Related papers: Symmetry classes in piezoelectricity from second-o…
The so-called Lounesto's classification engenders six distinct classes of spinors, divided into two sectors: one composed by regular spinors (single-helicity spinors) and the other composed by singular spinors (comprising dual-helicity…
The concept of symmetries in physics is briefly reviewed. In the first part of these lecture notes, some of the basic mathematical tools needed for the understanding of symmetries in nature are presented, namely group theory, Lie groups and…
A finite bosonic or fermionic symmetry can be described uniquely by a symmetric fusion category $\mathcal{E}$. In this work, we propose that 2+1D topological/SPT orders with a fixed finite symmetry $\mathcal{E}$ are classified, up to $E_8$…
We study the symmetric outer product decomposition which decomposes a fully (partially) symmetric tensor into a sum of rank-one fully (partially) symmetric tensors. We present iterative algorithms for the third-order partially symmetric…
General formulas of the two-electron operator representing either atomic or effective interactions are given in a coupled tensorial form in relativistic approximation. The alternatives of using uncoupled, coupled and antisymmetric…
We reconsider a class of heterotic string theories studied in 1989, based on tensor products of N=2 minimal models with asymmetric simple current invariants. We extend this analysis from (2,2) and (1,2) spectra to (0,2) spectra with SO(10)…
Nested parentheses are forms in an algebra which define orders of evaluations. A class of well-formed sets of associated opening and closing parentheses is well studied in conjunction with Dyck paths and Catalan numbers. Nested parentheses…
Let L/F be a dihedral extension of degree 2p, where p is an odd prime. Let K/F and k/F be subextensions of L/F with degrees p and 2, respectively. Then we will study relations between the p-ranks of the class groups Cl(K) and Cl(k).
Using electromagnetism to study analogue space-times is tantamount to considering consistency conditions for when a given (meta-)material would provide an analogue space-time model or --- vice versa --- characterizing which given metric…
Consider the smooth quadric Q_6 in P^7. The middle homology group H_6(Q_6,Z) is two-dimensional with a basis given by two classes of linear subspaces. We classify all threefolds of bidegree (1,p) inside Q_6.
This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial.…
This paper is a continuation of our previous work, where eleven basic classes of almost paracontact metric manifolds with respect to the covariant derivative of the structure tensor field were obtained. First we decompose one of the eleven…
Considering the importance of the flexoelectric coupling for the physical understanding of the gradient-driven couplings in mesoscale and nanoscale solids, one has to determine its full symmetry and numerical values. The totality of…
The origin of the functional properties of complex oxide superlattices can be resolved using time-resolved synchrotron x-ray diffraction into contributions from the component layers making up the repeating unit. The CaTiO3 layers of a…
Following a previous proposition of quaternity spacetime for electronic orbitals in neon shell, this paper describes the geometrical course each electron takes as it oscillates harmonically within a certain quaternity space dimension and…
We present a first-principles study of the relationship between stress, temperature and electronic properties in piezoelectric ZnO. Our method is a plane wave pseudopotential implementation of density functional theory and density…
A fundamental dichotomous classification for all physical systems is according to whether they are spinless or spinful. This is especially crucial for the study of symmetry-protected topological phases, as the two classes have distinct…
We consider first order symmetry operators for the equations of motion of differential $p$-form fields in general $D$-dimensional background geometry of any signature for both massless and massive cases. For $p=1$ and $p=2$ we give the…
In this paper we consider a class of the 2D integrable models. These models are higher spin XXZ chains with an extra condition of the commensurability between spin and anisotropy. The mathematics underlying this commensurability is provided…
In this article we present analytical results on the exact tensor network representations and correlation functions of the first examples of 2D ground states with quantum phase transitions between area law and extensive entanglement…