Showing papers on "Antisymmetry published in 2020"

Floquet higher-order topological insulators and superconductors with space-time symmetries

Abstract: Floquet higher-order topological insulators and superconductors (HOTI/SCs) with an order-two space-time symmetry or antisymmetry are classified. This is achieved by considering unitary loops, whose nontrivial topology leads to the anomalous Floquet topological phases, subject to a space-time symmetry/antisymmetry. By mapping these unitary loops to static Hamiltonians with an order-two crystalline symmetry/antisymmetry, one is able to obtain the K groups for the unitary loops and thus complete the classification of Floquet HOTI/SCs. Interestingly, we found that for every order-two nontrivial space-time symmetry/antisymmetry involving a half-period time translation, there exists a unique order-two static crystalline symmetry/antisymmetry, such that the two symmetries/antisymmetries give rise to the same topological classification. Moreover, by exploiting the frequency-domain formulation of the Floquet problem, a general recipe that constructs model Hamiltonians for Floquet HOTI/SCs is provided, which can be used to understand the classification of Floquet HOTI/SCs from an intuitive and complimentary perspective.

Antisymmetry: Fundamentals and Applications

Abstract: Symmetry is fundamental to understanding our physical world. An antisymmetry operation switches between two different states of a trait, such as two time states, position states, charge states, spi...

Antisymmetry: Fundamentals and Applications

Abstract: Symmetry is fundamental to understanding our physical world. An antisymmetry operation switches between two different states of a trait, such as two time-states, position-states, charge-states, spin-states, chemical-species etc. This review covers the fundamental concepts of antisymmetry, and focuses on four antisymmetries, namely spatial inversion in point groups, time reversal, distortion reversal and wedge reversion. The distinction between classical and quantum mechanical descriptions of time reversal is presented. Applications of these antisymmetries in crystallography, diffraction, determining the form of property tensors, classifying distortion pathways in transition state theory, finding minimum energy pathways, diffusion, magnetic structures and properties, ferroelectric and multiferroic switching, classifying physical properties in arbitrary dimensions, and antisymmetry-protected topological phenomena are presented.

Antisymmetry and word order in double object constructions in Zarma

Abstract: Double Object Construction in Zarma sometimes allows alternations in the order of its internal arguments and the order in some cases may also be fixed. This tendency does not make predictions about a canonical order for the occurrence of Theme and Recipient objects within the VP simple. The same condition applies to monotransitive structures which vary between a complement-head and a head-complement order. It is the aim of this paper to present and analyse the most salient features of the kind of variations found in Zarma word order, particularly the ones associated with the verb that encodes three-participant events. The paper adopts the minimalist program proposed by Chomsky and is complemented with the Antisymmetry Hypothesis proposed by Kayne (1994). The study shows that the language has a uniform linear order where the recipient canonically precedes the theme on the basis of animacy factor. This is particularly common with the pronoun as the recipient in double object structures. Employing different diagnostics, the paper concludes that the recipient only follows the theme when the theme is associated with a more prominent discourse status. It is also argued that asymmetric C-command always occurs between the theme and the recipient. It implies that the language symmetry is altered by movement to designated positions for the purpose of feature checking.

Fixed Points Theorems for Non-Transitive Relations.

Abstract: In this paper, we develop an Isabelle/HOL library of order-theoretic fixed-point theorems. We keep our formalization as general as possible: we reprove several well-known results about complete orders, often with only antisymmetry or attractivity, a mild condition implied by either antisymmetry or transitivity. In particular, we generalize various theorems ensuring the existence of a quasi-fixed point of monotone maps over complete relations, and show that the set of (quasi-)fixed points is itself complete. This result generalizes and strengthens theorems of Knaster-Tarski, Bourbaki-Witt, Kleene, Markowsky, Pataraia, Mashburn, Bhatta-George, and Stouti-Maaden.