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We consider the universal behavior of half-BPS correlators in $\mathcal N=4$ super-Yang-Mills in the cusp limit where two consecutive separations $x_{12}^2,x_{23}^2$ become lightlike. Through the Lagrangian insertion procedure, the Sudakov double-logarithmic divergence of the $n$-point correlator is related to the $(n+1)$-point correlator where the inserted Lagrangian ``pinches'' to the soft-collinear region of the cusp. We formulate this constraint as a new {\it graphical rule} for the $f$-graphs of the four-point correlator, which turns out to be the most constraining rule known so far. By exploiting this single graphical rule, we bootstrap the planar integrand of the four-point correlator up to ten loops ($n=14$) and fix all 22024902 but one coefficient at eleven loops ($n=15$); the remaining coefficient is then fixed using the triangle rule. We comment on the breakdown of a ``Catalan conjecture" for the coefficients of the family of $f$-graphs known as ``anti-prisms" where the coefficient of the twelve-loop ($n=16$) anti-prism is found to be $-38$ (as opposed to $-42$ if the conjecture should hold) by a local analysis of the bootstrap equations. We also comment on the implication of our graphical rule for the non-planar contributions., Comment: 26 pages, 5 figures

The non-uniform current distribution arisen from either current crowding effect or hot spot effect provides a method to tailor the interaction between thermal gradient and electron transport in magnetically ordered systems. Here we apply the device structural engineering to realize an in-plane inhomogeneous temperature distribution within the conduction channel, and the resulting geometric anomalous Nernst effect (GANE) gives rise to a non-zero 2nd -harmonic resistance whose polarity corresponds to the out-of-plane magnetization of Co/Pt multi-layer thin film, and its amplitude is linearly proportional to the applied current. By optimizing the aspect ratio of convex-shaped device, the effective temperature gradient can reach up to 0.3 K/$\mu$m along the y-direction, leading to a GANE signal of 28.3 $\mu$V. Moreover, we demonstrate electrical write and read operations in the perpendicularly-magnetized Co/Pt-based spin-orbit torque device with a simple two-terminal structure. Our results unveil a new pathway to utilize thermoelectric effects for constructing high-density magnetic memories

The manipulation of Rashba-type spin-orbit coupling (SOC) in molecular beam epitaxy-grown Al$_x$In$_{1-x}$Sb/InSb/CdTe quantum well heterostructures is reported. The effective band bending provides robust two-dimensional quantum confinement, while the unidirectional built-in electric field from the asymmetric hetero-interfaces results in pronounced Rashba SOC strength. By tuning the Al concentration in the top Al$_x$In$_{1-x}$Sb barrier layer, the optimal structure with $x = 0.15$ shows the largest Rashba coefficient of 0.23 eV-Angstrom. and the highest low-temperature electron mobility of 4400 cm$^2$/Vs . Quantitative investigations of the weak anti-localization effect further confirm the dominant D'yakonov-Perel (DP) spin relaxation mechanism during charge-to-spin conversion. These findings highlight the significance of quantum well engineering in shaping magneto-resistance responses, and narrow bandgap semiconductor-based heterostructures may offer a reliable platform for energy-efficient spintronic applications.

The leading order $N$-point energy correlators of maximally supersymmetric Yang-Mills theory in the limit where the $N$ detectors are collinear can be expressed as an integral of the $1\to N$ splitting function, which is given by the $(N{+}3)$-point squared super-amplitudes at tree level. This provides yet another example that the integrand of certain physical observable -- $N$-point energy correlator -- is computed by the canonical form of a positive geometry -- the (tree-level) "squared amplituhedron". By extracting such squared amplitudes from the $f$-graph construction, we compute the integrand of energy correlators up to $N=11$ and reveal new structures to all $N$; we also show important properties of the integrand such as soft and multi-collinear limits. Finally, we take a first look at integrations by studying possible residues of the integrand: our analysis shows that while this gives prefactors in front of multiple polylogarithm functions of $N=3,4$, the first unknown case of $N=5$ already involves elliptic polylogarithmic functions with many distinct elliptic curves, and more complicated curves and higher-dimensional varieties appear for $N>5$., Comment: 10 pages, several figures and tables, and an ancillary file with squared amplitudes up to 12 points, and explicit EC integrands up to 7 points

