Arbitrary Order Research Articles

Preservation of Topological Surface States in Millimeter-Scale Transferred Membranes.

Ultrathin topological insulator membranes are building blocks of exotic quantum matter. However, traditional epitaxy of these materials does not facilitate stacking in arbitrary orders, while mechanical exfoliation from bulk crystals is also challenging due to the non-negligible interlayer coupling therein. Here we liberate millimeter-scale films of the topological insulator Bi2Se3, grown by molecular beam epitaxy, down to 3 quintuple layers. We characterize the preservation of the topological surface states and quantum well states in transferred Bi2Se3 films using angle-resolved photoemission spectroscopy. Leveraging the photon-energy-dependent surface sensitivity, the photoemission spectra taken with 6 and 21.2 eV photons reveal a transfer-induced migration of the topological surface states from the top to the inner layers. By establishing clear electronic structures of the transferred films and unveiling the wave function relocation of the topological surface states, our work lays the physics foundation crucial for the future fabrication of artificially stacked topological materials with single-layer precision.

Semi-Riemannian manifolds with linear differential conditions on the curvature

Semi-Riemannian manifolds that satisfy (homogeneous) linear differential conditions of arbitrary order r on the curvature are analyzed. They include, in particular, the spaces with (rth-order) recurrent curvature, (rth-order) symmetric spaces, as well as entire new families of semi-Riemannian manifolds rarely, or never, considered before in the literature—such as the spaces whose derivative of the Riemann tensor field is recurrent, among many others. Definite proof that all types of such spaces do exist is provided by exhibiting explicit examples of all possibilities in all signatures, except in the Riemannian case with a positive definite metric. Several techniques of independent interest are collected and presented. Of special relevance is the case of Lorentzian manifolds, due to its connection to the physics of the gravitational field. This connection is discussed with particular emphasis on Gauss–Bonnet gravity and in relation with Penrose limits. Many new lines of research open up and a handful of conjectures, based on the results found hitherto, is put forward.

Nonlinear Stability of Equilibria in Hamiltonian Systems with Multiple Resonances without Interactions

In this work, we advance in the study of the Lyapunov stability and instability of equilibrium solutions of Hamiltonian flows. More precisely, we study the nonlinear stability in the Lyapunov sense of equilibrium solutions in autonomous Hamiltonian systems with n-degrees of freedom, assuming the existence of two resonance vectors k1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{k}^1$$\\end{document} and k2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{k}^2$$\\end{document} without interaction (|k1|≤|k2|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\ extbf{k}^1|\\le |\ extbf{k}^2|$$\\end{document}). We provide conditions to obtain a type of formal stability, called Lie stability. In particular, we need to normalize the Hamiltonian function to any arbitrary order, and our results take into account the sign of the components of the resonance vectors. Subsequently, we guarantee some sufficient conditions to obtain exponential stability in the sense of Nekhoroshev for Lie stable systems. In addition, we give sufficient conditions for the instability in the Lyapunov sense of the full system. For this, it is necessary to normalize the Hamiltonian function to an adequate order, and assuming that the components of at least one resonance vector change of sign.

The classical double copy in curved spacetimes: perturbative Yang-Mills from the bi-adjoint scalar

We formulate a version of the double copy for classical fields in curved spacetimes. We provide a correspondence between perturbative solutions to the bi-adjoint scalar equations and those of the Yang-Mills equations in position space. At the linear level, we show that there exists a map between these solutions for maximally symmetric spacetime backgrounds, that provides every Yang-Mills solution by the action of an appropriate differential operator on a bi-adjoint scalar solution. Given the existence of a linearized map, we show that it is possible to cast the solutions of the Yang-Mills equations at arbitrary perturbation order in terms of the corresponding bi-adjoint scalar solutions. This all-order map is reminiscent of the flat space BCJ double copy, and works for any curved spacetime where the perturbative expansion holds. We show that these results have the right flat space limit, and that the correspondence is agnostic to the choice of gauge.

