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arXiv 2022年

作者： Xu, Limin Mao, Jiahao Gao, Xingyu Liu, Zheng Department of Mathematical Sciences Tsinghua University Beijing100084 China State Key Laboratory of Low Dimensional Quantum Physics Department of Physics Tsinghua University Beijing100084 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China Institute for Advanced Study Tsinghua University Beijing100084 China

Hohenberg-Kohn (HK) theorem is a cornerstone of modern electronic structure calculations. For interacting electrons, given that the internal part of the Hamiltonian (Ĥint), containing the kinetic energy and Couloumb interaction of electrons, has a fixed form, the theorem states that when the electrons are subject to an external electrostatic field, the ground-state density can inversely determine the field, and thus the full Hamiltonian completely. For a general quantum system, a HK-type Hamiltonian in the form of Ĥhk{gi} = Ĥint+Pi giÔi can always be defined, by grouping those terms with fixed or preknown coefficients into Ĥint, and factorizing the remaining as superposition of a set of Hermitian operators {Ôi}. We ask whether the HK theorem can be extended, so that the ground-state expectation values of {Ôi} as the generalized density can in principle be used as the fundamental variables determining all the properties of the system. We show that the question can be addressed by introducing the concept of generalized density correlation matrix (GDCM) defined with respect to the {Ôi} operators. The invertibility of the GDCM represents a mathematically rigorous and practically useful criterion for the extension of HK theorem to be valid. We apply this criterion to several representative systems, including the quantum Ising dimer, the frustration-free systems, N-level quantum systems with fixed inter-level transition amplitude and tunable level energies, and a fermionic Hubbard chain with inhomogeneous on-site interactions. We suggest that for a finite-size system, finding an invertible GDCM under one single {gi} configuration is typically sufficient to establish the generic extensibility of the HK theorem in the entire parameter space. Copyright © 2022, The Authors. All rights reserved.

关键词： Hamiltonians

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Universality of the Dynamic Characteristic Relationship of Electron Correlation in the Two-Photon Double Ionization Process of a Helium-Like System

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Chinese physics Letters 2020年第11期37卷 27-32页

作者： Fei Li Yu-Jun Yang Jing Chen Xiao-Jun Liu Zhi-Yi Wei Bing-Bing Wang Laboratory of Optical Physics Beijing National Laboratory for Condensed Matter PhysicsInstitute of PhysicsChinese Academy of SciencesBeijing 100190China Institute of Atomic and Molecular Physics Jilin UniversityChangchun 130012China Institute of Applied Physics and Computational Mathematics Beijing 100088China HEDPS Center for Applied Physics and TechnologyPeking UniversityBeijing 100084China State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics Wuhan Institute of Physics and MathematicsInnovation Academy for Precision Measurement Science and TechnologyChinese Academy of SciencesWuhan 430071China University of Chinese Academy of Sciences Beijing 100049China

Universality of the dynamic characteristic relationship between the characteristic time tc and the two-electron Coulomb interaction energy V12 of the ground state in the two-photon double ionization process is investigated via changing the parameters of the two-electron atomic system and the corresponding laser *** numerical results show that the product tcV12 keeps constant around 4.1 in the cases of changing the nucleus charge,the electron charge,the electron mass,and changing simultaneously the nucleus charge and the electron *** results demonstrate that the dynamic characteristic relationship in the two-photon double ionization process is *** work sheds more light on the dynamic characteristic relationship in ultrafast processes and may find its application in measurements of attosecond pulses.

关键词： conditions. charge characteristic

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Erratum to:Influences of chemical reactions on polysulfide reduction reaction process on promotor surface in Li-S batteries

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Nano Research 2024年第5期17卷 4643-4643页

作者： Yufeng Luo Zhenhan Fang Zixin Hong Shaorong Duan Haitao Liu Hengcai Wu Qunqing Li Yuegang Zhang Shoushan Fan Wenhui Duan Jiaping Wang Tsinghua-Foxconn Nanotechnology Research Center Tsinghua UniversityBeijing 100084China Department of Physics Tsinghua UniversityBeijing 100084China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China Frontier Science Center for Quantum Information Tsinghua UniversityBeijing 100084China

Erratum to Nano Research,2024,17(4):2712-2718 https://***/10.1007/s12274-023-6129-5 The affiliation of the author,Wenhui Duan,is“2 Department of physics,Tsinghua University,Beijing 100084,China”,instead of“1 Tsinghua-Foxconn Nanotechnology Research Center,Tsinghua University,Beijing 100084,China;2 Department of physics,Tsinghua University,Beijing 100084,China”.And the affiliation of the author,Wenhui Duan,in the online version and the ESM file of this paper has been corrected.

