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Gyrokinetic simulation codes are used to understand the microturbulence in the linear and nonlinear regimes of the tokamak and stellarator core. The codes that use flux coordinates to reduce computational complexities introduced by the anisotropy due to the presence of confinement magnetic fields encounter a mathematical singularity of the metric on the magnetic separatrix surface. To overcome this constraint, we develop a neural network-assisted Global Gyrokinetic Code using Cylindrical Coordinates (G2C3) to study the electrostatic microturbulence in realistic tokamak geometries. In particular, G2C3 uses a cylindrical coordinate system for particle dynamics, which allows particle motion in arbitrarily shaped flux surfaces, including the magnetic separatrix of the tokamak. We use an efficient particle locating hybrid scheme, which uses a neural network and iterative local search algorithm, for the charge deposition and field interpolation. G2C3 uses the field lines estimated by numerical integration to train the neural network in universal function approximator mode to speed up the subroutines related to gathering and scattering operations of gyrokinetic simulation. Finally, as verification of the capability of the new code, we present results from self-consistent simulations of linear ion temperature gradient modes in the core region of the DIII-D tokamak.

An efficient approach to calculate approximate pure-state and transition reduced density matrices in the framework of the multireference relativistic Fock-space coupled cluster (FS CC) theory is proposed. The method is based on the effective operator formalism and consists of the direct substitution of the FS CC Ansatz for a wave operator into the effective operator expression with the subsequent truncation of expansion at the terms quadratic in cluster amplitudes. The final density matrix is defined by active-space density matrices of different ranks "dressed" with contributions from cluster operators. The method gives a connected expression for pure-state density matrices, provided that the intermediate normalization condition is fulfilled. Moreover, under some additional assumptions, the connectivity can also be ensured for calculated transition property matrix elements and natural transition spinors. The developed technique allows for fast and accurate calculations of one-particle reduced density matrices for a wide range of electronic states. A pilot application of the new technique to construct averaged atomic natural orbital (ANO) basis sets for fully relativistic electronic structure calculations is presented.

In this study, we employ molecular simulations to investigate the enhancement in thermal conductance at the solid/liquid interface in the presence of a meniscus reported previously (Klochko et al., Phys. Chem. Chem. Phys. 25(4):3298-3308, 2023). We vary the solid/liquid interaction strength at Lennard-Jones interfaces for both confined liquid and meniscus systems, finding that the presence of a meniscus yields an enhancement in the interfacial thermal conductance across all wettabilities. However, the magnitude of the enhancement is found to depend on the surface wettability, initially rising monotonously for low to moderate wettabilities, followed by a sharp rise between moderate and high wettabilities. The spectral decomposition of heat flux formalism was applied to understand the nature of this phenomenon further. By computing the in-plane and out-of-plane components of the heat fluxes within both the interfacial solid and liquid, we show that the initial monotonous rise in conductance enhancement predominantly stems from a rise in the coupling of out-of-plane vibrations within both the solid and the liquid. In contrast, the subsequent sharp rise at more wetting interfaces is linked to sharp increases in the utilization of the in-plane modes of the solid and liquid. These observations result from the interplay between the solid/liquid adhesive forces and the liquid/vapor interfacial tension. Our results can aid engineers in optimizing thermal transport at realistic interfaces, which is critical to designing effective cooling solutions for electronics, among other applications.

A percolation model inspired by crossword puzzle games is introduced. A game proceeds by solving words, which are segments of sites in a two-dimensional lattice. As test case, the \emph{iid} variant allows for independently occupying sites with letters, only the percolation criterion depends on the existence of solved words. For the \emph{game} variant, inspired by real crossword puzzles, it becomes more likely to solve crossing words which share sites with the already solved words. In this way avalanches of solved words may occur. Both model variants exhibit a percolation transition as function of the a-priori site or word solving probability, respectively. The \emph{iid} variant is in the universality class of standard two-dimensional percolation. The \emph{game} variant exhibits a non-universal critical exponent $\nu$ of the correlation length. The actual value of $\nu$ depends on the function which controls how much solved words accelerate the solved of crossing words., Comment: 6 pages, 7 figures

Silicon exhibits several metastable allotropes which recently attracted attention in the quest for materials with superior (e.g. optical) properties, compatible with Si technology. In this work we shed light on the atomic-scale mechanisms leading to phase transformations in Si under pressure. To do so, we synergically exploit different state-of-the-art approaches. In particular, we use the advanced GAP interatomic potential both in NPT molecular dynamics simulations and in solid-state nudged elastic band calculations, validating our predictions with ab initio DFT calculations. We provide a link between evidence reported in experimental nanoindentation literature and simulation results. Particular attention is dedicated to the investigation of atomistic transition paths allowing for the transformation between BC8/R8 phases to the hd one under pure annealing. In this case we show a direct simulation of the local nucleation of the hexagonal phase in a BC8/R8 matrix and its corresponding atomic-scale mechanism extracted by the use of SS-NEB. We extend our study investigating the effect of pressure on the nucleation barrier, providing an argument for explaining the heterogeneous nucleation of the hd phase observed in experiments reported in the literature.

Strong $E\times B$ plasma flow shear is beneficial for reducing turbulent transport. However, traditional methods of driving flow shear do not scale well to large devices such as future fusion power plants. In this paper, we use a large number of nonlinear gyrokinetic simulations to study a novel approach to increase flow shear: decreasing the momentum diffusivity to make the plasma ``easier to push''. We first use an idealized circular geometry and find that one can obtain low momentum diffusivity at tight aspect ratio, low safety factor, high magnetic shear and low temperature gradient. This is the so-called Low Momentum Diffusivity (LMD) regime. To drive intrinsic momentum flux, we then tilt the flux surface, making it up-down asymmetric. In the LMD regime, this intrinsic momentum flux drives strong flow shear that can significantly reduce the heat flux and increase the critical temperature gradient. We also consider the actual experimental geometry of the MAST tokamak to illustrate that this strategy can be practical and create experimentally significant flow shear. Lastly, a preliminary prediction for the SMART tokamak is made., Comment: 43 pages, 23 figures

