbolic $n$-space become equidistributed. In this paper we determine a formula for the pair correlation density for angles in such hyperbolic lattices. Using this formula we…
We consider the Anderson model on the multi-dimensional cubic lattice and prove a positive lower bound on the density of states under certain conditions. For example, if the random variables are independently and identically distributed and…
We analyze the obtained solutions of the non-linear Shroedinger equation for spherically and axially symmetrical electrons density oscillations in plasma. The conditions of the oscillations process existence are examined. It is shown that…
Very recently, the standard description of electrons in strained graphene has been completed by the explicit inclusion of the lattice deformation. Here, the effect of these lattice corrections is taken into account to find the mechanical…
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 consider the problem of electron transport across a quasi-one-dimensional disordered multiply-scattering medium, and study the statistical properties of the electron density inside the system. In the physical setup that we contemplate,…
The electromagnetic instabilities excited by the temperature anisotropy have been always one of the interesting issues in real high-density physical systems, where the relativistic and quantum effects due to spin can be important. This…
Electrons in condensed matter may transition into a variety of broken-symmetry phase states due to electron-electron interactions. Applying diverse mean-field approximations to the interaction term is arguably the simplest way to identify…
We propose a model for a two dimensional, associative water-like lattice gas with one single variable representing both long and short-range interactions. The corresponding hamiltonian was solved exactly, by state enumeration in a finite…
We consider the problem of electron transport along a one-dimensional disordered multiple-scattering conductor, and study the electron density for all the electronic levels. A model is proposed for the reduced density matrix of the system…
Reconstructing a density of states or similar distribution from moments or continued fractions is an important problem in calculating the electronic and vibrational structure of defective or non-crystalline solids. For single bands a…
We examine the linear and nonlinear modes of a one-dimensional nonlinear electrical lattice, where the usual discrete Laplacian is replaced by a fractional discrete Laplacian. This induces a long-range intersite coupling that, at long…