Translational Symmetry Research Articles

A Resonant Lyapunov Centre Theorem with an Application to Doubly Periodic Travelling Hydroelastic Waves

We present a Lyapunov centre theorem for an antisymplectically reversible Hamiltonian system exhibiting a nondegenerate 1 : 1 or 1:-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1:-1$$\\end{document} semisimple resonance as a detuning parameter is varied. The system can be finite- or infinite-dimensional (and quasilinear) and have a non-constant symplectic structure. We allow the origin to be a ‘trivial’ eigenvalue arising from a translational symmetry or, in an infinite-dimensional setting, to lie in the continuous spectrum of the linearised Hamiltonian vector field provided a compatibility condition on its range is satisfied. As an application, we show how Kirchgässner’s spatial dynamics approach can be used to construct doubly periodic travelling waves on the surface of a three-dimensional body of water (of finite or infinite depth) beneath a thin ice sheet (‘hydroelastic waves’). The hydrodynamic problem is formulated as a reversible Hamiltonian system in which an arbitrary horizontal spatial direction is the time-like variable, and the infinite-dimensional phase space consists of wave profiles which are periodic (with fixed period) in a second, different horizontal direction. Applying our Lyapunov centre theorem at a point in parameter space associated with a 1 : 1 or 1:-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1:-1$$\\end{document} semisimple resonance yields a periodic solution of the spatial Hamiltonian system corresponding to a doubly periodic hydroelastic wave.

Nonsymmetrical thermal conductivity along the director field in ferroelectric nematic liquid crystals.

The synthesis of ferroelectric nematic liquid crystals (FNLCs) concludes the long wait for their existence and potential usage in multiple liquid crystal based applications. In FNLCs, electric polarization in the nematic phase significantly decreases the switching time of in-on display pixels. In this article, we report the occurrence of translation symmetry breaking for heat propagation along the director field n[over ̂] in the ferroelectric nematic phase. Due to the C_{∞V} symmetry of such a phase and close similarity to the bent-core polar liquid crystal phase, a rank-3 tensor describes its scalar order parameter and algebraic deductions. The finite element simulations show the occurrence of the nonsymmetrical thermal conductivity along n[over ̂]. The preferential heat transport in FNLCs can allow them to work as an all-thermal monophase non-nanostructured single-material thermal rectifier. We expect that this study will contribute towards the FNLCs application as functional layers and inks.

Graph neural network coarse-grain force field for the molecular crystal RDX

Condense phase molecular systems organize in wide range of distinct molecular configurations, including amorphous melt and glass as well as crystals often exhibiting polymorphism, that originate from their intricate intra- and intermolecular forces. While accurate coarse-grain (CG) models for these materials are critical to understand phenomena beyond the reach of all-atom simulations, current models cannot capture the diversity of molecular structures. We introduce a generally applicable approach to develop CG force fields for molecular crystals combining graph neural networks (GNN) and data from an all-atom simulations and apply it to the high-energy density material RDX. We address the challenge of expanding the training data with relevant configurations via an iterative procedure that performs CG molecular dynamics of processes of interest and reconstructs the atomistic configurations using a pre-trained neural network decoder. The multi-site CG model uses a GNN architecture constructed to satisfy translational invariance and rotational covariance for forces. The resulting model captures both crystalline and amorphous states for a wide range of temperatures and densities.

Three-dimensional atomic insights into the metal-oxide interface in Zr-ZrO2 nanoparticles

Metal-oxide interfaces with poor coherency have specific properties comparing to bulk materials and offer broad applications in heterogeneous catalysis, battery, and electronics. However, current understanding of the three-dimensional (3D) atomic metal-oxide interfaces remains limited because of their inherent structural complexity and the limitations of conventional two-dimensional imaging techniques. Here, we determine the 3D atomic structure of metal-oxide interfaces in zirconium-zirconia nanoparticles using atomic-resolution electron tomography. We quantitatively analyze the atomic concentration and the degree of oxidation, and find the coherency and translational symmetry of the interfaces are broken. Atoms at the interface have low structural ordering, low coordination, and elongated bond length. Moreover, we observe porous structures such as Zr vacancies and nano-pores, and investigate their distribution. Our findings provide a clear 3D atomic picture of metal-oxide interface with direct experimental evidence. We anticipate this work could encourage future studies on fundamental problems of oxides, such as interfacial structures in semiconductor and atomic motion during oxidation process.