Arrays of coupled nanomagnets have wide-ranging fundamental and practical applications in artificial spin ices, neuromorphic computing and spintronics. However, lacking in these fields are nanomagnets with perpendicular magnetic anisotropy with sufficient magnetostatic interaction. This would not only open up new possibilities for artificial spin ice geometries but also enable novel coupling methods for applications. Here we demonstrate a method to engineer the energy landscape of artificial spin lattices with perpendicular magnetic anisotropy. With this, we are able to realize for the first time magnetostatically-coupled 2D lattices of out-of-plane Ising spins that spontaneously order at room temperature on timescales that can be precisely engineered. We show how this property, together with straightforward electrical interfacing, make this system a promising platform for reservoir computing. Our results open the way to investigate the thermodynamics of out-of-plane magnetostatically coupled nanomagnet arrays with novel spin ice geometries, as well as to exploit such nanomagnet arrays in unconventional computing, taking advantage of the adjustable temporal dynamics and strong coupling between nanomagnets.

Dynamics that are microscopic in space and time, so-called excitations, are considered the elementary unit of relaxation in the Dynamic Facilitation (DF) theory of the glass transition. Meanwhile, geometric motifs known as locally favored structures (LFS) are associated with vitrification in many glassformers. Recent work indicates that the probability of particles both found in locally favored structures (LFS) and excitations decreases significantly upon supercooling suggesting that there is an anti-correlation between them. [Ortlieb et al, Nature Commun. 14, 2621 (2023)]. However, the spatial relationship between excitations and LFS remains unclear. By employing state-of-the-art GPU computer simulations and colloid experiments, we analyze this relationship between LFS and excitations in model glassformers. We demonstrate that there is a spatial separation between the two in deeply supercooled liquids. This may be due to the fact that LFS are well-packed, thus they are solid and stable.

We point out that although a litany of studies have been published on atoms in hard-wall confinement, they have either not been systematic, having only looked at select atoms and/or select electronic configurations, or they have not used robust numerical methods. To remedy the situation, we perform in this work a methodical study of atoms in hard-wall confinement with the HelFEM program, which employs the finite element method (FEM) that trivially implements the hard-wall potential, guarantees variational results, and allows easily finding the numerically exact solution. We systematically examine low lying configurations of the H-Xe atoms and their monocations, and investigate how the states - especially the ground state - behave as a function of the position of the hard-wall boundary. Our fully numerical calculations are based on non-relativistic density functional theory (DFT), employing the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional and spherically averaged densities. We consider calculations with both spin-polarized as well as spin-restricted densities, and demonstrate that spin-polarization effects are significant in open shell configurations, even though some previous studies have only considered the spin-restricted model. We demonstrate the importance of considering ground state changes for confined atoms by computing the ionization radii for the H-Xe atoms and observe significant differences to earlier studies. Confirming previous observations, we identify electron shifts on the outermost shells for a majority of the elements: valence $s$ electrons are highly unfavored under strong confinement, and the high-lying $3d$ and $4f$ orbitals become occupied in atoms of periods 2-3 and 4, respectively., Comment: 20 pages, 3 figures

The mode-coupling theory (MCT) of the glass transition ranks among the most successful first-principles kinetic theories to describe glassy dynamics. However, MCT does not fully account for crucial aspects of the dynamics near the glass transition. To facilitate improving the theory, we critically test the approximations inherent in MCT for a supercooled mixture using Brownian dynamics simulations. Although each MCT approximation significantly impacts the predicted dynamics, our findings show that long-time cancellations of errors occur due to static and dynamic approximations of four-point correlation functions, with the validity of these approximations remaining relatively constant across different temperatures. Notably, the MCT form of the memory functional maintains remarkably high accuracy even in the supercooled regime when evaluated with the intermediate scattering function from simulations. The primary discrepancies between theoretical predictions and experimental results arise from the self-consistent nature of the MCT equations, which amplify minor errors in the memory kernel. This suggests that minor corrections to the memory functional could substantially enhance the theory's predictive accuracy.

The magnetite/water interface is commonly found in nature and plays a crucial role in various technological applications. However, our understanding of its structural and dynamical properties at the molecular scale remains still limited. In this study, we develop an efficient Behler-Parrinello neural network potential (NNP) for the magnetite/water system, paying particular attention to the accurate generation of reference data with density functional theory. Using this NNP, we performed extensive molecular dynamics simulations of the magnetite (001) surface across a wide range of water coverages, from the single molecule to bulk water. Our simulations revealed several new ground states of low coverage water on the Subsurface Cation Vacancy (SCV) model and yielded a density profile of water at the surface that exhibits marked layering. By calculating mean square displacements, we obtained quantitative information on the diffusion of water molecules on the SCV for different coverages, revealing significant anisotropy. Additionally, our simulations provided qualitative insights into the dissociation mechanisms of water molecules at the surface.

Resonances of open non-Hermitian systems are associated with the poles of the system scattering matrix. Perturbations of the system cause these poles to shift in the complex frequency plane. In this work, we introduce a novel method for calculating shifts in scattering matrix poles using generalized Wigner-Smith operators. We link our method to traditional cavity perturbation theory and validate its effectiveness through application to complex photonic networks. Our findings underscore the versatility of generalized Wigner-Smith operators for analyzing a broad spectrum of resonant systems and provides new insight into resonant properties of non-Hermitian systems.

