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The development of Digital Twins (DTs) represents a transformative advance for simulating and optimizing complex systems in a controlled digital space. Despite their potential, the challenge of constructing DTs that accurately replicate and predict the dynamics of real-world systems remains substantial. This paper introduces an intelligent framework for the construction and evaluation of DTs, specifically designed to enhance the accuracy and utility of DTs in testing algorithmic performance. We propose a novel construction methodology that integrates deep learning-based policy gradient techniques to dynamically tune the DT parameters, ensuring high fidelity in the digital replication of physical systems. Moreover, the Mean STate Error (MSTE) is proposed as a robust metric for evaluating the performance of algorithms within these digital space. The efficacy of our framework is demonstrated through extensive simulations that show our DT not only accurately mirrors the physical reality but also provides a reliable platform for algorithm evaluation. This work lays a foundation for future research into DT technologies, highlighting pathways for both theoretical enhancements and practical implementations in various industries.

We present JefiAtten, a novel neural network model employing the attention mechanism to solve Maxwell's equations efficiently. JefiAtten uses self-attention and cross-attention modules to understand the interplay between charge density, current density, and electromagnetic fields. Our results indicate that JefiAtten can generalize well to a range of scenarios, maintaining accuracy across various spatial distribution and handling amplitude variations. The model showcases an improvement in computation speed after training, compared to traditional integral methods. The adaptability of the model suggests potential for broader applications in computational physics, with further refinements to enhance its predictive capabilities and computational efficiency. Our work is a testament to the efficacy of integrating attention mechanisms with numerical simulations, marking a step forward in the quest for data-driven solutions to physical phenomena., Comment: 29 pages, 11 figures

Interlayer stacking order has recently emerged as a unique degree of freedom to control crystal symmetry and physical properties in two-dimensional van der Waals (vdW) materials and heterostructures. By tuning the layer stacking pattern, symmetry-breaking and electric polarization can be created in otherwise non-polar crystals, whose polarization reversal depends on the interlayer sliding motion. Herein, we demonstrate that in a vdW layered ferroelectric, its existing polarization is closely coupled to the interlayer sliding driven by hydrostatic pressure. Through combined structural, electrical, vibrational characterizations, and theoretical calculations, we clearly map out the structural evolution of CuInP2S6 under pressure. A tendency towards a high polarization state is observed in the low-pressure region, followed by an interlayer-sliding-mediated phase transition from a monoclinic to a trigonal phase. Along the transformation pathway, the displacive-instable Cu ion serves as a pivot point that regulates the interlayer interaction in response to external pressure. The rich phase diagram of CuInP2S6, which is enabled by stacking orders, sheds light on the physics of vdW ferroelectricity and opens an alternative route to tailoring long-range order in vdW layered crystals., Comment: 22 pages, 4 figures

Neural networks demonstrate inherent vulnerability to small, non-random perturbations, emerging as adversarial attacks. Such attacks, born from the gradient of the loss function relative to the input, are discerned as input conjugates, revealing a systemic fragility within the network structure. Intriguingly, a mathematical congruence manifests between this mechanism and the quantum physics' uncertainty principle, casting light on a hitherto unanticipated interdisciplinarity. This inherent susceptibility within neural network systems is generally intrinsic, highlighting not only the innate vulnerability of these networks but also suggesting potential advancements in the interdisciplinary area for understanding these black-box networks., Comment: 13 pages, 3 figures

This paper presents the RBG-Maxwell framework, a relativistic collisional plasma simulator on GPUs. We provide detailed discussions on the fundamental equations, numerical algorithms, implementation specifics, and key testing outcomes. The RBG-Maxwell framework is a robust numerical code designed for simulating the evolution of plasma systems through a kinetic approach on large-scale GPUs. It offers easy adaptability to a wide range of physical systems. Given the appropriate initial distributions, particle masses, charges, differential cross-sections, and external forces (which are not confined to electromagnetic forces), the RBG-Maxwell framework can direct the evolution of a particle system from a non-equilibrium state to a thermal state., Comment: 21 pages, 10 figures