Recently considerable efforts have been devoted to computing cosmological correlators and the corresponding wavefunction coefficients, as well as understanding their analytical structures. In this note, we revisit the computation of these ``cosmological amplitudes" associated with any tree or loop graph for conformal scalars with time-dependent interactions in the power-law FRW universe, directly in terms of iterated time integrals. We start by decomposing any such cosmological amplitude (for loop graph, the ``integrand" prior to loop integrations) as a linear combination of {\it basic time integrals}, one for each {\it directed graph}. We derive remarkably simple first-order differential equations involving such time integrals with edges ``contracted" one at a time, which can be solved recursively and the solution takes the form of Euler-Mellin integrals/generalized hypergeometric functions. By combining such equations, we then derive a complete system of differential equations for all time integrals needed for a given graph. Our method works for any graph: for a tree graph with $n$ nodes, this system can be transformed into the {\it canonical differential equations} of size $4^{n{-}1}$ quivalent to the graphic rules derived recently%so-called ``kinematic flow", and we also derive the system of differential equations for loop integrands {\it e.g.} of all-loop two-site graphs and one-loop $n$-gon graphs. Finally, we show how the differential equations truncate for the de Sitter (dS) case (in a way similar to differential equations for Feynman integrals truncate for integer dimensions), which immediately yields the complete symbol for the dS amplitude with interesting structures {\it e.g.} for $n$-site chains and $n$-gon cases., Comment: 43 pages; many figures

Electronic states play a crucial role in many quantum systems of moire superlattices, quasicrystals, and fractals. As recently reported in \textit{Sierpi\'{n}ski} lattices [Phys. Rev. B 107, 115424 (2023)], the critical states are revealed by the energy level-correlation spectra, which are caused by the interplay between aperiodicity and determined self-similarity characters. In the case of the \textit{Sierpi\'{n}ski Carpet}, our results further demonstrate that there is some degree of spatial overlap between these electronic states. These states could be strongly affected by its `seed lattice' of the $generator$, and slightly modulated by the dilation pattern and the geometrical self-similarity level. These electronic states are multifractal by scaling the $q$-order inverse participation ratio or fractal dimension, which correlates with the subdiffusion behavior. In the $gene$ pattern, the averaged state-based multifractal dimension of second-order would increase as its \textit{Hausdoff dimension} increases. Our findings could potentially contribute to understanding quantum transports and single-particle quantum dynamics in fractals., Comment: 10 pages, 6 figures. Accepted by Phys. Rev. B

We report the canonical properties of Bose-Einstein condensation of polaritons, seen previously in many low-temperature experiments, at room temperature in a GaAs/AlGaAs structure. These effects include a nonlinear energy shift of the polaritons, showing that they are not non-interacting photons, and dramatic line narrowing due to coherence, giving coherent emission with spectral width of 0.24 meV at room temperature with no external stabilization. This opens up the possibility of room temperature nonlinear optical devices based on polariton condensation.

We present a careful calibration of the exciton fraction of polaritons in high-$Q$ ($\sim 300,000$), long-lifetime ($\sim 300$ ps), GaAs/AlGaAs microcavities.This is a crucial parameter for many-body theories which include the polariton-polariton interactions.It is much harder to establish this number in high-$Q$ structures compared to low-$Q$ structures, because the upper polariton is nearly invisible in high-$Q$ cavities.We present a combination of photoluminescence, photoluminescence excitation, and reflectivity measurements to highly constrain the fit model, and compare the results of this model to the results from low-$Q$ structures.We present a fitted curve of exciton fraction as a function of the lower polariton energy for multiple samples which have been used in prior experiments., Comment: 16 pages, 11 figures