关键词： sulfide corrected tor

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Lax pairs informed neural networks solving integrable systems

arXiv

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arXiv 2024年

作者： Pu, Juncai Chen, Yong Institute of Applied Physics and Computational Mathematics Beijing100094 China School of Mathematical Sciences Key Laboratory of Mathematics and Engineering Applications Ministry of Education Shanghai Key Laboratory of PMMP East China Normal University Shanghai200241 China College of Mathematics and Systems Science Shandong University of Science and Technology Qingdao266590 China

Lax pairs are one of the most important features of integrable system. In this work, we propose the Lax pairs informed neural networks (LPNNs) tailored for the integrable systems with Lax pairs by designing novel network architectures and loss functions, comprising LPNN-v1 and LPNN-v2. The most noteworthy advantage of LPNN-v1 is that it can transform the solving of nonlinear integrable systems into the solving of a linear Lax pairs spectral problems, and it not only efficiently solves data-driven localized wave solutions, but also obtains spectral parameter and corresponding spectral function in Lax pairs spectral problems of the integrable systems. On the basis of LPNN-v1, we additionally incorporate the compatibility condition/zero curvature equation of Lax pairs in LPNN-v2, its major advantage is the ability to solve and explore high-accuracy data-driven localized wave solutions and associated spectral problems for integrable systems with Lax pairs. The numerical experiments focus on studying abundant localized wave solutions for very important and representative integrable systems with Lax pairs spectral problems, including the soliton solution of the Korteweg-de Vries (KdV) euqation and modified KdV equation, rogue wave solution of the nonlinear Schrödinger equation, kink solution of the sine-Gordon equation, non-smooth peakon solution of the Camassa-Holm equation and pulse solution of the short pulse equation, as well as the line-soliton solution of Kadomtsev-Petviashvili equation and lump solution of high-dimensional KdV equation. The innovation of this work lies in the pioneering integration of Lax pairs informed of integrable systems into deep neural networks, thereby presenting a fresh methodology and pathway for investigating data-driven localized wave solutions and Lax pairs spectral problems. Copyright © 2024, The Authors. All rights reserved.

关键词： Korteweg-de Vries equation

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Ground state phases of the two-dimension electron gas with a unified variational approach

arXiv

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arXiv 2024年

作者： Smith, Conor Chen, Yixiao Levy, Ryan Yang, Yubo Morales, Miguel A. Zhang, Shiwei Center for Computational Quantum Physics Flatiron Institute New YorkNY10010 United States Department of Electrical and Computer Engineering University of New Mexico AlbuquerqueNM87131 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The two-dimensional electron gas (2DEG) is a fundamental model, which is drawing increasing interest because of recent advances in experimental and theoretical studies of 2D materials. Current understanding of the ground state of the 2DEG relies on quantum Monte Carlo calculations, based on variational comparisons of different ansatze for different phases. We use a single variational ansatz, a general backflow-type wave function using a message-passing neural quantum state architecture, for a unified description across the entire density range. The variational optimization consistently leads to lower ground-state energies than previous best results. Transition into a Wigner crystal (WC) phase occurs automatically at rs = 37±1, a density lower than currently believed. Between the liquid and WC phases, the same ansatz and variational search strongly suggest the existence of intermediate states in a broad range of densities, with enhanced short-range nematic spin correlations. Copyright © 2024, The Authors. All rights reserved.

关键词： Message passing

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Improved Image Compressive Sensing Recovery with Low-Rank Prior and Deep Image Prior

SSRN

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SSRN 2022年

作者： Wu, Yumo Yin, Junping Chen, Wengu School of Mathematics and Statistics Northeast Normal University Changchun China Northeast Normal University Changchun China Beijing Institute of Applied Physics and Computational Mathematics Institute of Applied Physics and Computational Mathematics Beijing100094 China Shanghai Zhangjiang Academy of Mathematics Shanghai Zhangjiang Academy of Mathematics Shanghai201203 China

Compressive sensing (CS) is an advanced and worth exploring signal acquisition and processing method. Its reconstruction process aims to recover an image with more information from an undersampled image. Model-based recovery is a widely used mechanism to solve such an ill-posed imaging compressive sensing problem. Meanwhile, enormous progress has been made recently in combining deep learning with traditional models. Inspired by this, in our discussion, we choose a better non-convex low-rank approximation function as part of the regularization term. And the other part of the regularization term introduces a pre-trained deep denoiser as the image prior. To get a better approximation of the estimated rank, we exploit the weighted Schatten p-norm which could be a non-convex surrogate function of the rank function. The choice of p-values can enhance the generalization and flexibility of the model. We use the alternating direction method of multiplier (ADMM) to divide the energy function into some subproblems for different variables with closed-form solutions for numerical calculation. Further, the convergence of the proposed method is also illustrated. Finally, a large number of comparative experiments, including deep learning methods, prove the effectiveness of our method, especially at low sampling rates. © 2022, The Authors. All rights reserved.

