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Register a new userPermutable SOS (Symmetry Operational Similarity)
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Based on symmetry consideration, quasi-one-dimensional (1D) objects, relevant to numerous observables or phenomena, can be classified into eight different types. We provide various examples of each 1D type, and discuss their Symmetry Operational Similarity (SOS) relationships, which are often permutable. A number of recent experimental observations, including current-induced magnetization in polar or chiral conductors, non-linear Hall effect in polar conductors, spin-polarization of tunneling current to chiral conductors, and ferro-rotational domain imaging with linear gyration are discussed in terms of (permutable) SOS. In addition, based on (permutable) SOS, we predict a large number of new phenomena in low symmetry materials that can be experimentally verified in the future.
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Meta SOS is a software framework designed to integrate the results from the meta-theory of structural operational semantics (SOS). These results include deriving semantic properties of language constructs just by syntactically analyzing their rule-based definition, as well as automatically deriving sound and ground-complete axiomatizations for languages, when considering a notion of behavioural equivalence. This paper describes the Meta SOS framework by blending aspects from the meta-theory of SOS, details on their implementation in Maude, and running examples.
Force detectors rely on resonators to transduce forces into a readable signal. Usually these resonators operate in the linear regime and their signal appears amidst a competing background comprising thermal or quantum fluctuations as well as readout noise. Here, we demonstrate that a parametric symmetry breaking transduction leads to a novel and robust nonlinear force detection in the presence of noise. The force signal is encoded in the frequency at which the system jumps between two phase states which are inherently protected against phase noise. Consequently, the transduction effectively decouples from readout noise channels. For a controlled demonstration of the method, we experiment with a macroscopic doubly-clamped string. Our method provides a promising new paradigm for high-precision force detection.
The similarity renormalization group is used to transform a general Dirac Hamiltonian into diagonal form. The diagonal Dirac operator consists of the nonrelativistic term, the spin-orbit term, the dynamical term, and the relativistic modification of kinetic energy, which are very useful to explore the symmetries hidden in the Dirac Hamiltonian for any deformed system. As an example, the relativistic symmetries in an axially deformed nucleus are investigated by comparing the contributions of every term to the single particle energies and their correlations with the deformation. The result shows that the deformation considerably influences the spin-orbit interaction and dynamical effect, which play a critical role in the relativistic symmetries and its breaking.
As reflection symmetry or space-time inversion symmetry is preserved, with a non-contractible integral loop respecting the symmetry in the Brilliouin zone, Berry phase is quantized in proper basis. Topological nodal lines can be enclosed in the integral loop and $pi$-Berry phase topologically protects the nodal lines. In this work, we show that to have quantized Berry phase restricted by the symmetry in any crystal structure, we choose to use the cell-periodic convention and define the origin point in the real space at one of the reflection (inversion) centers. In addition, $pi$-Berry phase is not the sufficient condition leading to the presence of the stable surface states. Their presence crucially depends on the location of the termination and the crystal structure in the unit cell. By using these new conditions we further reexamine if stable surface states exist in the known topological nodal line materials stemming from reflection symmetry or space-time inversion symmetry.
In this paper, we present Vision Permutator, a conceptually simple and data efficient MLP-like architecture for visual recognition. By realizing the importance of the positional information carried by 2D feature representations, unlike recent MLP-like models that encode the spatial information along the flattened spatial dimensions, Vision Permutator separately encodes the feature representations along the height and width dimensions with linear projections. This allows Vision Permutator to capture long-range dependencies along one spatial direction and meanwhile preserve precise positional information along the other direction. The resulting position-sensitive outputs are then aggregated in a mutually complementing manner to form expressive representations of the objects of interest. We show that our Vision Permutators are formidable competitors to convolutional neural networks (CNNs) and vision transformers. Without the dependence on spatial convolutions or attention mechanisms, Vision Permutator achieves 81.5% top-1 accuracy on ImageNet without extra large-scale training data (e.g., ImageNet-22k) using only 25M learnable parameters, which is much better than most CNNs and vision transformers under the same model size constraint. When scaling up to 88M, it attains 83.2% top-1 accuracy. We hope this work could encourage research on rethinking the way of encoding spatial information and facilitate the development of MLP-like models. Code is available at https://github.com/Andrew-Qibin/VisionPermutator.
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