We construct Sierpinski-carpet (SC) based on AA or AB bilayer graphene by atom vacancies, namely, SC-AA and SC-AB, to investigate the effects of interlayer coupling on the electronic properties of fractals. Compared with monolayer graphene SC, their density of states have similar features, such as Van-Hove singularities and edge states corresponding to the central peaks near zero energy, but remarkable energy broadening of edge states emerges in SC-AA(AB). Calculated conductance spectrum shows that the conductance fluctuations still hold the Hausdorff fractal dimension behavior even with the interlayer coupling. Thus, the high correlation between quantum conductance and fractal geometry dimension is not affected by the interlayer coupling in bilayer graphene SC. We further reveal the quasi-eigenstates in fractal-like pressure-modulated bilayer graphene, namely, SC-pAA and SC-pAB. Numerical results show that the density of states of SC-pAA(pAB) show an asymptotic behavior to those of SC-AA(AB) especially for high energy quasi-eigenstates. Within a certain energy range, stronger pressure can lead to stronger localization, forming an efficient fractal space.

We introduce a novel approach for deriving one-loop Bern-Carrasco-Johansson (BCJ) numerators and reveal the worldsheet origin of the one-loop double copy. Our work shows that expanding Cachazo-He-Yuan half-integrands into generalized Parke-Taylor factors intrinsically generates BCJ numerators on quadratic propagators satisfying Jacobi identities. We validate our methodology by successfully reproducing one-loop BCJ numerators for Non-Linear Sigma Model as well as those of pure Yang-Mills theory in four dimensions with all-plus or single-minus helicities., Comment: 6+6 pages, three figures. v2: minimal cosmetic changes, matches the published version in PRD

Magnetoresistance effects are crucial for understanding the charge/spin transport as well as propelling the advancement of spintronic applications. Here we report the coexistence of magnetic moment-dependent (MD) and magnetic field-driven (FD) unidirectional magnetoresistance (UMR) effects in CoFeB/InSb/CdTe heterostructures. The strong spin-orbital coupling of InSb and the matched impedance at the CoFeB/InSb interface warrant a distinct MD-UMR effect at room temperature, while the interaction between the in-plane magnetic field and the Rashba effect at the InSb/CdTe interface induces the marked FD-UMR signal that dominates the high-field region. Moreover, owning to the different spin transport mechanisms, these two types of nonreciprocal charge transport show opposite polarities with respect to the magnetic field direction, which further enable an effective phase modulation of the angular-dependent magnetoresistance. Besides, the demonstrations of both the tunable UMR response and two-terminal spin-orbit torque-driven magnetization switching validate our CoFeB/InSb/CdTe system as a suitable integrated building block for multifunctional spintronic device design.

How to generate diverse, life-like, and unlimited long head/body sequences without any driving source? We argue that this under-investigated research problem is non-trivial at all, and has unique technical challenges behind it. Without semantic constraints from the driving sources, using the standard autoregressive model to generate infinitely long sequences would easily result in 1) out-of-distribution (OOD) issue due to the accumulated error, 2) insufficient diversity to produce natural and life-like motion sequences and 3) undesired periodic patterns along the time. To tackle the above challenges, we propose a systematic framework that marries the benefits of VQ-VAE and a novel token-level control policy trained with reinforcement learning using carefully designed reward functions. A high-level prior model can be easily injected on top to generate unlimited long and diverse sequences. Although we focus on no driving sources now, our framework can be generalized for controlled synthesis with explicit driving sources. Through comprehensive evaluations, we conclude that our proposed framework can address all the above-mentioned challenges and outperform other strong baselines very significantly.

We have created a spatially homogeneous polariton condensate in thermal equilibrium, up to very high condensate fraction. Under these conditions, we have measured the coherence as a function of momentum, and determined the total coherent fraction of this boson system from very low density up to density well above the condensation transition. These measurements reveal a consistent power law for the coherent fraction as a function of the total density over nearly three orders of its magnitude. The same power law is seen in numerical simulations solving the two-dimensional Gross-Pitaevskii equation for the equilibrium coherence. This power law has not been predicted by prior analytical theories.