关键词： Compressed sensing

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Axisymmetric weak solutions to stationary compressible Navier-Stokes equations with critical indices

arXiv

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arXiv 2023年

作者： Fan, Xinyu Jiang, Song Hua Loo-Keng Center for Mathematical Sciences AMSS Chinese Academy of Sciences Beijing100190 China Institute of Applied Physics and Computational Mathematics Beijing100088 China

This paper studies the isothermal stationary compressible Navier-Stokes equations on 2 × T and the cylinder ⅅ × T with ⅅ the 2-dimensional unit disc. There are two critical exponents in such settings: The heat ratio γ = 1 is an end point of the classical theory on weak solutions;the axisymmetric solutions in the unbounded domain 2 × T involve the critical index of Sobolev’s inequality. Some new observations based on the cancellation structure of the equations are collected to get over these obstacles due to critical exponents. Copyright © 2023, The Authors. All rights reserved.

关键词： Navier Stokes equations

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Numerical Study on the Whole Process of Fireball Evolution in Strong Explosion

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Communications in Theoretical physics 2019年第11期71卷 1388-1392页

作者： Yin Xia Chuang Xue Chen-Guang Li Guang-Wei Meng Ying-Kui Zhao Jun Yan Bai-Wen Li Institute of Applied Physics and Computational Mathematics

With the actual mean free path for radiation in air and a simplified nuclear device, a one-dimension simulation research on fireball phenomenon in a sea level atmosphere is carried out based on the multi-group radiation hydrodynamic codes(RDMG). It is shown that our theoretical calculations can describe the whole process of the fireball evolution for strong explosions from the early X-ray expansion stage to the shock wave propagation stage. The radius of the shock wave and the brightness of the fireball are in good agreement with the experimental results. The whole thermal radiation power curve of the fireball evolution for strong atmospheric explosion at sea level is plotted for the first time. The impact of radiation opacity of the nuclear device material on the early fireball phenomenon is also studied. It is found that trajectories of the radiation fronts and case shocks change with the opacity of equivalent device *** our simulations, we find that only the early fireball depends on the details of the nuclear device, and after the formation of main shock, the evolution is determined by the properties of hot air for strong atmospheric explosion.

关键词： fireball phenomenon radiation transfer equation the shock wave brightness

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Preliminary investigation on electrothermal instabilities in early phases of cylindrical foil implosions on primary test stand facility

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Chinese physics B 2019年第2期28卷 352-357页

作者： Guanqiong Wang Delong Xiao Jiakun Dan Yang Zhang Ning Ding Xianbin Huang Xiaoguang Wang Shunkai Sun Chuang Xue Xiaojian Shu Institute of Applied Physics and Computational Mathematics Institute of Fluid Physics Chinese Academy of Engineering Physics

Recent experiments on the implosions of 15-mm long and 2-μm thick aluminum liners having a diameter of 12.8 mm have been performed on the primary test stand(PTS) facility. The stratified structures are observed as alternating dark and light transverse stripes in the laser shadowgraph images. These striations perpendicular to the current flow are formed early in the implosion, i.e., at the stage when the bulk of the material mass was almost at rest. A two-dimensional(2 D)magnetohydrodynamics(MHD) code is employed to simulate the behavior of liner dynamics in the early phases. It is found that the striations may be produced by the electrothermal instability(ETI) that results from non-uniform Joule heating due to the characteristic relation between the resistivity and the temperature. In 2 D simulations, the stratified structures can be seen obviously in both density and temperature contours as the liner expands rapidly. By analyzing instability spectrum, the dominant wavelengths of the perturbations are 8.33 μm–20.0 μm, which agree qualitatively with the theoretical *** is also interesting to show that ETI provides a significant seed to the subsequent magneto Rayleigh–Taylor(MRT)instability.

关键词： Z-pinch electrothermal instability magnetohydrodynamics(MHD) simulations

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Atomic determination of the nuclear quadrupole moment Q(209Bi) using the multi-configuration Dirac-Hartree-Fock method

arXiv

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arXiv 2025年

作者： Li, Jiguang Bieron, Jacek Godefroid, Michel Jönsson, Per Institute of Applied Physics and Computational Mathematics Beijing100088 China Instytut Fizyki Teoretycznej Uniwersytet Jagielloński Kraków Poland Université Libre de Bruxelles Brussels1050 Belgium Department of Materials Science and Applied Mathematics Malmö University MalmöS-20506 Sweden

The multiconfiguration Dirac-Hartree-Fock method implemented in the Grasp2018 package was employed to calculate the magnetic dipole hyperfine interaction constants and electric field gradients of levels in the ground configuration of the neutral bismuth atom. Combining the calculated electric field gradient of the ground state with the measured electric quadrupole hyperfine interaction constant, we extracted the nuclear quadrupole moment for the 209Bi isotope, Q(209Bi) = −422(22) mb. This value, together with other results obtained from atomic- and molecular-structure calculations, created the "world average" nuclear quadrupole moment of this isotope, Q(209Bi) = −420(17) mb. © 2025, CC BY.

关键词： Atoms

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