Combining optical flow and Swin Transformer for Space-Time video super-resolution

Space–time video super-resolution is a task that aims to interpolate low frame rate, low resolution videos to high frame rate, high resolution ones. While existing Transformer-based methods have achieved results comparable to convolutional neural networks-based methods, the computational cost of Transformer limits its performance with constrained computational resources. Moreover, Swin Transformer may fail to fully exploit the spatio-temporal information of video frames due to the limitation of window size, impeding its effectiveness in handling large motions. To address these limitations, we propose an end-to-end space–time video super-resolution architecture based on optical flow alignment and Swin Transformer. The alignment module is introduced to extract spatio-temporal information from adjacent frames without significantly increasing the computational burden. Additionally, we design a residual convolution layer to enhance the translational invariance of the features extracted by Swin Transformer and introduces additional nonlinear transformations. Experimental results demonstrate that our proposed method achieves superior performance on various benchmark datasets compared to state-of-the-art methods. In terms of Peak Signal-to-Noise Ratio, our method outperforms the state-of-the-art methods by at least 0.15 dB on Vimeo-Medium dataset.

Derivative learning of tensorial quantities-Predicting finite temperature infrared spectra from first principles.

We develop a strategy that integrates machine learning and first-principles calculations to achieve technically accurate predictions of infrared spectra. In particular, the methodology allows one to predict infrared spectra for complex systems at finite temperatures. The method's effectiveness is demonstrated in challenging scenarios, such as the analysis of water and the organic-inorganic halide perovskite MAPbI3, where our results consistently align with experimental data. A distinctive feature of the methodology is the incorporation of derivative learning, which proves indispensable for obtaining accurate polarization data in bulk materials and facilitates the training of a machine learning surrogate model of the polarization adapted to rotational and translational symmetries. We achieve polarization prediction accuracies of about 1% for the water dimer by training only on the predicted Born effective charges.

Multi-Scale Depthwise Separable Capsule Network for hyperspectral image classification.

Addressing the challenges in effectively extracting multi-scale features and preserving pose information during hyperspectral image (HSI) classification, a Multi-Scale Depthwise Separable Capsule Network (MDSC-Net) is proposed in this article for HSI classification. Initially, hierarchical features are extracted by MDSC-Net through the employment of parallel multi-scale convolutional kernels, while computational complexity is reduced via depthwise separable convolutions, thus reducing the overall computational load and achieving efficient feature extraction. Subsequently, to enhance the translational invariance of features and reduce the loss of pose information, features of various scales are processed in parallel by independent capsule networks, with improvements in max pooling achieved through dynamic routing. Lastly, features of different scales are concatenated and integrated through the concatenate operation, thereby facilitating precise analysis of multi-level information in the hyperspectral image classification process. Experimental comparisons demonstrate that MDSC-Net achieves average accuracies of 94%, 98%, and 99% on the Kennedy Space Center, University of Pavia, and Salinas datasets, respectively, indicating a significant performance advantage over recent HSI classification models and validating the effectiveness of the proposed model.

A parametric modeling method for 3D woven composites considering realistic meso-structural characteristics

The precision of mesoscale simulation for three-dimensional woven composites (3DWCs) is intricately linked to the fidelity of the geometric representation. This paper aims to present a novel parametric modeling approach for generating representative volume element (RVE) of the 3DWCs while considering its realistic meso-structural characteristics. The real architecture of 3DWCs is defined to consider the squeezed surface warp tow. Tow geometry is specified, accounting for torsion of tow cross-section and crimp of weft tow path. The RVEs of the composites are geometrically assembled via a specific translational symmetry. The tensile response of the composites with the novel geometry is scrutinized utilizing a progressive damage model, compared with that of the ideal geometry. Additionally, the impact of weft tow size on the tensile response of the composites is explored.