We solve the geodesic equation in the space of K\"ahler metrics under the setting of asymptotically locally Euclidean (ALE) K\"ahler manifolds and we prove global $\mathcal{C}^{1,1}$ regularity of the solution. Then, we relate the solution of the geodesic equation to the uniqueness of scalar-flat ALE metrics. To this end, we study the asymptotic behavior of $\varepsilon$-geodesics at spatial infinity. Under the assumption that the Ricci curvature of a reference ALE K\"ahler metric is non-positive, convexity of the Mabuchi $K$-energy along $\varepsilon$-geodesics. However, we will also prove that on the line bundle $\mathcal{O}(-k)$ over $\mathbb{C}\mathbb{P}^{n-1}$ with $n \geq 2$ and $k \neq n$, no ALE K\"ahler metric can have non-positive (or non-negative) Ricci curvature., Comment: 27 pages. Just to update financial support information

We elaborate on aspects of a new positive geometry proposed recently, which was conjectured to be the four-point amplituhedron for ABJM theory. We study generalized unitarity cuts from the geometry, and in particular we prove that (1) the four-point integrand satisfies perturbative unitarity (or optical theorem) to all loops, which follows directly from the geometry, and (2) vanishing cuts involving odd-point amplitudes follow from the ``bipartite" nature of the associated ``negative geometries", which justifies their appearance in ABJM theory. We also take a first step in integrating the forms of these negative geometries and obtain an infrared-finite quantity up to two loops, from which we extract the cusp anomalous dimension at leading order., Comment: 21 pages, many figures,minor changes

The kagome-lattice crystal hosts various intriguing properties including the frustrated magnetism, charge order, topological state, superconductivity and correlated phenomena. To achieve high-performance kagome-lattice compounds for electronic and spintronic applications, careful tuning of the band structure would be desired. Here, the electronic structures of kagome-lattice crystal Ni3In2S2 were investigated by transport measurements, angle-resolved photoemission spectroscopy as well as ab initio calculations. The transport measurements reveal Ni3In2S2 as a compensated semimetal with record-high carrier mobility (~8683 cm2 V-1 S-1 and 7356 cm2 V-1 S-1 for holes and electrons) and extreme magnetoresistance (15518% at 2 K and 13 T) among kagome-lattice materials. These extraordinary properties are well explained by its band structure with indirect gap, small electron/hole pockets and large bandwidth of the 3d electrons of Ni on the kagome lattice. This work demonstrates that the crystal field and doping serve as the key tuning knobs to optimize the transport properties in kagome-lattice crystals. Our work provides material basis and optimization routes for kagome-lattice semimetals as electronics and spintronics applications.

In this communication, we study the level-spectra statistics when a noninteracting electron gas is confined in \textit{Sierpi\'{n}ski Carpet} (\textit{SC}) lattices. These \textit{SC} lattices are constructed under two representative patterns of the $self$ and $gene$ patterns, and classified into two subclass lattices by the area-perimeter scaling law. By the singularly continuous spectra and critical traits using two level-statistic tools\iffalse the nearest spacing distribution and alternative gap-ratio distribution\fi, we ascertain that both obey the critical phase due to broken translation symmetry and the long-range order of scaling symmetry. The Wigner-like conjecture is confirmed numerically since both belong to the Gaussian orthogonal ensemble. An analogy was observed in a quasiperiodic lattice~\cite{Zhong1998Level}. In addition, this critical phase isolates the crucial behavior near the metal-insulator transition edge in Anderson model. The lattice topology of the self-similarity feature can induce level clustering behavior., Comment: 11 pages, 6 figures, 2 Tables