Permutation-adapted complete and independent basis for atomic cluster expansion descriptors

Atomic cluster expansion (ACE) methods provide a systematic way to describe particle local environments of arbitrary body order. For practical applications it is often required that the basis of cluster functions be symmetrized with respect to rotations and permutations. Existing methodologies yield sets of symmetrized functions that are over-complete. These methodologies thus require an additional numerical procedure, such as singular value decomposition (SVD), to eliminate redundant functions. In this work, it is shown that analytical linear relationships for subsets of cluster functions may be derived using recursion and permutation properties of generalized Wigner symbols. From these relationships, subsets (blocks) of cluster functions can be selected such that, within each block, functions are guaranteed to be linearly independent. It is conjectured that this block-wise independent set of permutation-adapted rotation and permutation invariant (PA-RPI) functions forms a complete, independent basis for ACE. Along with the first analytical proofs of block-wise linear dependence of ACE cluster functions and other theoretical arguments, numerical results are offered to demonstrate this. The utility of the method is demonstrated in the development of an ACE interatomic potential for tantalum. Using the new basis functions in combination with Bayesian compressive sensing sparse regression, some high degree descriptors are observed to persist and help achieve high-accuracy models.

Computing eigenfrequency sensitivities near exceptional points

Exceptional points are spectral degeneracies of non-Hermitian systems where both eigenfrequencies and eigenmodes coalesce. The eigenfrequency sensitivities near an exceptional point are significantly enhanced, whereby they diverge directly at the exceptional point. Capturing this enhanced sensitivity is crucial for the investigation and optimization of exceptional-point-based applications, such as optical sensors. We present a numerical framework based on contour integration and algorithmic differentiation to accurately and efficiently compute eigenfrequency sensitivities near exceptional points. We demonstrate the framework for an optical microdisk cavity and derive a semianalytical solution to validate the numerical results. The computed eigenfrequency sensitivities are used to track the exceptional point along an exceptional surface in the parameter space. The presented framework can be applied to any kind of resonance problem, e.g., with arbitrary geometry or with exceptional points of arbitrary order. Published by the American Physical Society 2024

Asymptotic analysis of the nonsteady micropolar fluid flow through a system of thin pipes

In this paper, we analyze the time‐dependent flow of an incompressible micropolar fluid in a multiple‐pipe system. Motivated by the applications, we assume that the pipes have circular cross‐section and that the ratio between pipes' thickness and its length is small, denoted by the parameter . Far from the junction, the fluid exhibits different behavior depending on the magnitude of the viscosity coefficients with respect to the small parameter . Focusing on the critical case described by the strong coupling between velocity and microrotation, the complete asymptotic expansion of the solution (up to an arbitrary order) is built. To improve the accuracy of the asymptotic approximation, we introduce the boundary layer correctors near the pipes' ends and take into account the interior layer correction in the vicinity of the junction as well. The convergence is also proved via error estimates, providing the rigorous justification of the proposed effective model.

A geometric framework for interstellar discourse on fundamental physical structures

This paper considers the possibility that abstract thinking and advanced synthesis skills might encourage extraterrestrial civilizations to accept communication with mankind on Earth. For this purpose, a notation not relying upon the use of alphabet and numbers is proposed, in order to denote just some basic geometric structures of current physical theories: vector fields, [Formula: see text]-form fields, and tensor fields of arbitrary order. An advanced civilization might appreciate the way here proposed to achieve a concise description of electromagnetism and general relativity, and hence it might accept the challenge of responding to our signals. The abstract symbols introduced in this paper to describe the basic structures of physical theories are encoded into black and white bitmap images that can be easily converted into short bit sequences and modulated on a carrier wave for radio transmission.

The updates in Libcint 6: More integrals, API refinements, and SIMD optimization techniques.

Libcint is a library designed for the evaluation of analytical integrals for Gaussian type orbitals. It prioritizes simplicity, ease of use, and efficiency for the development of quantum chemistry programs. In the release of version 6.0, Libcint supports the computation of integrals for various operators, such as overlap, Coulomb, Gaunt, Breit, attenuated Coulomb, Slater-type geminals, and Yukawa potential, as well as arbitrary orders of derivatives for these operators. To enhance the usability of the library, Libcint provides a uniform function signature for all integral functions. A code generator is included to automate the implementation of new integrals. To achieve better performance on modern central processing unit architectures, the library employs explicit single instruction multiple data parallelization in the code implementation.

Amplification of the anomalous scaling in the Kazantsev-Kraichnan model with finite-time correlations and spatial parity violation.