This paper presents a novel 3-D full electromagnetic particle-in-cell (PIC) code called JefiPIC, which uses Jefimenko's equations as the electromagnetic (EM) field solver through a full-space integration method. Leveraging the power of state-of-the-art graphic processing units (GPUs), we have made the challenging integral task of PIC simulations achievable. Our proposed code offers several advantages by utilizing the integral method. Firstly, it offers a natural solution for modeling non-neutral plasmas without the need for pre-processing such as solving Poisson's equation. Secondly, it eliminates the requirement for designing elaborate boundary layers to absorb fields and particles. Thirdly, it maintains the stability of the plasma simulation regardless of the time step chosen. Lastly, it does not require strict charge-conservation particle-to-grid apportionment techniques or electric field divergence amendment algorithms, which are commonly used in finite-difference time-domain (FDTD)-based PIC simulations. To validate the accuracy and advantages of our code, we compared the evolutions of particles and fields in different plasma systems simulated by three other codes. Our results demonstrate that the combination of Jefimenko's equations and the PIC method can produce accurate particle distributions and EM fields in open-boundary plasma systems. Additionally, our code is able to accomplish these computations within an acceptable execution time. This study highlights the effectiveness and efficiency of JefiPIC, showing its potential for advancing plasma simulations., Comment: 21 pages, 18 figures

Despite the successes in many fields, it is found that neural networks are difficult to be both accurate and robust, i.e., high accuracy networks are often vulnerable. Various empirical and analytic studies have substantiated that there is more or less a trade-off between the accuracy and robustness of neural networks. If the property is inherent, applications based on the neural networks are vulnerable with untrustworthy predictions. To more deeply explore and understand this issue, in this study we show that the accuracy-robustness trade-off is an intrinsic property whose underlying mechanism is closely related to the uncertainty principle in quantum mechanics. By relating the loss function in neural networks to the wave function in quantum mechanics, we show that the inputs and their conjugates cannot be resolved by a neural network simultaneously. This work thus provides an insightful explanation for the inevitability of the accuracy-robustness dilemma for general deep networks from an entirely new perspective, and furthermore, reveals a potential possibility to study various properties of neural networks with the mature mathematical tools in quantum physics., Comment: 8 pages, 5 figures

Two-dimensional magnets are promising for nanoscale spintronic applications. Currently, most available candidates are based on $3d$ transition metal compounds, with hexagonal or honeycomb lattice geometry. Here, a GdCl$_3$ monolayer with $4f$ moments is theoretically studied, which can be exfoliated from its existing bulk. Its orthorhombic structure and hendecahedral ion cages are unique in two-dimensional. Furthermore, a significant structural reconstruction is caused by the implantation of Li atoms into its interstitial position, which also lead to ferromagnetism via a double-exchange-like process. Its highly anisotropic conductance may be peculiarly useful for nanoelectronics., Comment: 5 figures

We have calculated the directed flow $v_{1}$ and charge-dependent directed flow $\Delta v_{1}$ for pions and protons in Au+Au collisions at $\sqrt{s_{NN}}=200$GeV by solving the coupled Boltzmann-Maxwell equations self-consistently. Our numerical results show that $v_{1}$ for pions and protons are all negative in the positive mid rapidity region and have similar behavior and magnitude. In contrast we find a quite different behavior in $\Delta v_{1}$ for pions and protons. The difference lies in that $\Delta v_{1}$ for protons mainly comes from pressure gradients of the medium, while the dominant contribution to $\Delta v_{1}$ for pions is from electromagnetic fields. Our results indicate that the effect of the electric field will slightly exceed that of the magnetic and lead to a small negative slope of $\Delta v_{1}$ for pions, Comment: 9 pages, 6 figures; accepted by Phys. Rev. Research

Two-dimensional metals offer intriguing possibilities to explore metallicity and other related properties in systems with reduced dimensionality. Here, following recent experimental reports of synthesis of two-dimensional metallic gallium (gallenene) on insulating substrates, we conduct a computational search of gallenene structures using the Particle Swarm Optimization algorithm, and identify stable low energy structures. Our calculations of the critical temperature for conventional superconductivity yield values $\sim 7$ K for gallenene. We also emulate the presence of the substrate by introducing the external confining potential and test its effect on the structures with unstable phonons.