Based on the covariant color-kinematics duality, we investigate combinatorial and algebraic structures underlying their Bern-Carrasco-Johansson (BCJ) numerators of tree-level amplitudes in Yang-Mills-scalar (YMS) theory. The closed-formulae for BCJ numerators of YMS amplitudes and the pure-Yang-Mills (YM) ones exhibit nice quasi-shuffle Hopf algebra structures, and interestingly they can be viewed as summing over boundaries of all dimensions of a combinatorial permutohedron. In particular, the numerator with two scalars and $n{-}2$ gluons contains Fubini number ( $F_{n{-}2}$ ) of terms in one-to-one correspondence with boundaries of a $(n{-}3)$-dimensional permutohedron, and each of them has its own spurious-pole structures and a gauge-invariant numerator (both depending on reference momenta). From such Hopf algebra or permutohedron structure, we derive new recursion relations for the numerators and intriguing "factorization" on each spurious pole/facet of the permutohedron. Similar results hold for general YMS numerators and the pure-YM ones. Finally, with a special choice of reference momenta, our results imply BCJ numerators in a heavy-mass effective field theory with two massive particles and $n{-}2$ gluons/gravitons: we observe highly nontrivial cancellations in the heavy-mass limit, leading to new formulae for the effective numerators which resemble those obtained in recent works., Comment: 8 pages+appendices, 16 figures

Current weakly supervised video anomaly detection algorithms mostly use multiple instance learning (MIL) or their varieties. Almost all recent approaches focus on how to select the correct snippets for training to improve the performance. They overlook or do not realize the power of video classification in boosting the performance of anomaly detection. In this paper, we study explicitly the power of video classification supervision using a BERT or LSTM. With this BERT or LSTM, CNN features of all snippets of a video can be aggregated into a single feature which can be used for video classification. This simple yet powerful video classification supervision, combined into the MIL framework, brings extraordinary performance improvement on all three major video anomaly detection datasets. Particularly it improves the mean average precision (mAP) on the XD-Violence from SOTA 78.84\% to new 82.10\%. The source code is available at https://github.com/wjtan99/BERT_Anomaly_Video_Classification., Comment: arXiv admin note: text overlap with arXiv:2101.10030 by other authors

Non-volatile memristors offer a salient platform for artificial neural network (ANN), but the integration of different function blocks into one hardware system remains challenging. Here we demonstrate the implementation of brain-like synaptic (SOT-S) and neuronal (SOT-N) functions in the Bi2Te3/CrTe2 heterostructure-based spin-orbit torque (SOT) device. The SOT-S unit exhibits highly linear (linearity error < 4.19%) and symmetrical long-term potentiation/depression process, resulting in better performance compared to other memristor synapses. Meanwhile, the Sigmoid-shape transition curve inherited in the SOT-N cell replaces the software-based activation function block, hence reducing the system complexity. On this basis, we employ a serial-connected, voltage-mode sensing ANN architecture to enhance the vector-matrix multiplication signal strength with low reading error of 0.61%. Furthermore, the trainable activation function of SOT-N enables the integrated SOT-ANN to execute the Batch Normalization algorithm and activation operation within one clock cycle, which bring about improved on/off-chip training performance close to the ideal baseline.

It is now routine to make Bose-Einstein condensates of polaritons with long enough lifetime and low enough disorder to travel ballistically for hundreds of microns in quasi-one-dimensional (1D) wires. We present observations of a polariton condensate injected at one point in a quasi-1D ring, with a well-defined initial velocity and direction. A clear precession of the circular polarization is seen, which arises from an effective spin-orbit coupling term in the Hamiltonian. Our theoretical model accurately predicts the experimentally observed behavior, and shows that "zitterbewegung" behavior plays a role in the motion of the polaritons., Comment: accepted by Phys. Rev. B