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In this correspondence, we deduce the non-parabolic band dispersion within the framework of effective mass representation (EMR) using k→⋅π→ perturbation theory in the presence of s.o interaction, magnetic impurity and external magnetic field. We measure the electronic parameters like Fermi energy, density of states, effective g factor and effective mass etc. in p-type Sn1−xEuxTe by taking into account a 6-level band structure with normal and bumped band edges. In the study, we use the experimental and simulated band gap values as functions of Eu+2 impurity and temperature. Apart from the general trend, the electronic parameters exhibit extreme behaviour near the band inversion point x=0.020 at T=300 K (Nayak et. al.2023), but in the range of impurity concentration and temperature considered; from x=0.0005 to x=0.001 and T=1.5 K to T=300 K, the behaviour is normal. Again, we follow the expression for spin-electron paramagnetic resonance (EPR) shift (Ps) where the perturbation expansion of Green’s function is used in the presence of the above-mentioned interactions. To get around the problem of loss of translational symmetry in the presence of the magnetic field, Green’s function is redefined in terms of Peierl’s phase factor. Here we have made an extensive study of the shift of Eu+2 ion in p-type Sn1−xEuxTe for several impurity concentrations from x=0.0005 to x=0.001 in the temperature range T=1.4 K to T=300 K. Lastly, we analyze the EPR shift and other electronic parameters and their anisotropies in p-type Sn1−xEuxTe as functions of carrier concentration and Eu impurity from T=1.5K to T=300K. We report the EPR shift is 2.97×10−3 at T=300 K and 3.31×10−3 at T=1.5 K with anisotropy at p=5×1020cm−3 in contrast to the experimental observation of +(3.4±0.4)×10−3 in the same system. The discrepancy is attributed to the reduction in the density of available states at Fermi energy at the L-band caused by the simultaneous rise in that at the Σ− band noticeable particularly at/above high hole concentrations p≥5×1020cm−3.

Transformer-CNN for small image object detection

Object recognition in computer vision technology has been a popular research field in recent years. Although the detection success rate of regular objects has achieved impressive results, small object detection (SOD) is still a challenging issue. In the Microsoft Common Objects in Context (MS COCO) public dataset, the detection rate of small objects is typically half that of regular-sized objects. The main reason is that small objects are often affected by multi-layer convolution and pooling, leading to insufficient details to distinguish them from the background or similar objects, resulting in poor recognition rates or even no results. This paper presents a network architecture, Transformer-CNN, that combines a self-attention mechanism-based transformer and a convolutional neural network (CNN) to improve the recognition rate of SOD. It captures global information through a transformer and uses the translation invariance and translation equivalence of CNN to maximize the retention of global and local features while improving the reliability and robustness of SOD. Our experiments show that the proposed model improves the small object recognition rate by 2∼5 % than the general transformer architectures.

Self-similar blow-up solutions in the generalised Korteweg-de Vries equation: spectral analysis, normal form and asymptotics

In the present work we revisit the problem of the generalised Korteweg–de Vries equation parametrically, as a function of the relevant nonlinearity exponent, to examine the emergence of blow-up solutions, as traveling waveforms lose their stability past a critical point of the relevant parameter p, here at p = 5. We provide a normal form of the associated collapse dynamics, and illustrate how this captures the collapsing branch bifurcating from the unstable traveling branch. We also systematically characterise the linearisation spectrum of not only the traveling states, but importantly of the emergent collapsing waveforms in the so-called co-exploding frame where these waveforms are identified as stationary states. This spectrum, in addition to two positive real eigenvalues which are shown to be associated with the symmetries of translation and scaling invariance of the original (non-exploding) frame features complex patterns of negative eigenvalues that we also fully characterise. We show that the phenomenology of the latter is significantly affected by the boundary conditions and is far more complicated than in the corresponding symmetric Laplacian case of the nonlinear Schrödinger problem that has recently been explored. In addition, we explore the dynamics of the unstable solitary waves for p > 5 in the co-exploding frame.

