Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry

We introduce the notion of algebraic higher symmetry, which generalizes higher symmetry and is beyond higher group. We show that an algebraic higher symmetry in a bosonic system in $n$-dimensional space is characterized and classified by a local fusion $n$-category. We find another way to describe algebraic higher symmetry by restricting to symmetric sub Hilbert space where symmetry transformations all become trivial. In this case, algebraic higher symmetry can be fully characterized by a non-invertible gravitational anomaly (i.e. an topological order in one higher dimension). Thus we also refer to non-invertible gravitational anomaly as categorical symmetry to stress its connection to symmetry. This provides a holographic and entanglement view of symmetries. For a system with a categorical symmetry, its gapped state must spontaneously break part (not all) of the symmetry, and the state with the full symmetry must be gapless. Using such a holographic point of view, we obtain (1) the gauging of the algebraic higher symmetry; (2) the classification of anomalies for an algebraic higher symmetry; (3) the equivalence between classes of systems, with different (potentially anomalous) algebraic higher symmetries or different sets of low energy excitations, as long as they have the same categorical symmetry; (4) the classification of gapped liquid phases for bosonic/fermionic systems with a categorical symmetry, as gapped boundaries of a topological order in one higher dimension (that corresponds to the categorical symmetry). This classification includes symmetry protected trivial (SPT) orders and symmetry enriched topological (SET) orders with an algebraic higher symmetry.Comment: 61 pages, 31 figure

Scanning Kerr microscopy study of current induced switching in Ta/CoFeB/MgO films with perpendicular magnetic anisotropy

This is the author accepted manuscript. The final version is available from AIP Publishing via the DOI in this recordTa/CoFeB/MgO trilayers with perpendicular magnetic anisotropy are expected to play a key role in the next generation of current and electric field switched memory and logic devices. In this study, we combine scanning Kerr microscopy with electrical transport measurements to gain insight into the underlying mechanisms of current-induced switching within such devices.We find switching to be a stochastic, domain-wall-driven process, the speed of which is strongly dependent on the switching current. Kerr imaging shows domain nucleation at one edge of the device, which modeling reveals is likely assisted by the out-of-plane component of the Oersted field. Further domain growth, leading to magnetization reversal, may still be dominated by spin torques, but the Oersted field provides an additional mechanism with which to control the switching process.University of ExeterInstitute for Nanoelectronics Discovery and Exploration (INDEX)National Science Foundatio

Systematic study of proton radioactivity of spherical proton emitters within various versions of proximity potential formalisms

In this work we present a systematic study of the proton radioactivity half-lives of spherical proton emitters within the Coulomb and proximity potential model. We investigate 28 different versions of the proximity potential formalisms developed for the description of proton radioactivity, $\mathcal{\alpha}$ decay and heavy particle radioactivity. It is found that 21 of them are not suitable to deal with the proton radioactivity, because the classical turning points $r_{\text{in}}$ cannot be obtained due to the fact that the depth of the total interaction potential between the emitted proton and the daughter nucleus is above the proton radioactivity energy. Among the other 7 versions of the proximity potential formalisms, it is Guo2013 which gives the lowest rms deviation in the description of the experimental half-lives of the known spherical proton emitters. We use this proximity potential formalism to predict the proton radioactivity half-lives of 13 spherical proton emitters, whose proton radioactivity is energetically allowed or observed but not yet quantified, within a factor of 3.71.Comment: 10 pages, 5 figures. This paper has been accepted by The European Physical Journal A (in press 2019

Classification of topological phases with finite internal symmetries in all dimensions

We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approaches with an emphasis on the second approach. The first approach is to gauge the symmetry in the same dimension by adding topological excitations as it was done in the 2d case, in which the gauging process is mathematically described by the minimal modular extensions of unitary braided fusion 1-categories. This 2d result immediately generalizes to all dimensions except in 1d, which is treated with special care. The second approach is to use the 1-dimensional higher bulk of the SPT/SET order and the boundary-bulk relation. This approach also leads us to a precise mathematical description and a classification of SPT/SET orders in all dimensions. The equivalence of these two approaches, together with known physical results, provides us with many precise mathematical predictions.Comment: 41 pages, 6 figures; add more results on anomalies; final version to appear in JHE

Afforestation and Reforestation: Drivers, Dynamics, and Impacts

Afforestation/reforestation (or forestation) has been implemented worldwide as an effective measure towards sustainable ecosystem services and addresses global environmental problems such as climate change. The conversion of grasslands, croplands, shrublands, or bare lands to forests can dramatically alter forest water, energy, and carbon cycles and, thus, ecosystem services (e.g., carbon sequestration, soil erosion control, and water quality improvement). Large-scale afforestation/reforestation is typically driven by policies and, in turn, can also have substantial socioeconomic impacts. To enable success, forestation endeavors require novel approaches that involve a series of complex processes and interdisciplinary sciences. For example, exotic or fast-growing tree species are often used to improve soil conditions of degraded lands or maximize productivity, and it often takes a long time to understand and quantify the consequences of such practices at watershed or regional scales. Maintaining the sustainability of man-made forests is becoming increasingly challenging under a changing environment and disturbance regime changes such as wildland fires, urbanization, drought, air pollution, climate change, and socioeconomic change. Therefore, this Special Issue focuses on case studies of the drivers, dynamics, and impacts of afforestation/reforestation at regional, national, or global scales. These new studies provide an update on the scientific advances related to forestation. This information is urgently needed by land managers and policy makers to better manage forest resources in today’s rapidly changing environments