scholarly journals Dynamical symmetry indicators for Floquet crystals

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Jiabin Yu ◽  
Rui-Xing Zhang ◽  
Zhi-Da Song
Keyword(s):  
General Theory ◽  
Topological Insulator ◽  
Mathematical Theory ◽  
High Efficiency ◽  
Dynamical Symmetry ◽  
Symmetry Groups ◽  
Topological Phases ◽  
Computationally Efficient ◽  
First Order ◽  
Crystalline Symmetry

AbstractVarious exotic topological phases of Floquet systems have been shown to arise from crystalline symmetries. Yet, a general theory for Floquet topology that is applicable to all crystalline symmetry groups is still in need. In this work, we propose such a theory for (effectively) non-interacting Floquet crystals. We first introduce quotient winding data to classify the dynamics of the Floquet crystals with equivalent symmetry data, and then construct dynamical symmetry indicators (DSIs) to sufficiently indicate the inherently dynamical Floquet crystals. The DSI and quotient winding data, as well as the symmetry data, are all computationally efficient since they only involve a small number of Bloch momenta. We demonstrate the high efficiency by computing all elementary DSI sets for all spinless and spinful plane groups using the mathematical theory of monoid, and find a large number of different nontrivial classifications, which contain both first-order and higher-order 2+1D anomalous Floquet topological phases. Using the framework, we further find a new 3+1D anomalous Floquet second-order topological insulator (AFSOTI) phase with anomalous chiral hinge modes.

A N. Bourbaki Type General Theory and the Properties of Contracting Symbols and Corresponding Contracted Forms

1999 ◽  
Vol 6 (2) ◽  
pp. 179-190
Author(s):  
SH. Pkhakadze
Keyword(s):  
General Theory ◽  
Mathematical Theory ◽  
General Mathematical Theory

Abstract A system of contracting symbols is introduced for a N. Bourbaki type general mathematical theory corresponding to a general classical mathematical theory .

scholarly journals Tunable dynamical magnetoelectric effect in antiferromagnetic topological insulator MnBi2Te4 films

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Tongshuai Zhu ◽  
Huaiqiang Wang ◽  
Haijun Zhang ◽  
Dingyu Xing
Keyword(s):  
Topological Insulator ◽  
Condensed Matter ◽  
Simons Theory ◽  
Spin Wave Excitations ◽  
Axion Field ◽  
Chern Simons ◽  
Related Compounds ◽  
The Universe ◽  
Crystalline Symmetry ◽  
Chern Simons Theory

AbstractAxion was postulated as an elementary particle to solve the strong charge conjugation and parity puzzle, and later axion was also considered to be a possible component of dark matter in the universe. However, the existence of axions in nature has not been confirmed. Interestingly, axions arise out of pseudoscalar fields derived from the Chern–Simons theory in condensed matter physics. In antiferromagnetic insulators, the axion field can become dynamical due to spin-wave excitations and exhibits rich exotic phenomena, such as axion polariton. However, antiferromagnetic dynamical axion insulator has yet been experimentally identified in realistic materials. Very recently, MnBi2Te4 was discovered to be an antiferromagnetic topological insulator with a quantized static axion field protected by inversion symmetry $${\mathcal{P}}$$ P and magnetic-crystalline symmetry $${\mathcal{S}}$$ S . Here, we studied MnBi2Te4 films in which both the $${\mathcal{P}}$$ P and $${\mathcal{S}}$$ S symmetries are spontaneously broken and found that substantially enhanced dynamical magnetoelectric effects could be realized through tuning the thickness of MnBi2Te4 films, temperature, or element substitutions. Our results show that thin films of MnBi2Te4 and related compounds could provide a promising material platform to experimentally study axion electrodynamics.