The electric dipole characteristics of well-deformed 171,173Yb

The electric dipole response of well-deformed 171,173Yb in the giant dipole resonance (GDR) and pygmy dipole resonance (PDR) range has been theoretically analyzed using the translation and Galileo invariant quasiparticle phonon nuclear model (TGI-QPNM). The TGI-QPNM consists of an axially symmetric Woods-Saxon Potential, monopole pairing, dipole-dipole residual interaction, and the restoration terms for broken translation and Galilean symmetries. Numerical calculations show the existence of considerable E1 excitations around the neutron separation threshold (S n ) in both isotopes. The TGI-QPNM results of the photoabsorption cross-section give a double-humped shape in both nuclei, consistent with the available experimental data. The integrated moments (σ 0, σ −1) and the centroid energies in the GDR region are also reproduced well.

Physics and chemistry from parsimonious representations: image analysis via invariant variational autoencoders

Electron, optical, and scanning probe microscopy methods are generating ever increasing volume of image data containing information on atomic and mesoscale structures and functionalities. This necessitates the development of the machine learning methods for discovery of physical and chemical phenomena from the data, such as manifestations of symmetry breaking phenomena in electron and scanning tunneling microscopy images, or variability of the nanoparticles. Variational autoencoders (VAEs) are emerging as a powerful paradigm for the unsupervised data analysis, allowing to disentangle the factors of variability and discover optimal parsimonious representation. Here, we summarize recent developments in VAEs, covering the basic principles and intuition behind the VAEs. The invariant VAEs are introduced as an approach to accommodate scale and translation invariances present in imaging data and separate known factors of variations from the ones to be discovered. We further describe the opportunities enabled by the control over VAE architecture, including conditional, semi-supervised, and joint VAEs. Several case studies of VAE applications for toy models and experimental datasets in Scanning Transmission Electron Microscopy are discussed, emphasizing the deep connection between VAE and basic physical principles. Python codes and datasets discussed in this article are available at https://github.com/saimani5/VAE-tutorials and can be used by researchers as an application guide when applying these to their own datasets.

Spontaneous emergence of temporal structures in a continuously driven many-body system

Abstract The spontaneous emergence of temporal structures challenges the conventional understanding that systems governed by time-invariant laws remain unchanged over time. Recent experiments have observed this time translation symmetry breaking in quantum atomic systems that either exhibit strong atom-atom interactions or have low dissipation rates. While current theoretical frameworks reveal the importance of strong atom-atom interactions, they fall short in explaining this phenomenon observed in low-dissipation atomic systems. Here, we present a theoretical study on the spontaneous breaking of time translation symmetry in materials with low
dissipation rates. By constructing phase diagrams for a system of four-level atoms driven by a continuous-wave optical field, we identify the essential requirements for self-sustained temporal motions. These include a driven open system, nonlinear interactions, and sufficient degrees of freedom that facilitate competing processes. Our findings contribute to a better understanding of the emergence of spontaneous time translation symmetry breaking in these materials.