We predict "intrinsic" spin relaxation times ($T_{1}$) of graphite due to spin-orbit-phonon interaction, i.e., the combination of spin-orbit coupling and electron-phonon interaction, using our developed first-principles density-matrix approach. We obtain ultralong $T_{1}$, e.g., $\sim$600 ns at 300 K, which leads to ultralong in-plane spin diffusion length $\sim$110 $\mu$m within the drift-diffusion model. Our prediction sets the upper bound of $T_{1}$ of graphite at each given temperature and Fermi level. The anisotropy ratios of $T_{1}$ or values of $T_{1z}/T_{1x}$ are found small and around 0.6. We examine the applicability of the well-known Elliot-Yafet (EY) relation, which declares that spin relaxation rate $T_{1\alpha}^{-1}$ ($\alpha=x,y,z$) is proportional to the product of the ensemble average of spin mixing parameter $\left\langle b_{\alpha}^{2}\right\rangle $ and carrier relaxation rate $\tau_{p}^{-1}$. Our numerical tests suggest that the EY relation works qualitatively if the degeneracy threshold $t^{\mathrm{deg}}$ for evaluating $b_{\alpha}^{2}$ is elatively large (not much smaller than or comparable to $k_{B}T$), e.g., $10^{-3}$ eV or larger, but fails if $t^{\mathrm{deg}}$ is too tiny (much smaller than $k_{B}T$), e.g., $10^{-6}$ eV or smaller., Comment: 9 pages, 4 figures

This work presents the results of modelling the ion dynamics in the ART-MS (Autoresonant Trap Mass Spectrometry) device in the quasi-static approximation. This instrument utilizes an anharmonic, purely electrostatic trap for ion confinement and a radio frequency (RF) voltage source with decrementally varying frequency for selective ion extraction. The autoresonant interaction between the oscillatory motion of the ion and the RF voltage causes an increase in the amplitude of certain confined ions, allowing their selective extraction. Numerical modelling shows that the extraction of ions with a given mass occurs not only at the fundamental frequency but also at its harmonics. This effect reduces the selective properties of devices of this type because along with the main mass component for a given frequency, it is possible to enter the detector channel of ions with another mass, for which this frequency corresponds to the second or higher harmonics, even a superposition of some of these harmonics of different ions., Comment: 9 pages, 6 figures

In this paper we propose a semi-Lagrangian discontinuous Galerkin solver for the simulation of the scrape off layer for an electron-ion plasma. We use a time adaptive velocity space to deal with fast particles leaving the computational domain, a block structured mesh to resolve the sharp gradient in the plasma sheath, and limiters to avoid oscillations in the density function. In particular, we propose a limiter that can be computed directly from the information used in the semi-Lagrangian discontinuous Galerkin advection step. This limiter is particularly efficient on graphic processing units (GPUs) and compares favorable with limiters from the literature. We provide numerical results for a set of benchmark problems and compare different limiting strategies.

Relative free energy calculations are now widely used in academia and industry, but the accuracy is often limited by poor sampling of the complexes conformational ensemble. To address this, we have developed a novel method termed Multi-Topology Replica Exchange of Expanded Ensembles (MT-REXEE). This method enables parallel expanded ensemble calculations, facilitating iterative relative free energy computations while allowing conformational exchange between parallel transformations. These iterative transformations are adaptable to any set of systems with a common backbone or central substructure. We demonstrate that the MT-REXEE method maintains thermodynamic cycle closure to the same extent as standard expanded ensemble for both solvation free energy and relative binding free energy. The transformations tested involve simple systems that incorporate diverse heavy atoms and multi-site perturbations of a small molecule core resembling multi-site $\lambda$ dynamics, without necessitating modifications to the MD code, which in our initial implementation is GROMACS. We outline a systematic approach for topology set-up and provide instructions on how to perform inter-replicate coordinate modifications. This work shows that MT-REEXE can be used to perform accurate and reproducible free energy estimates and prompts expansion to more complex test systems and other molecular dynamics simulation infrastructures.

Here we show that shadow tomography can generate an efficient and exact ansatz for the many-fermion wave function on quantum devices. We derive the shadow ansatz -- a product of transformations applied to the mean-field wave function -- by exploiting a critical link between measurement and preparation. Each transformation is obtained by measuring a classical shadow of the residual of the contracted Schr\"odinger equation (CSE), the many-electron Schr\"odinger equation (SE) projected onto the space of two electrons. We show that the classical shadows of the CSE vanish if and only if the wave function satisfies the SE and, hence, that randomly sampling only the two-electron space yields an exact ansatz regardless of the total number of electrons. We demonstrate the ansatz's advantages for scalable simulations -- fewer measurements and shallower circuits -- by computing H$_{3}$ on simulators and a quantum device.

Excited-state properties of highly correlated systems are key to understanding photosynthesis, luminescence, and the development of novel optical materials, but accurately capturing their interactions is computationally costly. We present an algorithm that combines classical shadow tomography with physical constraints on the two-electron reduced density matrix (2-RDM) to treat excited states. The method reduces the number of measurements of the many-electron 2-RDM on quantum computers by (i) approximating the quantum state through a random sampling technique called shadow tomography and (ii) ensuring that the 2-RDM represents an $N$-electron system through imposing $N$-representability constraints by semidefinite programming. This generalizes recent work on the $N$-representability-enhanced shadow tomography of ground-state 2-RDMs. We compute excited-state energies and 2-RDMs of the H$_4$ chain and analyze the critical points along the photoexcited reaction pathway from gauche-1,3-butadiene to bicyclobutane via a conical intersection. The results show that the generalized shadow tomography retains critical multireference correlation effects while significantly reducing the number of required measurements, offering a promising avenue for the efficient treatment of electronically excited states on quantum devices.

In a recent class of phase field crystal (PFC) models, the density order parameter is coupled to powers of its mean field. This effectively introduces a phenomenology of higher-order direct correlation functions acting on long wavelengths, which is required for modelling solid-liquid-vapor systems. The present work generalizes these models by incorporating, into a single-field theory, higher-order direct correlations, systematically constructed in reciprocal space to operate across long {\it and} short wavelengths. The correlation kernels introduced are also readily adaptable to describe distinct crystal structures. We examine the three-phase equilibrium properties and phase diagrams of the proposed model, and reproduce parts of the aluminum phase diagram as an example of its versatile parametrization. We assess the dynamics of the model, showing that it allows robust control of the interface energy between the vapor and condensed phases (liquid and solid). We also examine the dynamics of solid-vapor interfaces over a wide range of parameters and find that dynamical artifacts reported in previous PFC models do not occur in the present formalism. Additionally, we demonstrate the capacity of the proposed formalism for computing complex microstructures and defects such as dislocations, grain boundaries, and voids in solid-liquid-vapor systems, all of which are expected to be crucial for investigating rapid solidification processes.

