Related papers: Universal building block for (1 1 0)-family silico…

We reexamine the longstanding no-go excluding all potentially viable SO(10) -> SU(3)_c x SU(2)_L x U(1)_Y symmetry breaking patterns within the minimal renormalizable non-supersymmetric SO(10) GUT framework featuring the 45-dimensional…

In the recent paper by Teys [JETP Letters 105 (8), 477-483 (2017)], an atomic model for the Si(331) reconstructed surface (hereby referred to as T-model) was proposed on the basis of high-resolution scanning tunneling microscopy (STM)…

We consider the action of the group $\mathrm{PGL}_4(K)$ on the smooth cubic surfaces of $\mathbb{P}^3_K$ ($K$ an algebraically closed field of characteristic zero). We classify, in an explicit way, all the smooth cubic surfaces with non…

Low-energy universality in atomic few-body systems as a result of a large two-body scattering length has gained a lot of attention recently. Here, I discuss recent progress in describing the three-body recombination of cold atoms in terms…

We discuss here geometric structures of condensed matters by means of a fundamental topological method. Any geometric pattern can be universally represented by a decomposition space of a topological space consisting of the infinite product…

We propose a new scalable platform for quantum computing (QC) -- an array of optically trapped symmetric-top molecules (STMs) of the alkaline earth monomethoxide (MOCH$_3$) family. Individual STMs form qubits, and the system is readily…

With the reported synthesis of a fully planar 2D silicon carbide (SiC) allotrope, the possibilities of its technological applications are enormous. Recently, several authors have computationally studied the structures and electronic…

We investigate the atomic and electronic structure of a single layer of pentacene on the Au(111) surface using density functional theory. To find the candidate structures we strain match the pentacene crystal geometry with the Au(111)…

Given a 2-dimensional surface M and a constant C we construct a Riemannian metric g, so that diameter diam(M,g)=1 and every 1-cycle dividing M into two regions of equal area has length >C. It follows that there exists no universal…

Using equivariant geometry, we find a universal formula that computes the number of times a general cubic surface arises in a family. As applications, we show that the PGL(4) orbit closure of a generic cubic surface has degree 96120, and…

Mutually Unbiased Bases (MUBs) constitute a fundamental geometric structure in quantum theory, known for providing an optimal measurement scheme for quantum state tomography. In prime and prime-power dimensions, analytical constructions of…

Basic matrices are defined which provide unique building blocks for the class of normal matrices which include the classes of unitary and Hermitian matrices. Unique builders for quantum logic gates are hence derived since a quantum logic…

This paper gives a construction of group divisible designs on the binary extension fields with block sizes 3, 4, 5, 6, and 7, respectively, which is motivated from the decoding of binary quadratic residue codes. A conjecture is proposed for…

This article describes an entirely algebraic construction for developing conformal geometries, which provide models for, among others, the Euclidean, spherical and hyperbolic geometries. On one hand, their relationship is usually shown…

This study introduces a new unified structural framework for orbifold sigma models that incorporates twisted sectors, singularities, and smooth regions into a single algebraic object. Traditional approaches to orbifold theories often treat…

Endohedrally doped Si20 fullerenes appear as appealing building blocks for nanoscale materials. We investigate their structural stability with an unbiased and systematic global geometry optimization method within density-functional theory.…

Functional properties of nanomaterials strongly depend on their surface atomic structure, but they often become largely different from their bulk structure, exhibiting surface reconstructions and relaxations. However, most of the surface…

The design space for a self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. Using a…

We study the vacuum structure in 5D SO(10) grand unified theory (GUT) compactified on $S^1/Z_2$ orbifold, where SO(10) is broken into $SU(3)\times SU(2)\times U(1)^2$ through the boundary conditions. Although a lot of people extended to 6D…

The Si(111) - 7 x 7 surface is one of the most interesting semiconductor surfaces because of its complex reconstruction and fascinating electronic properties. While it is known that the Si - 7 x 7 is a conducting surface, the exact surface…