Doping Induced Enhancement of Activity and Stability for Oxygen Evolution Reaction with Isomaterially Heterostructured MnO2

A “Non-Native” phase (NNP) differs from the thermodynamically most stable bulk Native in its discrete translational symmetry. The relative difference in surface and bulk energy with respect to the native phase (NP)determines the stability of NNP. The isomaterial hetero-structured NP-NNP composite provides a pathway to assemble structures that have optimal properties of NNP and NP. The surface and sub-surface energies can also be modulated by doping as the dopants may segregate and stabilize grain boundaries. This study demonstrates that the isomaterial heterostructure of the NP, β-N MnO2, and Ramsdellite, r-NN1 MnO2, known as γ-N-NN1-MnO2 intergrowth, enhances the OER activity and stability.The hydrothermal route was used to synthesize isomaterial heterostructured γ/N-NN1-MnO2 with varying concentrations of dopants (10%, 15%, and 20% Ni and Co). X-ray diffraction was used to characterize the material, and after Rietveld refinement, phase quantification revealed that as the dopant concentration increased, the amount of the thermodynamically stable β-N MnO2 phase increased. Planes identified in XRD were also confirmed using high-resolution transmission electron microscopy (HRTEM) and the analysis of selective area electron diffraction (SAED) patterns. It appears that doping was successful based on the shifting of peaks in XRD and differences in unit cell volume and crystallite size calculated using the Debye-Scherrer equation before and after doping. With an increase in dopant concentration and thus improved OER activity, the average oxidation state as determined by X-ray photoelectron spectroscopy followed a downward trend, which is known to improve OER activity. The peaks shifted to lower frequency values as seen by Raman spectroscopy, which implies a weakening of Mn—O bond strength, indicating that dopants Ni and Co may have replaced part of the Mn atoms in the MnO2 intergrowth structure. Scanning electron microscopy (SEM) revealed spherical-shaped nanoparticles with spike-like overgrowths, which were further confirmed by HRTEM. The uniform dispersion of dopants was demonstrated by SEM and energy dispersive spectroscopy (EDS). Elemental quantification of the samples was done using EDS and scanning transmission electron microscopy (STEM). Using HRTEM, the presence of grain boundaries was confirmed.The study of dopants segregating to the grain boundary is conducted through DFT simulations. In many instances, the dopants actively contribute to the OER activity, except for the case of Ni in the NN1 sub-phase of the γ-N-NN1-MnO2 intergrowth, which is apparent by the slightly lower activity of Ni-doped samples compared to Co. This is because Ni remains in the bulk while Co segregates to the surface. A three-electrode setup (Ag/AgCl as the reference electrode, Pt mesh as the counter electrode, and catalyst as the working electrode) was used in 1M KOH to conduct electrochemical experiments. To achieve 10 mA/cm2, the 15% Co-doped electrocatalyst used the least amount of overpotential, 320 mV. According to electrochemical measurements and analysis, the doped samples show low Tafel slope, high specific activity, roughness factor, and charge transfer resistance from electrochemical impedance spectroscopy, all of which suggest improved overall activity for the oxygen evolution process (OER) for the doped over undoped samples. DFT simulations rationalize the enhancement of OER using the Bader charge analysis, the associated Gibbs free energy of the Sabatier principle plotted as the volcano plot.

Spectra of correlators in the relaxation time approximation of kinetic theory

The relaxation time approximation (RTA) of the kinetic Boltzmann equation is likely the simplest window into the microscopic properties of collective real-time transport. Within this framework, we analytically compute all retarded two-point Green’s functions of the energy-momentum tensor and a conserved U(1) current in thermal states with classical massless particles (a ‘CFT’) at non-zero density, and in the absence and presence of broken translational symmetry. This is done in 2 + 1 and 3 + 1 dimensions. RTA allows a full explicit analysis of the analytic structure of different correlators (poles versus branch cuts) and the transport properties that they imply (the thermoelectric conductivities, and the hydrodynamic, quasihydrodynamic and gapped mode dispersion relations). Our inherently weakly coupled analysis thereby also enables a direct comparison with previously known strongly coupled results in holographic CFTs dual to the Einstein-Maxwell-axion theories.