By using the field theoretic renormalization group technique together with the operator product expansion, simultaneous influence of the spatial parity violation and finite-time correlations of an electrically conductive turbulent environment on the inertial-range scaling behavior of correlation functions of a passively advected weak magnetic field is investigated within the corresponding generalized Kazantsev-Kraichnan model in the second order of the perturbation theory (in the two-loop approximation). The explicit dependence of the anomalous dimensions of the leading composite operators on the fixed point value of the parameter that controls the presence of finite-time correlations of the turbulent field as well as on the parameter that drives the amount of the spatial parity violation (helicity) in the system is found even in the case with the presence of the large-scale anisotropy. In accordance with the Kolmogorov's local isotropy restoration hypothesis, it is shown that, regardless of the amount of the spatial parity violation, the scaling properties of the model are always driven by the anomalous dimensions of the composite operators near the isotropic shell. The asymptotic (inertial-range) scaling form of all single-time two-point correlation functions of arbitrary order of the passively advected magnetic field is found. The explicit dependence of the corresponding scaling exponents on the helicity parameter as well as on the parameter that controls the finite-time velocity correlations is determined. It is shown that, regardless of the amount of the finite-time correlations of the given Gaussian turbulent environment, the presence of the spatial parity violation always leads to more negative values of the scaling exponents, i.e., to the more pronounced anomalous scaling of the magnetic correlation functions. At the same time, it is shown that the stronger the violation of spatial parity, the larger the anomalous behavior of magnetic correlations.

KFVM-WENO: A High-order Accurate Kernel-based Finite Volume Method for Compressible Hydrodynamics

This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Nonoscillatory reconstruction is achieved through an adaptive-order weighted essentially nonoscillatory (WENO) method cast into a form suited to multidimensional reconstruction. A kernel-based approach inspired by radial basis functions and Gaussian process modeling, which we call kernel-based finite volume method with WENO, is presented here. This approach allows the creation of a scheme of arbitrary order of accuracy with simply defined multidimensional stencils and substencils. Furthermore, the fully multidimensional nature of the reconstruction allows for a more straightforward extension to higher spatial dimensions and removes the need for complicated boundary conditions on intermediate quantities in modified dimension-by-dimension methods. In addition, a new simple yet effective set of reconstruction variables is introduced, which could be useful in existing schemes with little modification. The proposed scheme is applied to a suite of stringent and informative benchmark problems to demonstrate its efficacy and utility. A highly parallel multi-GPU implementation using Kokkos and the message-passing interface is also provided.

Realization of a Programmable Multipurpose Photonic Quantum Memory with Over-Thousand Qubit Manipulations

Quantum networks can enable various applications such as distributed quantum computing, long-distance quantum communication, and network-based quantum sensing with unprecedented performances. One of the most important building blocks for a quantum network is a photonic quantum memory which serves as the interface between the communication channel and the local functional unit. A programmable quantum memory which can process a large stream of flying qubits and fulfill the requirements of multiple core functions in a quantum network is still to be realized. Here we report a high-performance quantum memory which can simultaneously store 72 optical qubits carried by 144 spatially separated atomic ensembles and support up to a thousand consecutive write or read operations in a random access way, 2 orders of magnitude larger than the previous record. Because of the built-in programmability, this quantum memory can be adapted on demand for several functions. As example applications, we realize quantum queue, stack, and buffer which closely resemble the counterpart devices for classical information processing. We further demonstrate the storage and reshuffle of four entangled pairs of photonic pulses with probabilistic arrival time and arbitrary release order via the memory, which is an essential requirement for the realization of quantum repeaters and efficient routing in quantum networks. Realization of this multipurpose programmable quantum memory thus constitutes a key enabling building block for future large-scale fully functional quantum networks. Published by the American Physical Society 2024

Numerical analysis of multi-dimensional Navier–Stokes equation based on Yang–Abdel–Cattani fractional operator

The Navier–Stokes equation is a key governing equation for the motion of viscous fluid flow. The main target of our work is to obtain the solution to multi-dimensional Navier–Stokes equations in the Yang–Abdel–Cattani fractional sense. The results of the model are in terms of the three-parameter Prabhakar function. Three examples are discussed that depend on the recommended method for a novel Yang–Abdel–Cattani arbitrary order operator. The obtained results are plotted with the help of MATLAB R2016a mathematical software.

Ladder broadband damping filters

RELEVANCE. The large proliferation of various nonlinear loads has led to serious power-quality related problems in power systems. THE PURPOSE. In this paper, we consider design procedure of broadband passive filters with flat frequency characteristics. METHODS. A general method for optimally design the arbitrary order broadband passive filters (BBF) is considered. The base structure of BBF has the form of resistively loaded reactive two-port. Conditions of low fundamental frequency loss and required filer selectivity have been determined. The BBF design procedure minimizes the grid total current distortion and takes into account the power system performance. RESULTS. New broadband passive filter scheme are proposed. Compensating performances of different BBF configurations are discussed. Case studies demonstrated that proposed scheme can filter characteristic and damp non-characteristic harmonic simultaneously. CONCLUSION. The results show that proposed broadband damping filters are the effective instrument for the power quality normalization in industrial power systems.