The phonon Boltzmann transport equation (BTE) is widely used for describing multiscale heat conduction (from nm to $\mu$m or mm) in solid materials. Developing numerical approaches to solve this equation is challenging since it is a 7-dimensional integral-differential equation. In this work, we propose Monte Carlo physics-informed neural networks (MC-PINNs), which do not suffer from the "curse of dimensionality", to solve the phonon BTE to model the multiscale heat conduction in solid materials. MC-PINNs use a deep neural network to approximate the solution to the BTE, and encode the BTE as well as the corresponding boundary/initial conditions using the automatic differentiation. In addition, we propose a novel two-step sampling approach to address inefficiency and inaccuracy issues in the widely used sampling methods in PINNs. In particular, we first randomly sample a certain number of points in the temporal-spatial space (Step I), and then draw another number of points randomly in the solid angular space (Step II). The training points are constructed using the tensor product of the data drawn from the above two steps. The two-step sampling strategy enables MC-PINNs (1) to model the heat conduction from ballistic to diffusive regimes, and (2) is more memory-efficient compared to conventional numerical solvers or existing PINNs for BTE. A series of numerical examples including quasi-one-dimensional (quasi-1D) steady/unsteady heat conduction in a film, and the heat conduction in a quasi-two- and three-dimensional square domain, are conducted to justify the effectiveness of the MC-PINN for heat conduction spanning diffusive and ballistic regimes. Finally, we compare the computational time and memory usage of the MC-PINN and a state-of-art numerical methods to demonstrate the potential of the MC-PINN for large scale problems in real-world applications.

The transition matrix, frequently abbreviated as T-matrix, contains the complete information in a linear approximation of how a spatially localized object scatters an incident field. The T-matrix is used to study the scattering response of an isolated object and describes the optical response of complex photonic materials made from ensembles of individual objects. T-matrices of certain common structures, potentially, have been repeatedly calculated all over the world again and again. This is not necessary and constitutes a major challenge for various reasons. First, the resources spent on their computation represent an unsustainable financial and ecological burden. Second, with the onset of machine learning, data is the gold of our era, and it should be freely available to everybody to address novel scientific challenges. Finally, the possibility of reproducing simulations could tremendously improve if the considered T-matrices could be shared. To address these challenges, we found it important to agree on a common data format for T-matrices and to enable their collection from different sources and distribution. This document aims to develop the specifications for storing T-matrices and associated metadata. The specifications should allow maximum freedom to accommodate as many use cases as possible without introducing any ambiguity in the stored data. The common format will assist in setting up a public database of T-matrices., Comment: Submitted to the Journal of Quantitative Spectroscopy and Radiative Transfer

Spatiotemporal partial differential equations (PDEs) find extensive application across various scientific and engineering fields. While numerous models have emerged from both physics and machine learning (ML) communities, there is a growing trend towards integrating these approaches to develop hybrid architectures known as physics-aware machine learning models. Among these, the finite volume neural network (FINN) has emerged as a recent addition. FINN has proven to be particularly efficient in uncovering latent structures in data. In this study, we explore the capabilities of FINN in tackling the shallow-water equations, which simulates wave dynamics in coastal regions. Specifically, we investigate FINN's efficacy to reconstruct underwater topography based on these particular wave equations. Our findings reveal that FINN exhibits a remarkable capacity to infer topography solely from wave dynamics, distinguishing itself from both conventional ML and physics-aware ML models. Our results underscore the potential of FINN in advancing our understanding of spatiotemporal phenomena and enhancing parametrization capabilities in related domains.

Abstract. Creating soft-Coulomb-type (SC) molecular potential within single-active-electron approximation (SAE) is essential since it allows solving time-dependent Schr\"odinger equations with fewer computational resources compared to other multielectron methods. The current available SC potentials can accurately reproduce the energy of the highest occupied molecular orbital (HOMO), which is sufficient for analyzing nonlinear effects in laser-molecule interactions like high-order harmonic generation (HHG). However, recent discoveries of significant effects of deep-lying molecular orbitals call for more precise potentials to analyze them. In this study, we present a fast and accurate method based on machine learning to construct SC potentials that simultaneously reproduce various molecular features, including energies, symmetries, and dipole moments of HOMO, HOMO-1, and HOMO-2. We use this ML model to create SC SAE potentials of the HCN molecule and then comprehensively analyze the fingerprints of lower-lying orbitals in HHG spectra emitted during the H-CN stretching. Our findings reveal that HOMO-1 plays a role in forming the second HHG plateau. Additionally, as the H-C distance increases, the plateau structure and the smoothness of HHG spectra are altered due to the redistribution of orbital electron density. These results are in line with other experimental and theoretical studies. Lastly, the machine learning approach using deconvolution and convolution neural networks in the present study is so general that it can be applied to construct molecular potential for other molecules and molecular dynamic processes.

Determinant quantum Monte Carlo (DQMC), formulated in complex-fermion representation, has played a key role in studying strongly-correlated fermion systems. However, its applicability is limited due to the requirement of particle-number conservation after Hubbard-Stratonovich transformation. In going beyond the conventional DQMC, one encouraging development occurred when Majorana fermions were introduced for QMC [1,2]. But in previous Majorana-based QMC, Boltzmann weight is determined often with a sign ambiguity. Here we successfully resolved this ambiguity by deriving a closed-form Pfaffian formula for the weight, enabling efficient calculation of the weight with its sign in polynomial time. We call it ''Pfaffian quantum Monte Carlo'' (PfQMC), which can be applied to generic interacting fermion models. We have successfully employed PfQMC to explore how robust Majorana edge modes in Kitaev chain are against strong interactions. By offering greater flexibility, PfQMC can potentially enhance existing sign-mitigating and approximation methods and help address challenging issues such as the ground-state properties of the doped Hubbard model., Comment: 18 pages (including supplemental materials), 5 figures

