Search results for " Algebra"

Acoustic Su-Schrieffer-Heeger lattice: Direct mapping of acoustic waveguides to the Su-Schrieffer-Heeger model

2021

Topological physics strongly relies on prototypical lattice model with particular symmetries. We report here on a theoretical and experimental work on acoustic waveguides that is directly mapped to the one-dimensional Su-Schrieffer-Heeger chiral model. Starting from the continuous two dimensional wave equation we use a combination of monomadal approximation and the condition of equal length tube segments to arrive at the wanted discrete equations. It is shown that open or closed boundary conditions topological leads automatically to the existence of edge modes. We illustrate by graphical construction how the edge modes appear naturally owing to a quarter-wavelength condition and the conserv…

A minimal tight-binding model for the quasi-one-dimensional superconductor K2Cr3As3

2019

We present a systematic derivation of a minimal five-band tight-binding model for the description of the electronic structure of the recently discovered quasi one-dimensional superconductor K2Cr3As3. Taking as a reference the density-functional theory (DFT) calculation, we use the outcome of a Lowdin procedure to refine a Wannier projection and fully exploit the predominant weight at the Fermi level of the states having the same symmetry of the crystal structure. Such states are described in terms of five atomic-like d orbitals: four planar orbitals, two dxy and two dx2-y2, and a single out-of-plane one, dz2 . We show that this minimal model reproduces with great accuracy the DFT band struc…

A short proof of the self-improving regularity of quasiregular mappings

2005

. The theoryof quasiregular mappings is a central topic in modern analysis withimportant connections to a variety of topics as elliptic partial differen-tial equations, complex dynamics, differential geometry and calculus ofvariations [13] [10].A remarkable feature of quasiregular mappings is the self-improvingregularity. In 1957 [2], Bojarski proved that for planar quasiregularmappings, there exists an exponent

Quotients of Fermat curves and a Hecke character

2005

AbstractWe explicitly identify infinitely many curves which are quotients of Fermat curves. We show that some of these have simple Jacobians with complex multiplication by a non-cyclotomic field. For a particular case we determine the local zeta functions with two independent methods. The first uses Jacobi sums and the second applies the general theory of complex multiplication, we verify that both methods give the same result.

Quotients of Hypersurfaces in Weighted Projective Space

2009

Abstract In [Bini, van Geemen, Kelly, Mirror quintics, discrete symmetries and Shioda maps, 2009] some quotients of one-parameter families of Calabi–Yau varieties are related to the family of Mirror Quintics by using a construction due to Shioda. In this paper, we generalize this construction to a wider class of varieties. More specifically, let A be an invertible matrix with non-negative integer entries. We introduce varieties XA and in weighted projective space and in , respectively. The variety turns out to be a quotient of a Fermat variety by a finite group. As a by-product, XA is a quotient of a Fermat variety and is a quotient of XA by a finite group. We apply this construction to som…

Symmetries and equations of smooth quartic surfaces with many lines

2017

We provide explicit equations of some smooth complex quartic surfaces with many lines, including all 10 quartics with more than 52 lines. We study the relation between linear automorphisms and some configurations of lines such as twin lines and special lines. We answer a question by Oguiso on a determinantal presentation of the Fermat quartic surface.

A theoretical study of the collinear reaction F+H2→HF+H using multiconfigurational second-order perturbation theory (CASPT2)

1993

Abstract The second-order perturbation method (CASPT2) with a single state multiconfigurational reference function generated in complete active self-consistent field (CASSCF) calculations has been used to compute the collinear barrier height, saddle point geometry, and exothermicity of the reaction F+H 2 →HF+H. Comparison with full configuration (FCI) calculations with small basis sets shows that the CASPT2 method is capable of reproducing accurately the exact benchmark results correlating seven electrons. Large atomic natural orbital basis sets are used at the seven- and nine-electron level of correlation. With the largest ANO basis set used, F[7s6p5d4f2g]/H[6s5p4d2f], the computed nine-el…

Lines on K3 quartic surfaces in characteristic 2

2016

We prove that a K3 quartic surface defined over a field of characteristic 2 can contain at most 68 lines. If it contains 68 lines, then it is projectively equivalent to a member of a 1-dimensional family found by Rams and Sch\"utt.

On the canonical algebra of smoothings of sandwiched singularities

2004

Integral curves of derivations

1988

We integrate, by a constructive method, derivations of even degree on the sections of an exterior bundle by families of Z 2-graded algebra automorphisms, dependent on a real parameter, and which satisfy a flow condition. We also study the case of local endomorphisms when their components of degree zero and derivations and with no component of negative degree, but then we have integral families of R-linear automorphisms. This integration method can be applied to the Frolicher—Nijenhuis derivations on the Cartan algebra of differential forms, and to the integration of superfields on graded manifolds.