To harness the intriguing properties of two-dimensional van der Waals (vdW) ferromagnets (FMs) for versatile applications, the key challenge lies in the reliable material synthesis for scalable device production. Here, we demonstrate the epitaxial growth of single-crystalline 1T-CrTe2 thin films on 2-inch sapphire substrates. Benefiting from the uniform surface energy of the dangling bond-free Al2O3(0001) surface, the layer-by-layer vdW growth mode is observed right from the initial growth stage, which warrants precise control of the sample thickness and atomically smooth surface morphology across the entire wafer. Moreover, the presence of the Coulomb interaction at the CrTe2/Al2O3 interface serves as an effective tuning parameter to tailor the anomalous Hall response, and the structural optimization of the CrTe2-based spin-orbit torque device leads to a substantial switching power reduction by 54%. Our results may lay out a general framework for the design of energy-efficient spintronics based on configurable vdW FMs., Comment: 20 pages, 4 figures

We propose an automatic COVID1-19 diagnosis framework from lung CT-scan slice images using double BERT feature extraction. In the first BERT feature extraction, A 3D-CNN is first used to extract CNN internal feature maps. Instead of using the global average pooling, a late BERT temporal pooing is used to aggregate the temporal information in these feature maps, followed by a classification layer. This 3D-CNN-BERT classification network is first trained on sampled fixed number of slice images from every original CT scan volume. In the second stage, the 3D-CNN-BERT embedding features are extracted on all slice images of every CT scan volume, and these features are averaged into a fixed number of segments. Then another BERT network is used to aggregate these multiple features into a single feature followed by another classification layer. The classification results of both stages are combined to generate final outputs. On the validation dataset, we achieve macro F1 score of 0.9164., Comment: arXiv admin note: text overlap with arXiv:2106.14403

We prove an expansion theorem on scalar-flat asymptotically conical K\"ahler metrics. Consider an AC K\"ahler manifold with asymptotic to a Ricci-flat K\"ahler metric cone with complex dimension n. Assuming the weak decay conditions required for the mass to be well-defined, then each scalar-flat AC K\"ahler metric admits an expansion that the main term is given by the standard K\"ahler metric of the metric cone and the leading error term is of O(r^{2-2n}) with coefficient only depending on the ADM mass and its dimension. Besides, the mass formula by Hein-LeBrun also can be proved in our setting. As an application, a new version of the positive mass theorem will be discussed in the cases of the resolutions of the Ricci-flat K\"ahler cones., Comment: 28 pages

It is well known that forward limits of tree-level amplitudes (and those trivalent diagrams they consist of) produce one-loop amplitudes and trivalent diagrams with propagators linear in the loop momentum. They naturally arise from one-loop worldsheet formulae, and an important open problem is how to recombine them into usual one-loop diagrams with quadratic propagators. In this paper, we study a new collection of worldsheet functions: generalized one-loop Parke-Taylor factors with tensor numerators, which are conjectured to serve as a basis for one-loop worldsheet functions with this nice property. We present all-multiplicity, closed-form expressions for combinations of one-loop trivalent diagrams with quadratic propagators and tensor numerators to arbitrary rank (including possible tadpole contributions), produced by any pair of Parke-Taylor factors. We also briefly comment on reducing worldsheet functions onto such a basis, and applications to one-loop amplitudes in physical theories., Comment: 27+11 pages,2 figures; minor changes, clarifications added, published version

We define a new geometry obtained from the all-loop amplituhedron in ${\cal N}=4$ SYM by reducing its four-dimensional external and loop momenta to three dimensions. Focusing on the simplest four-point case, we provide strong evidence that the canonical form of this ``reduced amplituhedron" gives the all-loop integrand of the ABJM four-point amplitude. In addition to various all-loop cuts manifested by the geometry, we present explicitly new results for the integrand up to five loops, which are much simpler than results in ${\cal N}=4$ SYM. One of the reasons for such all-loop simplifications is that only a very small fraction of the so-called negative geometries survive the dimensional reduction, which corresponds to bipartite graphs. Our results suggest an unexpected relation between four-point amplitudes in these two theories., Comment: 5 pages + appendices, version accepted in PRL