Interplays between variations of arbitrarily partitionable graphs under minimality constraints

An arbitrarily partitionable (AP) graph is a graph that can be partitioned into arbitrarily many connected graphs with arbitrary orders. Since independent seminal works by Barth, Baudon, and Puech, and Horňák and Woźniak, AP graphs have been receiving increasing attention in the literature, dedicated to understanding several of their aspects, including structural aspects, algorithmic aspects, and their connections with Hamiltonian graphs. Other aspects of interest cover variants of AP graphs, such as AP graphs that can be partitioned in an online way (OLAP graphs), AP graphs that can be partitioned in a recursive way (RAP graphs), and AP graphs that are edge-minimal (minAP graphs).In the current work, we initiate the study of the latter notion of minimality for OLAP and RAP graphs. That is, we wonder about OLAP and RAP graphs that are not spanned by any strictly smaller OLAP or RAP graph, respectively, leading to the notions of minOLAP and minRAP graphs. We prove that such non-trivial graphs exist, and explore connections between minAPness, minOLAPness, and minRAPness. In particular, we prove that some fundamental connections between APness, OLAPness, and RAPness do not generalise to their minimal counterparts. We also investigate small minOLAP and minRAP graphs, as well as sufficient conditions guaranteeing an OLAP or RAP graph is not minimal, thereby generalising known results on AP graphs. This work also includes many open questions and problems for further work on the topic, that are disseminated throughout.

Dual-polarization MZM-based photonic nonlinear analog self-interference cancellation for in-band full-duplex radios

In this paper, we propose a dual-polarization Mach-Zehnder modulator-based photonic nonlinear analog self-interference cancellation (SIC) technique for in-band full duplex (IBFD) systems. By using the proposed technique, an arbitrary 4th order nonlinear transfer function can be generated, meaning the performance limitation caused by the nonlinearity of the analog SIC circuit can be overcome by imitating the nonlinear transfer function of the analog SIC circuit before cancellation. This paper also presents a performance analysis through simulations and the results of a proof-of-concept demonstration. In the experiment, the proposed nonlinear SIC technique could achieve 29 dB cancellation over 500 MHz bandwidth centered at 1.25 GHz frequency along various degree of distortion caused by nonlinearity. In addition, the performance enhancements achieved by the proposed technique are evaluated in terms of error vector magnitudes (EVMs) and constellations of the signal-of-interest (SOI) in the simulation which is based on the experimental SIC results. More than 3 dB of SOI power gain could be obtained in evaluated EVM performances.

Flexible Ansatz for N-Body Perturbation Theory.

We propose a new perturbation theory framework that can be used to help with the projective solution of the Schrödinger equation for arbitrary wave functions. This Flexible Ansatz for N-body Perturbation Theory (FANPT) is based on our previously proposed Flexible Ansatz for the N-body Configuration Interaction (FANCI). We derive recursive FANPT expressions, including arbitrary orders in the perturbation hierarchy. We show that the FANPT equations are well-behaved across a wide range of conditions, including static correlation-dominated configurations and highly nonlinear wave functions.

Switchable hybrid-order optical vortex lattice.

Optical vortex (OV) modulation is a powerful technique for enhancing the intrinsic degrees-of-freedom in structured light applications. Particularly, the lattices involving multiple OVs have garnered significant academic interest owing to their wide applicability in optical tweezers and condensed matter physics. However, all OVs in a lattice possess the same order, which cannot be modulated individually, limiting its versatile application. Herein, we propose, to our knowledge, a novel concept, called the hot-swap method, to design a switchable hybrid-order OV lattice, in which each OV is easily replaced by arbitrary orders. We experimentally generated the switchable hybrid-order OV lattice and studied its characteristics, including interferograms, retrieved phase, energy flow, and orbital angular momentum. Furthermore, the significant advantages of the switchable hybrid-order OV lattice are demonstrated through the independent manipulation of multiple yeast cells. This study provides a novel scheme for accurate control and modulation of OV lattices, which greatly facilitates the diverse applications of optical manipulation and particle trapping and control.

Linear vector recursions of arbitrary order

Linear vector recursions of arbitrary order

Ferrers Functions of Arbitrary Degree and Order and Related Functions

Ferrers Functions of Arbitrary Degree and Order and Related Functions