A major challenge of AI + Science lies in their inherent incompatibility: today's AI is primarily based on connectionism, while science depends on symbolism. To bridge the two worlds, we propose a framework to seamlessly synergize Kolmogorov-Arnold Networks (KANs) and science. The framework highlights KANs' usage for three aspects of scientific discovery: identifying relevant features, revealing modular structures, and discovering symbolic formulas. The synergy is bidirectional: science to KAN (incorporating scientific knowledge into KANs), and KAN to science (extracting scientific insights from KANs). We highlight major new functionalities in the pykan package: (1) MultKAN: KANs with multiplication nodes. (2) kanpiler: a KAN compiler that compiles symbolic formulas into KANs. (3) tree converter: convert KANs (or any neural networks) to tree graphs. Based on these tools, we demonstrate KANs' capability to discover various types of physical laws, including conserved quantities, Lagrangians, symmetries, and constitutive laws., Comment: 27 pages, 14 figures

The development of atomic many-body methods, capable of incorporating electron correlation effects accurately, is required for isotope shift (IS) studies. In combination with precise measurements, such calculations help to extract nuclear charge radii differences, and to probe for signatures of physics beyond the Standard Model of particle physics. We review here a few recently-developed methods in the relativistic many-body perturbation theory (RMBPT) and relativistic coupled-cluster (RCC) theory frameworks for calculations of IS factors in the highly charged ions (HCIs), and neutral or singly-charged ions, respectively. The results are presented for a wide range of atomic systems in order to demonstrate the interplay between quantum electrodynamics (QED) and electron correlation effects. In view of this, we start our discussions with the RMBPT calculations for a few HCIs by rigorously treating QED effects; then we outline methods to calculate IS factors in the one-valence atomic systems using two formulations of the RCC approach. Then we present calculations for two valence atomic systems, by employing the Fock-space RCC methods. For completeness, we briefly discuss theoretical input required for the upcoming experiments, their possibilities to probe nuclear properties and implications to fundamental physics studies., Comment: Topical Review Preprint for J. Phys. B, Comments and Suggestions are welcome!

Nested sampling (NS) is a stochastic method for computing the log-evidence of a Bayesian problem. It relies on stochastic estimates of prior volumes enclosed by likelihood contours, which limits the accuracy of the log-evidence calculation. We propose to transform the prior volume estimation into a Bayesian inference problem, which allows us to incorporate a smoothness assumption for likelihood-prior volume relations. As a result, we aim to increase the accuracy of the volume estimates and thus improve the overall log-evidence calculation using NS. The method presented works as a post-processing step for NS and provides posterior samples of the likelihood-prior-volume relation, from which the log-evidence can be calculated. We demonstrate an implementation of the algorithm and compare its results with plain NS on two synthetic datasets for which the underlying evidence is known. We find a significant improvement in accuracy for runs with less than one hundred active samples in NS, but are prone to numerical problems beyond this point.

This survey examines the broad suite of methods and models for combining machine learning with physics knowledge for prediction and forecast, with a focus on partial differential equations. These methods have attracted significant interest due to their potential impact on advancing scientific research and industrial practices by improving predictive models with small- or large-scale datasets and expressive predictive models with useful inductive biases. The survey has two parts. The first considers incorporating physics knowledge on an architectural level through objective functions, structured predictive models, and data augmentation. The second considers data as physics knowledge, which motivates looking at multi-task, meta, and contextual learning as an alternative approach to incorporating physics knowledge in a data-driven fashion. Finally, we also provide an industrial perspective on the application of these methods and a survey of the open-source ecosystem for physics-informed machine learning., Comment: 56 pages, 8 figures, 2 tables

We present and analyze a framework for designing symplectic neural networks (SympNets) based on geometric integrators for Hamiltonian differential equations. The SympNets are universal approximators in the space of Hamiltonian diffeomorphisms, interpretable and have a non-vanishing gradient property. We also give a representation theory for linear systems, meaning the proposed P-SympNets can exactly parameterize any symplectic map corresponding to quadratic Hamiltonians. Extensive numerical tests demonstrate increased expressiveness and accuracy -- often several orders of magnitude better -- for lower training cost over existing architectures. Lastly, we show how to perform symbolic Hamiltonian regression with SympNets for polynomial systems using backward error analysis., Comment: 33 pages including appendices but not references, 7 figures

Building subsurface velocity models is essential to our goals in utilizing seismic data for Earth discovery and exploration, as well as monitoring. With the dawn of machine learning, these velocity models (or, more precisely, their distribution) can be stored accurately and efficiently in a generative model. These stored velocity model distributions can be utilized to regularize or quantify uncertainties in inverse problems, like full waveform inversion. However, most generators, like normalizing flows or diffusion models, treat the image (velocity model) uniformly, disregarding spatial dependencies and resolution changes with respect to the observation locations. To address this weakness, we introduce VelocityGPT, a novel implementation that utilizes Transformer decoders trained autoregressively to generate a velocity model from shallow subsurface to deep. Owing to the fact that seismic data are often recorded on the Earth's surface, a top-down generator can utilize the inverted information in the shallow as guidance (prior) to generating the deep. To facilitate the implementation, we use an additional network to compress the velocity model. We also inject prior information, like well or structure (represented by a migration image) to generate the velocity model. Using synthetic data, we demonstrate the effectiveness of VelocityGPT as a promising approach in generative model applications for seismic velocity model building.

Electronic structure analysis is performed to study the properties of several Pb-containing 3d-intermetallics. Our study reveals that binary metastable Co3Pb and Fe3Pb intermetallic compounds exhibit very attractive intrinsic magnetic properties. We primarily focus on the magnetic anisotropic properties arising from the high spin-orbit coupling of the Pb atom. Decomposing the total anisotropy into intra- and interatomic contributions reveals a significant deviation from single ion anisotropy model with strong symmetric anisotropic pair interactions present. Furthermore, we consider magnetic properties of ternary Pb-based 3d-intermetallics which recently have been reported as stable or metastable. Giant magnetic anisotropy is found on Pb atoms in these systems. The origin of such strong anisotropy in La18Co28Pb3 appears from two sources: spin-orbit and interelectronic Breit couplings. The significance of Breit interaction for magnetic anisotropy in bulk systems has not been reported previously. It is expected that Breit coupling induced anisotropy is dominating in magnetic Pb-based magnets with lower dimensionality including thin films., Comment: 21 pages, 9 figures

The specialized language and complex concepts in physics pose significant challenges for information extraction through Natural Language Processing (NLP). Central to effective NLP applications is the text embedding model, which converts text into dense vector representations for efficient information retrieval and semantic analysis. In this work, we introduce PhysBERT, the first physics-specific text embedding model. Pre-trained on a curated corpus of 1.2 million arXiv physics papers and fine-tuned with supervised data, PhysBERT outperforms leading general-purpose models on physics-specific tasks including the effectiveness in fine-tuning for specific physics subdomains.