Deep neural networks as variational solutions for correlated open quantum systems

In this work we apply deep neural networks to find the non-equilibrium steady state solution to correlated open quantum many-body systems. Motivated by the ongoing search to find more powerful representations of (mixed) quantum states, we design a simple prototypical convolutional neural network and show that parametrizing the density matrix directly with more powerful models can yield better variational ansatz functions and improve upon results reached by neural density operator based on the restricted Boltzmann machine. Hereby we give up the explicit restriction to positive semi-definite density matrices. However, this is fulfilled again to good approximation by optimizing the parameters. The great advantage of this approach is that it opens up the possibility of exploring more complex network architectures that can be tailored to specific physical properties. We show how translation invariance can be enforced effortlessly and reach better results with fewer parameters. We present results for the dissipative one-dimensional transverse-field Ising model and a two-dimensional dissipative Heisenberg model compared to exact values.

Adaptation of the BaAl4 Type to Small Cations: The Case of NaGa4.

Single-phase NaGa4 samples were prepared by annealing stoichiometric element mixtures at 200 °C, 300 °C, and 450 °C in closed tantalum ampoules. No compositional homogeneity range was detected. While single crystals annealed at 200 °C feature a fully ordered crystal structure, a crystal annealed at 300 °C reveals a defect with mutual exchange of Na atoms and Ga2 dumbbells. The structure motif caused by the violation of translational symmetry resembles the CeMg2Si2 type of structure. The NaGa4 structure constitutes a branch of the BaAl4 type distinguished by a notably high c/a ratio (space group I4/mmm; a=4.2261(1) Å, c=11.2633(6) Å, c/a=2.67). This distortion enables the adaption of the BaAl4-type to small cations, when the further shortening of the apical-apical distance d(Ga-Ga) is not possible any more. Therefore, NaGa4 offers an adaption alternative to the monoclinic distortion observed in CaGa4 and YbGa4. Conductivity measurements validate the metallic behavior anticipated by NMR measurements in earlier studies.

Approximation of translation invariant Koopman operators for coupled non-linear systems.

Many physical systems exhibit translational invariance, meaning that the underlying physical laws are independent of the position in space. Data driven approximations of the infinite dimensional but linear Koopman operator of non-linear dynamical systems need to be physically informed in order to respect such physical symmetries. In the current work, we introduce a translation invariant extended dynamic mode decomposition (tieDMD) for coupled non-linear systems on periodic domains. This is achieved by exploiting a block-diagonal structure of the Koopman operator in Fourier space. Variants of tieDMD are applied to data obtained on one-dimensional periodic domains from the non-linear phase-diffusion equation, the Burgers equation, the Korteweg-de Vries equation, and a coupled FitzHugh-Nagumo system of partial differential equations. The reconstruction capability of tieDMD is compared to existing linear and non-linear variants of the dynamic mode decomposition applied to the same data. For the regarded data, tieDMD consistently shows superior capabilities in data reconstruction.

Quantum engineering for compactly localized states in disordered Lieb lattices

Blending ordering within an uncorrelated disorder potential in families of 3D Lieb lattices preserves the macroscopic degeneracy of compact localized states and yields unconventional combinations of localized and delocalized phases—as shown in Liu et al. (Phys Rev B 106:214204, 2022). We proceed to reintroduce translation invariance in the system by further ordering the disorder, and discuss the spectral structure and eigenstates features of the resulting perturbed lattices. We restore order in steps by first (i) rendering the disorder binary—i.e., yielding a randomized checkerboard potential, then (ii) reordering the randomized checkerboard into an ordered one, and at last (iii) realigning all the checkerboard values yielding a constant potential shift, but only on a sub-lattice. Along this path, we test the influence of additional random impurities on the order restoration. We find that in each of these steps, about half of the dispersive states are projected upon the unperturbed sites hosting the degenerate compact states, while the remaining ones are localized in the perturbed sites with energy determined by the strength of checkerboard. This strategy, herewith implemented in the 3D Lieb lattice, highlights order restoration as experimental pathway to engineer spectral and states features in disordered lattice structures in the pursuit of quantum storage and memory applications.Graphic abstract