Based on the Wigner function in local equilibrium, we derive hydrodynamical quantities for a system of polarized spin-1/2 particles: the particle number current density, the energy-momentum tensor, the spin tensor, and the dipole moment tensor. Comparing with ideal hydrodynamics without spin, additional terms at first and second order in the Knudsen number $\text{Kn}$ and the average spin polarization $\chi_s$ have been derived. The Wigner function can be expressed in terms of matrix-valued distributions, whose equilibrium forms are characterized by thermodynamical parameters in quantum statistics. The equations of motions for these parameters are derived by conservation laws at the leading and next-to-leading order $\text{Kn}$ and $\chi_s$., Comment: 8 pages, no figure

In this new version of ZMCintegral, we have added the functionality of multi-function integrations, i.e. the ability to integrate more than $10^{3}$ different functions on GPUs. The Python API remains the similar as the previous versions. For integrands less than 5 dimensions, it usually takes less than 10 minutes to finish the evaluation of $10^{3}$ integrations on one Tesla v100 card. The performance scales linearly with the increasing of the GPUs., Comment: 5pages, 1figure

We have implemented a GPU version of the Jefimenko's equations -- JefiGPU. Given the proper distributions of the source terms $\rho$ (charge density) and $\mathbf{J}$ (current density) in the source volume, the algorithm gives the electromagnetic fields in the observational region (not necessarily overlaps the vicinity of the sources). To verify the accuracy of the GPU implementation, we have compared the obtained results with that of the theoretical ones. Our results show that the deviations of the GPU results from the theoretical ones are around 5\%. Meanwhile, we have also compared the performance of the GPU implementation with a CPU version. The simulation results indicate that the GPU code is significantly faster than the CPU version. Finally, we have studied the parameter dependence of the execution time and memory consumption on one NVIDIA Tesla V100 card. Our code can be consistently coupled to RBG (Relativistic Boltzmann equations on GPUs) and many other GPU-based algorithms in physics., Comment: 21 pages, 8 figures, 4 tables

We have numerically studied the evolution of the heavy ions that expand in a cold background plasma at a large scale. Two typical collective behaviors of the heavy ions are identified with the conditions where only the traversing heavy ion's initial total mass is different. Our work has demonstrated that a difference in the initial total mass of the moving heavy ions is able to induce completely different collective behaviors of the plasma. The simulation is performed via the hybrid model, in which the ions and electrons are treated as classical particles and mass-less fluid, respectively. Due to the imbalance of the electric and magnetic force on the heavy ions, these particles will evolve into different collective patterns at the later time. These patterns manifest a rather different stopping behavior of the moving ions and an opposite drifting direction of the electron fluid at the rim of the expanding plasma. Further numerical and analytical calculations show that the imbalance depends not only on the number densities of the plasma ions, but also on the spatial variations of the magnetic fields. Our work reveals that the collective behavior of the heavy ions is highly non-linear, and the non-linearity is able to induce different phenomena in the evolution of the system at a large scale., Comment: 8 pages, 8 figures

Based on the result in our previous work, we calculate the polarization of quarks from parton scatterings in high energy heavy ion collisions. The result is compared with the STAR data at $\sqrt{s_{NN}}=200$ GeV., Comment: Contribution to the Proceedings of the 28th international conference on ultrarelativistic nucleus-nucleus collisions, Quark Matter 2019

We have developed a numerical framework for a full solution of the relativistic Boltzmann equations for the quark-gluon matter using the multiple Graphics Processing Units (GPUs) on distributed clusters. Including all the $2 \to 2$ scattering processes of 3-flavor quarks and gluons, we compute the time evolution of distribution functions in both coordinate and momentum spaces for the cases of pure gluons, quarks and the mixture of quarks and gluons. By introducing a symmetrical sampling method on GPUs which ensures the particle number conservation, our framework is able to perform the space-time evolution of quark-gluon system towards thermal equilibrium with high performance. We also observe that the gluons naturally accumulate in the soft region at the early time, which may indicate the gluon condensation., Comment: 32 pages, 12 figures

In this updated vesion of ZMCintegral, we have added the functionality of integrations with parameter scan on distributed Graphics Processing Units(GPUs). Given a large parameter grid (up to 10^{10} parameter points to be scanned), the code will evaluate integrations for each parameter grid value. To ensure the evaluation speed, this new functionality employs a direct Monte Carlo method for the integraion. The Python API is kept the same as the previous ones and users have a full flexibility to define their own integrands. The performance of this new functionality is tested for both one node and multi-nodes conditions., Comment: 14 pages, 7 figures(including sub-figures)