Reliable quantum computation requires systematic identification and correction of errors that occur and accumulate in quantum hardware. To diagnose and correct such errors, standard quantum error-correcting protocols utilize $\textit{global}$ error information across the system obtained by mid-circuit readout of ancillary qubits. We investigate circuit-level error-correcting protocols that are measurement-free and based on $\textit{local}$ error information. Such a local error correction (LEC) circuit consists of faulty multi-qubit gates to perform both syndrome extraction and ancilla-controlled error removal. We develop and implement a reinforcement learning framework that takes a fixed set of faulty gates as inputs and outputs an optimized LEC circuit. To evaluate this approach, we quantitatively characterize an extension of logical qubit lifetime by a noisy LEC circuit. For the 2D classical Ising model and 4D toric code, our optimized LEC circuit performs better at extending a memory lifetime compared to a conventional LEC circuit based on Toom's rule in a sub-threshold gate error regime. We further show that such circuits can be used to reduce the rate of mid-circuit readouts to preserve a 2D toric code memory. Finally, we discuss the application of the LEC protocol on dissipative preparation of quantum states with topological phases., Comment: 15 + 11 pages, 16 figures

X-ray diffraction is ideal for probing sub-surface state during complex or rapid thermomechanical loading of crystalline materials. However, challenges arise as the size of diffraction volumes increase due to spatial broadening and inability to deconvolute the effects of different lattice deformation mechanisms. Here we present a novel approach to use combinations of physics-based modeling and machine learning to deconvolve thermal and mechanical elastic strains for diffraction data analysis. The method builds on a previous effort to extract thermal strain distribution information from diffraction data. The new approach is applied to extract the evolution of thermomechanical state during laser melting of an Inconel 625 wall specimen which produces significant residual stress upon cooling. A combination of heat transfer and fluid flow, elasto-plasticity, and X-ray diffraction simulations are used to generate training data for machine-learning (Gaussian Process Regression, GPR) models that map diffracted intensity distributions to underlying thermomechanical strain fields. First-principles density functional theory is used to determine accurate temperature-dependent thermal expansion and elastic stiffness used in the elasto-plasticity modeling. The trained GPR models are found to be capable of deconvoluting the effects of thermal and mechanical strains, in addition to providing information about underlying strain distributions, even from complex diffraction patterns with irregularly shaped peaks.

Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification, solutions of those PDEs need to be evaluated at numerous points in the parameter space. While physics-informed neural networks (PINNs) have emerged as a new strong competitor as a surrogate, their usage in this scenario remains underexplored due to the inherent need for repetitive and time-consuming training. In this paper, we address this problem by proposing a novel extension, parameterized physics-informed neural networks (P$^2$INNs). P$^2$INNs enable modeling the solutions of parameterized PDEs via explicitly encoding a latent representation of PDE parameters. With the extensive empirical evaluation, we demonstrate that P$^2$INNs outperform the baselines both in accuracy and parameter efficiency on benchmark 1D and 2D parameterized PDEs and are also effective in overcoming the known "failure modes".

Tunnel ionization (TI) underlies many important ultrafast processes, such as high-harmonic generation and strong-field ionization. Among the existing theories for TI, many-electron weak-field asymptotic theory (ME-WFAT) is by design capable of accurately treating many-electron effects in TI. An earlier version of ME-WFAT relied on an accurate representation of the asymptotic tail of the orbitals, which hindered its implementation in Gaussian-basis-set-based quantum chemistry programs. In this work, we reformulate ME-WFAT in the integral representation, which makes the quality of the asymptotic tail much less critical, hence greatly facilitating its implementation in standard quantum chemistry packages. The integral reformulation introduced here is therefore much more robust when applied to molecules with arbitrary geometry. We present several case studies, among which is the CO molecule where some earlier theories disagree with experiments. Here, we find that ME-WFAT produces the largest ionization probability when the field points from C to O, as experiments suggest. An attractive feature of ME-WFAT is that it can be used with various types of multi-electron methods whether of density functional [Phys. Rev. A 106, 052211 (2022)] or multiconfiguration types, which facilitates tunnel ionization calculation in systems exhibiting a strong multireference character, such as transition-metal-containing molecules., Comment: 20 pages and 6 figures

An exponential growth in computing power, which has brought more sophisticated and higher resolution simulations of the climate system, and an exponential increase in observations since the first weather satellite was put in orbit, are revolutionizing climate science. Big data and associated algorithms, coalesced under the field of Machine Learning (ML), offer the opportunity to study the physics of the climate system in ways, and with an amount of detail, infeasible few years ago. The inference provided by ML has allowed to ask causal questions and improve prediction skills beyond classical barriers. Furthermore, when paired with modeling experiments or robust research in model parameterizations, ML is accelerating computations, increasing accuracy and allowing for generating very large ensembles at a fraction of the cost. In light of the urgency imposed by climate change and the rapidly growing role of ML, we review its broader accomplishments in climate physics. Decades long standing problems in observational data reconstruction, representation of sub-grid scale phenomena and climate (and weather) prediction are being tackled with new and justified optimism. Ultimately, this review aims at providing a perspective on the benefits and major challenges of exploiting ML in studying complex systems., Comment: 25 pages, 4 figures

Multiscale rarefied gas flows with moving boundaries pose significant challenges to the numerical simulation, where the primary difficulties involve robustly managing the mesh movement and ensuring computational efficiency across all flow regimes. Build upon recent advancements of the general synthetic iterative scheme (GSIS), this paper presents an efficient solver to simulate the large displacement of rigid-body in rarefied gas flows. The newly developed solver utilizes a dual time step method to solve the mesoscopic kinetic and macroscopic synthetic equations alternately, in an arbitrary Lagrangian-Eulerian framework. Additionally, the overset mesh is used and the six degree-of-freedom rigid body dynamics equation is integrated to track the motion of solids. Four moving boundary problems encompassing a wide range of flow velocities and gas rarefaction are simulated, including the periodic pitching of airfoil, particle motion in lid-driven cavity flow, two-body separation in supersonic flow, and three-dimensional lunar landing, demonstrating the accuracy and efficiency of the GSIS in handling multi-scale moving boundary problems within an overset framework.

