scholarly journals Tri- and Tetrahyperbolic Isofrequency Topologies Complete Classification of Bianisotropic Materials

2020 ◽  
Vol 10 (3) ◽  
pp. 763 ◽  
Author(s):  
Maxim Durach ◽  
Robert Williamson ◽  
Morgan Laballe ◽  
Thomas Mulkey
Keyword(s):  
Phase Transitions ◽  
Optical Materials ◽  
Complete Classification ◽  
Topological Phases ◽  
Longitudinal Polarization ◽  
Polarization Impedance ◽  
High K ◽  
All Optical ◽  
Zero Group

We describe novel topological phases of isofrequency k-space surfaces in bianisotropic optical materials—tri- and tetrahyperbolic materials—which are induced by the introduction of chirality. This completes the classification of isofrequency topologies for bianisotropic materials, as we showed that all optical materials belong to one of the following topological classes—tetra-, tri-, bi-, mono-, or nonhyperbolic. We showed that phase transitions between these classes occur in the k-space directions with zero group velocity at high k-vectors. This classification is based on the sets of high-k polaritons (HKPs), supported by materials. We obtained the equation describing these sets and characterized the longitudinal polarization-impedance of HKPs.

Complete classification of second-order phase transitions in two-dimensional systems

1982 ◽  
Vol 44 (2) ◽  
pp. 163-165 ◽  
Author(s):  
L.A. Maksimov ◽  
I.Ya. Polishchuk ◽  
V.A. Somenkov
Keyword(s):  
Phase Transitions ◽  
Complete Classification ◽  
Second Order ◽  
Two Dimensional

scholarly journals Symmetry-enriched phases obtained via pseudo anyon condensation

2014 ◽  
Vol 28 (24) ◽  
pp. 1450172 ◽  
Author(s):  
Ling-Yan Hung ◽  
Yidun Wan
Keyword(s):  
Physical Properties ◽  
Complete Classification ◽  
Topological Phases ◽  
Topological Order ◽  
Edge States ◽  
Symmetric Phase ◽  
Internal Symmetries

We propose a framework to describe topological phases with global internal symmetries. This involves embedding the phase of interest into an intrinsic topological-order. Such an embedding is related to the physics of anyon condensation, although no physical condensation actually occurs here. Crucial physical properties of the symmetric phase, such as edge states and global charges of anyons are easily recovered from the embedding. The framework naturally reproduces all phases that are currently known in 2+1 d, and potentially provides a complete classification of symmetric topological phases in 2+1 d. We illustrate our idea with simple examples.

A complete classification of stable symmetries of the Jahn-Teller systems

1990 ◽  
Vol 55 (9) ◽  
pp. 2119-2130 ◽  
Author(s):  
Martin Breza
Keyword(s):  
Phase Transitions ◽  
Electronic States ◽  
Complete Classification ◽  
Symmetry Groups ◽  
Jahn Teller

The classification of stable symmetries of the Jahn-Teller systems for common symmetry groups with degenerate relativistic and non-relativistic electronic states is elaborated. The results obtained by epikernel principle and by the method of step-by-step symmetry descent are compared. The deficiency of the epikernel principle is demonstrated on some examples of the Jahn-Teller phase transitions.

scholarly journals Multiplicative automatic sequences

2021 ◽  
Author(s):  
Jakub Konieczny ◽  
Mariusz Lemańczyk ◽  
Clemens Müllner
Keyword(s):  
Complete Classification ◽  
Automatic Sequences ◽  
Complex Valued

AbstractWe obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

scholarly journals Characteristic cohomology and observables in higher spin gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alexey Sharapov ◽  
Evgeny Skvortsov
Keyword(s):  
Higher Spin Gravity ◽  
Complete Classification ◽  
Gravity Models ◽  
Simons Theory ◽  
Surface Charges ◽  
Higher Spin ◽  
Dynamical Invariants ◽  
Chern Simons ◽  
Conserved Currents

Abstract We give a complete classification of dynamical invariants in 3d and 4d Higher Spin Gravity models, with some comments on arbitrary d. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved p-form currents with various p. The last fact, being in tension with ‘no nontrivial conserved currents in quantum gravity’ and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley-Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

scholarly journals Nil-clean quadratic elements

2017 ◽  
Vol 16 (10) ◽  
pp. 1750197 ◽  
Author(s):  
Janez Šter
Keyword(s):  
Complete Classification ◽  
Strong Condition ◽  
Clean Rings

We provide a strong condition holding for nil-clean quadratic elements in any ring. In particular, our result implies that every nil-clean involution in a ring is unipotent. As a consequence, we give a complete classification of weakly nil-clean rings introduced recently in [Breaz, Danchev and Zhou, Rings in which every element is either a sum or a difference of a nilpotent and an idempotent, J. Algebra Appl. 15 (2016) 1650148, doi: 10.1142/S0219498816501486].

Ricci inheritance collineations in Bianchi type II spacetime

2016 ◽  
Vol 31 (17) ◽  
pp. 1650102 ◽  
Author(s):  
Tahir Hussain ◽  
Sumaira Saleem Akhtar ◽  
Ashfaque H. Bokhari ◽  
Suhail Khan
Keyword(s):  
Lie Algebra ◽  
Ricci Tensor ◽  
Bianchi Type ◽  
Complete Classification ◽  
Type Ii

In this paper, we present a complete classification of Bianchi type II spacetime according to Ricci inheritance collineations (RICs). The RICs are classified considering cases when the Ricci tensor is both degenerate as well as non-degenerate. In case of non-degenerate Ricci tensor, it is found that Bianchi type II spacetime admits 4-, 5-, 6- or 7-dimensional Lie algebra of RICs. In the case when the Ricci tensor is degenerate, majority cases give rise to infinitely many RICs, while remaining cases admit finite RICs given by 4, 5 or 6.

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