Achieving multiferroic two-dimensional (2D) materials should enable numerous functionalities in nanoscale devices. Until now, however, predicted 2D multiferroics are very few and with coexisting yet only loosely coupled (type-I) ferroelectricity and magnetism. Here, a type-II multiferroic MXene Hf$_{2}$VC$_{2}$F$_{2}$ monolayer is identified, where ferroelectricity originates directly from its magnetism. The noncollinear Y-type spin order generates a polarization perpendicular to the spin helical plane. Remarkably, the multiferroic transition is estimated to occur above room temperature. Our investigation should open the door to a new branch of 2D materials for pursuit of intrinsically strong magnetoelectricity., Comment: 4 figures

We propose a microscopic description for the polarization from the first principle through the spin-orbit coupling in particle collisions. The model is different from previous ones based on local equilibrium assumptions for the spin degree of freedom. It is based on scatterings of particles as wave packets, an effective method to deal with particle scatterings at specified impact parameters. The polarization is then the consequence of particle collisions in a non-equilibrium state of spins. The spin-vorticity coupling naturally emerges from the spin-orbit one encoded in polarized scattering amplitudes of collisional integrals when one assumes local equilibrium in momentum but not in spin., Comment: RevTex 4, 54 pages, 4 figures

We have developed a Python package ZMCintegral for multi-dimensional Monte Carlo integration on multiple Graphics Processing Units(GPUs). The package employs a stratified sampling and heuristic tree search algorithm. We have built three versions of this package: one with Tensorflow and other two with Numba, and both support general user defined functions with a user-friendly interface. We have demonstrated that Tensorflow and Numba help inexperienced scientific researchers to parallelize their programs on multiple GPUs with little work. The precision and speed of our package is compared with that of VEGAS for two typical integrands, a 6-dimensional oscillating function and a 9-dimensional Gaussian function. The results show that the speed of ZMCintegral is comparable to that of the VEGAS with a given precision. For heavy calculations, the algorithm can be scaled on distributed clusters of GPUs., Comment: 18 pages, 9 figures

For two-dimensional superconductors, the high stability in ambient conditions is critical for experiments and applications. Few-layer antimonene can be non-degradative over a couple of months, which is superior to the akin black phosphorus. Based on the anisotropic Migdal-Eliashberg theory and maximally-localised Wannier functions, this work predicts that electron-doping and Ca-intercalation can transform $\beta$-Sb bilayer from a semimetal to a superconductor. However, the stability of antimonene bilayer in air trends to be decreased due to the electron doping. To overcome this drawback, two kinds of protective layers (graphene and $h$-BN) are proposed to enhance the stability. Interestingly, the superconducting transition temperature will also be enhanced to $9.6$ K, making it a promising candidate as nanoscale superconductor., Comment: 7 pages, 11 figures

The discovery of superconductivity in the two-leg ladder compound BaFe$_2$S$_3$ has established the 123-type iron chalcogenides as a novel and interesting subgroup of the iron-based superconductors family. However, in this 123 series, BaFe$_2$Se$_3$ is an exceptional member, with a magnetic order and crystalline structure different from all others. Recently, an exciting experiment reported the emergence of superconductivity in BaFe$_2$Se$_3$ at high pressure [J.-J. Ying, et al., Phys. Rev. B 95, 241109 (R) (2017)]. In this publication, we report a first principles study of BaFe$_2$Se$_3$. Our analysis unveils a variety of qualitative differences between BaFe$_2$S$_3$ and BaFe$_2$Se$_3$, including in the latter an unexpected chain of transitions with increasing pressure. First, by gradually reducing the tilting angle of iron ladders, the crystalline structure smoothly transforms from Pnma to Cmcm at ~6 GPa. Second, the system becomes metallic at 10.4 GPa. Third, its unique ambient pressure Block antiferromagnetic ground state is replaced by the more common CX antiferromagnetic order at ~12 GPa, the same magnetic state of the 123-S ladder. This transition is found at a pressure very similar to the experimental superconducting transition. Finally, all magnetic moments vanish at 30 GPa. This reported theoretical diagram of the complete phase evolution is important because of the technical challenges to capture many physical properties in high-pressure experiments. The information obtained in our calculations suggest different characteristics for superconductivity in BaFe$_2$Se$_3$ and BaFe$_2$S$_3$: in 123-S pairing occurs when magnetic moments vanish, while in 123-Se the transition region from Block- to CX-type magnetism appears to catalyze superconductivity. Finally, an additional superconducting dome above ~30 GPa is expected to occur., Comment: 8 pages, 5 figures