The promise of quantum computing to circumvent the exponential scaling of quantum chemistry has sparked a race to develop chemistry algorithms for quantum architecture. However, most works neglect the quantum-inherent shot noise, let alone the effect of current noisy devices. Here, we present a comprehensive study of quantum linear response (qLR) theory obtaining spectroscopic properties on simulated fault-tolerant quantum computers and present-day near-term quantum hardware. This work introduces novel metrics to analyze and predict the origins of noise in the quantum algorithm, proposes an Ansatz-based error mitigation technique, and highlights the significant impact of Pauli saving in reducing measurement costs and noise. Our hardware results using up to cc-pVTZ basis set serve as proof-of-principle for obtaining absorption spectra on quantum hardware in a general approach with the accuracy of classical multi-configurational methods. Importantly, our results exemplify that substantial improvements in hardware error rates and measurement speed are necessary to lift quantum computational chemistry from proof-of-concept to an actual impact in the field.

Modifications to Swisdak [Phys. Plasmas 20, 062110 (2013)]'s rejection sampling algorithm for drawing a Maxwell-J\"{u}ttner distribution in particle simulations are presented. Handy approximations for $e$-folding points and a linear slope in the envelope function are proposed, to make the algorithm self-contained and more efficient., Comment: To appear in Physics of Plasmas

Recent experimental and theoretical results have demonstrated the possibility of accelerating electrons in the MeV range by focusing tightly a few-cycle laser beam in ambient air. Using Particle-In-Cell (PIC) simulations, this configuration is revisited within a more accurate modelling approach to analyze and optimize the mechanism responsible for electron acceleration. In particular, an analytical model for a linearly polarized tightly-focused ultrashort laser field is derived and coupled to a PIC code, allowing us to model the interaction of laser beams reflected by high-numerical aperture mirrors with laser-induced plasmas. A set of 3D PIC simulations is performed where the laser wavelength is varied from 800 nm to 7.0 $\mu$m while the normalized amplitude of the electric field is varied from $a_{0} = 3.6$ to $a_{0} = 7.0$. The preferential forward acceleration of electrons, as well as the analysis of the laser intensity evolution in the plasma and data on electron number density, confirm that the relativistic ponderomotive force is responsible for the acceleration. We also demonstrate that the electron kinetic energy reaches a maximum of $\approx1.6$ MeV when the central wavelength is of 2.5 $\mu$m., Comment: 16 pages, 17 figures

Observational evidence strongly supports the existence of a Super Massive Black Hole (SMBH) at the Galactic center, surrounded by dense stellar clusters. Modeling galactic centers with intricate structures like shells and rings pose challenges, prompting the use of simplified models such as a spherical monopole potential with a multipolar halo mass distribution. This approach, employing a multipolar expansion model, provides versatility for numerical analyses, revealing the complex dynamics of stars in this region. Pseudo-Potentials like Paczynsky-Wiita and Artemova-Bjornsson-Novikov are utilized to simulate the impacts of strong gravity from non-rotating and rotating compact objects respectively, elucidating their influence on stellar dynamics. Chaos naturally arises due to non-central forces, visualized using the Poincar\'e section technique. Of particular importance is the utilization of the Smaller Alignment Index (SALI), a powerful nonlinear dynamical tool, which categorizes particle orbits as escaping, regular, sticky, or chaotic. We exhaustively examine all combinations of multipolar moments up to the octupolar term along with spin using this tool, which had not been studied earlier. SALI provides a straightforward yet efficient method for assessing the interplay between the system's different multipolar moments, their combinations, and spin. Thus, our findings offer insights into the dynamics of compact objects enshrouded in a halo mass distribution and lay the groundwork for understanding complex astrophysical systems in galactic centers., Comment: 16 pages, 7 figures

During relativistic magnetic reconnection, antiparallel magnetic fields undergo a rapid change in topology, releasing a large amount of energy in the form of non-thermal particle acceleration. This work explores the application of mesh refinement to 2D reconnection simulations to efficiently model the ineherent disparity in length-scales. We have systematically investigated the effects of mesh refinement and determined necessary modifications to the algorithm required to mitigate non-physical artifacts at the coarse-fine interface. We have used the ultrahigh-order Pseudo-Spectral Analytical Time-Domain (PSATD) Maxwell solver to analyze how its use can mitigate the numerical dispersion that occurs with the finite-difference time-domain (FDTD) (or ``Yee'') method. Absorbing layers are introduced at the coarse-fine interface to eliminate spurious effects that occur with mesh refinement. We also study how damping the electromagnetic fields and current density in the absorbing layer can help prevent the non-physical accumulation of charge and current density at the coarse-fine interface. Using a mesh refinement ratio of 8 for two-dimensional magnetic reconnection simulations, we obtained good agreement with the high resolution baseline simulation, using only 36% of the macroparticles and 71% of the node-hours needed for the baseline. The methods presented here are especially applicable to 3D systems where higher memory savings are expected than in 2D, enabling comprehensive, computationally efficient 3D reconnection studies in the future.