Representation of symmetric probability models

1969 ◽  
Vol 34 (2) ◽  
pp. 183-193 ◽  
Author(s):  
Peter H. Krauss
Keyword(s):  
Mathematical Theory ◽  
Preceding Paper ◽  
Probability Logic ◽  
Probability Models ◽  
Additional Material ◽  
First Order ◽  
Order Probability ◽  
Joint Publication

This paper is a sequel to the joint publication of Scott and Krauss [8] in which the first aspects of a mathematical theory are developed which might be called “First Order Probability Logic”. No attempt will be made to present this additional material in a self-contained form. We will use the same notation and terminology as introduced and explained in Scott and Krauss [8], and we will frequently refer to the theorems stated and proved in the preceding paper.

Geometric, Spatial Path Tracking Using Non-Redundant Manipulators via Speed-Ratio Control

2010 ◽  
Author(s):  
Satyajit Ambike ◽  
James P. Schmiedeler ◽  
Michael M. Stanisˇic´
Keyword(s):  
Path Tracking ◽  
Speed Ratio ◽  
Redundant Manipulators ◽  
Computationally Efficient ◽  
Third Order ◽  
Practical Advantage ◽  
First Order ◽  
Canonical Frame ◽  
Special Cases ◽  
Six Degree Of Freedom

Path tracking can be accomplished by separating the control of the desired trajectory geometry and the control of the path variable. Existing methods accomplish tracking of up to third-order geometric properties of planar paths and up to second-order properties of spatial paths using non-redundant manipulators, but only in special cases. This paper presents a novel methodology that enables the geometric tracking of a desired planar or spatial path to any order with any non-redundant regional manipulator. The governing first-order coordination equation for a spatial path-tracking problem is developed, the repeated differentiation of which generates the coordination equation of the desired order. In contrast to previous work, the equations are developed in a fixed global frame rather than a configuration-dependent canonical frame, providing a significant practical advantage. The equations are shown to be linear, and therefore, computationally efficient. As an example, the results are applied to a spatial 3-revolute mechanism that tracks a spatial path. Spatial, rigid-body guidance is achieved by applying the technique to three points on the end-effector of a six degree-of-freedom robot. A spatial 6-revolute robot is used as an illustration.

scholarly journals General Theory of Lee-Yang Zeros in Models with First-Order Phase Transitions

2000 ◽  
Vol 84 (21) ◽  
pp. 4794-4797 ◽  
Author(s):  
M. Biskup ◽  
C. Borgs ◽  
J. T. Chayes ◽  
L. J. Kleinwaks ◽  
R. Kotecký
Keyword(s):  
Phase Transitions ◽  
General Theory ◽  
First Order ◽  
First Order Phase

Elastic phononic plates with first-order and second-order topological phases

2020 ◽  
Vol 53 (11) ◽  
pp. 115303
Author(s):  
Liang Tong ◽  
Haiyan Fan ◽  
Baizhan Xia
Keyword(s):  
Second Order ◽  
Topological Phases ◽  
First Order

scholarly journals Learned Video Compression via Joint Spatial-Temporal Correlation Exploration

2020 ◽  
Vol 34 (07) ◽  
pp. 11580-11587
Author(s):  
Haojie Liu ◽  
Han Shen ◽  
Lichao Huang ◽  
Ming Lu ◽  
Tong Chen ◽  
...  
Keyword(s):  
Video Coding ◽  
Video Compression ◽  
High Efficiency ◽  
Temporal Correlation ◽  
Second Order ◽  
Compression Method ◽  
High Efficiency Video Coding ◽  
First Order ◽  
Coding Efficiency ◽  
The Common

Traditional video compression technologies have been developed over decades in pursuit of higher coding efficiency. Efficient temporal information representation plays a key role in video coding. Thus, in this paper, we propose to exploit the temporal correlation using both first-order optical flow and second-order flow prediction. We suggest an one-stage learning approach to encapsulate flow as quantized features from consecutive frames which is then entropy coded with adaptive contexts conditioned on joint spatial-temporal priors to exploit second-order correlations. Joint priors are embedded in autoregressive spatial neighbors, co-located hyper elements and temporal neighbors using ConvLSTM recurrently. We evaluate our approach for the low-delay scenario with High-Efficiency Video Coding (H.265/HEVC), H.264/AVC and another learned video compression method, following the common test settings. Our work offers the state-of-the-art performance, with consistent gains across all popular test sequences.

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