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Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…
Using the matrix product formalism, we introduce a two parameter family of exactly solvable $xyz$ spin 1/2 Heisenberg chains in magnetic field (with nearest neighbor interactions) and calculate the ground state and correlation functions in…
Overlaying commensurate optical lattices with various configurations called superlattices can lead to exotic lattice topologies and, in turn, a discovery of novel physics. In this study, by overlapping the maxima of lattices, a new isolated…
We prove a decomposition theorem for orthocomplemented state property systems. More specifically we prove that an orthocomplemented state property system is isomorphic to the direct union of the non classical components of this state…
We consider a sequence of quantum states, $\rho_N$, associated with a submanifold $\Lambda$ of product of two integral compact K\"ahler manifolds. We show that, when $\Lambda$ is a product submanifold, then, in the semiclassical limit,…
Sectional pseudocomplementation (sp-complementation) on a poset is a partial operation $*$ which associates with every pair $(x,y)$ of elements, where $x \ge y$, the pseudocomplement $x*y$ of $x$ in the upper section $[y)$. Any total…
Constructing lattice isomorphic line arrangements that are not lattice isotopic is a complex yet fundamental task. In this paper, we focus on such pairs but which are not Galois conjugated, referred to as nonarithmetic pairs. Splitting…
We study one dimensional supersymmetric (SUSY) quantum mechanics of a spin 1/2 particle moving in a rotating magnetic field and scalar potential. We also discuss SUSY breaking and it is shown that SUSY breaking essentially depends on the…
In this paper we characterize the definiteness of the discrete symplectic system, study a nonhomogeneous discrete symplectic system, and introduce the minimal and maximal linear relations associated with these systems. Fundamental…
We derive the spin Boltzmann equations for spin-1/2 fermions in a non-relativistic model with four-fermion contact interaction which conserves spin degrees of freedom. A great advantage of the model is that the spin matrix elements in…
Materials with interesting physical properties are often designed based on our understanding of the target physical effects. The physical properties can be either explicitly observed ("apparent") or concealed by the perceived symmetry…
We consider the number of configurations of a surface in two dimensions that has a prescribed length and encloses a prescribed perimeter with respect to a baseline. An approximate analytical treatment in a semi--continuum compares…
Interest in finite-size systems has risen in the last decades, due to the focus on nanotechnological applications and because they are convenient for numerical treatment that can subsequently be extrapolated to infinite lattices.…
The double-layer electron system with total filling factor $\nu=1/2$ can be regarded as two separate Fermi-liquid-like states with $\nu=1/4$ when the layer separation is sufficiently large and there is no tunneling. The weak tunneling in…
A coupled atomistic spin and lattice dynamics approach is developed which merges the dynamics of these two degrees of freedom into a single set of coupled equations of motion. The underlying microscopic model comprises local exchange…
Weakly orthomodular and dually weakly orthomodular lattices were introduced by the authors in a recent paper. Similarly as for orthomodular lattices we try to introduce an implication in these lattices which can be easily axiomatized and…
Bilattices (that is, sets with two lattice structures) provide an algebraic tool to model simultaneously the validity of, and knowledge about, sentences in an appropriate language. In particular, certain bilattices have been used to model…
This article present the double-periodical lattice made of infinite elastic fibers that withstand bending and tension. The model describes the elastic properties of flat periodic structure. With this model the behavior of a two-dimensional…
When the dynamics of a spin ensemble are expressible solely in terms of symmetric processes and collective spin operators, the symmetric collective states of the ensemble are preserved. These many-body states, which are invariant under…
Strong interactions between electrons in two dimensions can realize phases where their spins and charges separate. We capture this phenomenon within a dual formulation. Focusing on square lattices, we analyze the long-wavelength structure…