With advancements in computational molecular modeling and powerful structure search methods, it is now possible to systematically screen crystal structures for small organic molecules. In this context, we introduce the Python package High-throughput Organic Crystal Structure Prediction (HTOCSP), which enables the prediction and screening of crystal packing for small organic molecules in an automated, high-throughput manner. Specifically, we describe the workflow, which encompasses molecular analysis, force field generation, and crystal generation and sampling, all within customized constraints based on user input. We demonstrate the application of \texttt{HTOCSP} by systematically screening organic crystals for 100 molecules using different sampling strategies and force field options. Furthermore, we analyze the benchmark results to understand the underlying factors that influence the complexity of the crystal energy landscape. Finally, we discuss the current limitations of the package and potential future extensions., Comment: 14 pages, 6 figures

The split-charge equilibration method is extended to describe dissipative charge transfer similarly as the Drude model, whereby the generic frequency-dependent dielectric permitivitties or conductivities of dielectrics and metals can be mimicked. To demonstrate the feasibility of the approach, a resistor-capacitor circuit is simulated using an all-atom representation for resistor and capacitor. The simulated dynamics reproduce the expected charging process and Nyquist noise, the latter resulting from the thermal voltages acting on individual split charges. The method bears promise to model friction caused by the motion of charged particles past metallic or highly polarizable media., Comment: 8 pages, 5 figures

A significant limitation of wide-bandgap materials is their low hole mobility related to localized holes with heavy effective masses ($m_h^*$). We identify in low-symmetric wide-bandgap compounds an anion-anion antibonding coupling (AAAC) effect as the intrinsic factor behind hole localization, which explains the extremely heavy $m_h^*$ and self-trapped hole (STH) formation observed in gallium oxide ($\beta$-$Ga_{2}O_{3}$). We propose a design principle for achieving light holes by manipulating AAAC, demonstrating that specific strain conditions can reduce $m_h^*$ in $\beta$-$Ga_{2}O_{3}$ from 4.77 $m_0$ to 0.38 $m_0$, making it comparable to the electron mass (0.28 $m_0$), while also suppressing STH. The light holes show significant anisotropy, potentially enabling two-dimensional transport in bulk material. This study provides a fundamental understanding of hole mass enhancement and STH formation in novel wide-bandgap materials and suggest new pathways for engineering hole mobilities., Comment: 22 pages, 1 table, 5 figures

In this paper, we propose QWalkVec, a quantum walk-based node embedding method. A quantum walk is a quantum version of a random walk that demonstrates a faster propagation than a random walk on a graph. We focus on the fact that the effect of the depth-first search process is dominant when a quantum walk with a superposition state is applied to graphs. Simply using a quantum walk with its superposition state leads to insufficient performance since balancing the depth-first and breadth-first search processes is essential in node classification tasks. To overcome this disadvantage, we formulate novel coin operators that determine the movement of a quantum walker to its neighboring nodes. They enable QWalkVec to integrate the depth-first search and breadth-first search processes by prioritizing node sampling. We evaluate the effectiveness of QWalkVec in node classification tasks conducted on four small-sized real datasets. As a result, we demonstrate that the performance of QWalkVec is superior to that of the existing methods on several datasets. Our code will be available at \url{https://github.com/ReiSato18/QWalkVec}., Comment: This paper is accepted at 28th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD 2024). This paper is a slightly revised version

Quantum few-body systems are deceptively simple. Indeed, with the notable exception of a few special cases, their associated Schrodinger equation cannot be solved analytically for more than two particles. One has to resort to approximation methods to tackle quantum few-body problems. In particular, variational methods have been proposed to ease numerical calculations and obtain precise solutions. One such method is the Stochastic Variational Method, which employs a stochastic search to determine the number and parameters of correlated Gaussian basis functions used to construct an ansatz of the wave function. Stochastic methods, however, face numerical and optimization challenges as the number of particles increases. We introduce a family of gradient variational methods that replace stochastic search with gradient optimization. We comparatively and empirically evaluate the performance of the baseline Stochastic Variational Method, several instances of the gradient variational method family, and some hybrid methods for selected few-body problems. We show that gradient and hybrid methods can be more efficient and effective than the Stochastic Variational Method. We discuss the role of singularities, oscillations, and gradient optimization strategies in the performance of the respective methods.

We present a particle tracking method for unstructured meshes in two and three dimensions. Our tracking algorithm is based on a patch searching and includes two steps. We first locate the given point to a patch near a vertex, and then the host element is determined within the patch domain. We prove that the patch in the first step can be rapidly identified by constructing an auxiliary Cartesian grid with a prescribed resolution. Then, the second step can be converted into a searching problem, which can be easily solved by searching algorithms. Only coordinates to particles are required in our method. We conduct a series of numerical tests in two and three dimensions to illustrate the robustness and efficiency in our method.

Low-dimensional nanostructures such as nanotubes, nanoscrolls, and nanofilms have found applications in a wide variety of fields such as photocatalysis, sensing, and drug delivery. Recently, Chu et al. demonstrated that nanoscrolls of Mo and W transition metal oxides, which do not exhibit van der Waals (vdW) layering in their bulk counterparts, can be successfully synthesized using a plasma processing of corresponding layered transition metal dichalcogenides. In this work, we employ data mining, first-principles simulations, and physio-mechanical models to theoretically examine the potential of other dichalcogenide precursors to form oxide nanoscrolls. Through data mining of bulk and two-dimensional materials databases, we first identify dichalcogenides that would be mostly amenable to plasma processing on the basis of their vdW layering and thermodynamic stability. To determine the propensity of forming a nanoscroll, we develop a first-principles simulation-based physio-mechanical model to determine the thermodynamic stability of nanoscrolling as well as the equilibrium structure of the nanoscrolls, i.e. their inner radius, outer radius, and interlayer spacing. We validate this model using the experimental observations of Chu et al.'s study and find an excellent agreement for the equilibrium nanoscroll structure. Furthermore, we demonstrate that the model's energies can be utilized for a generalized quantitative categorization of nanoscroll stability. We apply the model to study the oxide nanoscroll formation in MoS$_2$, WS$_2$, MoSe$_2$, WSe$_2$, PdS$_2$, HfS$_2$ and GeS$_2$, paving the way for a systematic study of oxide nanoscroll formation atop other dichalcogenide substrates.