arXiv - PHYS - Statistical Mechanics最新文献

筛选
英文 中文
Breaking the Brownian Barrier: Models and Manifestations of Molecular Diffusion in Complex Fluids 打破布朗障碍:复杂流体中的分子扩散模型与表现形式
arXiv - PHYS - Statistical Mechanics Pub Date : 2024-09-06 DOI: arxiv-2409.04199
Harish Srinivasan, V. K. Sharma, S. Mitra
{"title":"Breaking the Brownian Barrier: Models and Manifestations of Molecular Diffusion in Complex Fluids","authors":"Harish Srinivasan, V. K. Sharma, S. Mitra","doi":"arxiv-2409.04199","DOIUrl":"https://doi.org/arxiv-2409.04199","url":null,"abstract":"Over a century ago, Einstein formulated a precise mathematical model for\u0000describing Brownian motion. While this model adequately explains the diffusion\u0000of micron-sized particles in fluids, its limitations become apparent when\u0000applied to molecular self-diffusion in fluids. The foundational principles of\u0000Gaussianity and Markovianity, central to the Brownian diffusion paradigm, are\u0000insufficient for describing molecular diffusion, particularly in complex fluids\u0000characterized by intricate intermolecular interactions and hindered relaxation\u0000processes. This perspective delves into the nuanced behavior observed in\u0000diverse complex fluids, including molecular self-assembly, deep eutectic\u0000solvents, and ionic liquids, with a specific focus on modeling self-diffusion\u0000within these media. We explore the potential of extending diffusion models to\u0000incorporate non-Gaussian and non-Markovian effects by augmenting the Brownian\u0000model using non-local diffusion equations. Further, we validate the\u0000applicability of these models by utilizing them to describe results from\u0000quasielastic neutron scattering and MD simulations.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"2012 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding and Majorana-Schrödinger Cat States 拓扑量子位的腔体控制:融合规则、安永编织和马约拉纳-薛定谔猫态
arXiv - PHYS - Statistical Mechanics Pub Date : 2024-09-06 DOI: arxiv-2409.04515
Luis Quiroga, Fernando J. Gómez-Ruiz, Ivan A. Bocanegra-Garay, Ferney J. Rodríguez, Carlos Tejedor
{"title":"Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding and Majorana-Schrödinger Cat States","authors":"Luis Quiroga, Fernando J. Gómez-Ruiz, Ivan A. Bocanegra-Garay, Ferney J. Rodríguez, Carlos Tejedor","doi":"arxiv-2409.04515","DOIUrl":"https://doi.org/arxiv-2409.04515","url":null,"abstract":"We investigate the impact of introducing a local cavity within the center of\u0000a topological chain, revealing profound effects on the system's quantum states.\u0000Notably, the cavity induces a scissor-like effect that bisects the chain,\u0000liberating Majorana zero modes (MZMs) within the bulk. Our results demonstrate\u0000that this setup enables the observation of non-trivial fusion rules and\u0000braiding -- key signatures of non-Abelian anyons -- facilitated by the\u0000spatially selective ultra-strong coupling of the cavity photon field. These MZM\u0000characteristics can be directly probed through fermionic parity readouts and\u0000photon Berry phases, respectively. Furthermore, by leveraging the symmetry\u0000properties of fermion modes within a two-site cavity, we propose a novel method\u0000for generating MZM-polariton Schr\"odinger cat states. Our findings present a\u0000significant advancement in the control of topological quantum systems, offering\u0000new avenues for both fundamental research and potential quantum computing\u0000applications.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Colloidoscope: Detecting Dense Colloids in 3d with Deep Learning 胶体镜:利用深度学习检测 3D 中的致密胶体
arXiv - PHYS - Statistical Mechanics Pub Date : 2024-09-06 DOI: arxiv-2409.04603
Abdelwahab Kawafi, Lars Kürten, Levke Ortlieb, Yushi Yang, Abraham Mauleon Amieva, James E. Hallett, C. Patrick Royall
{"title":"Colloidoscope: Detecting Dense Colloids in 3d with Deep Learning","authors":"Abdelwahab Kawafi, Lars Kürten, Levke Ortlieb, Yushi Yang, Abraham Mauleon Amieva, James E. Hallett, C. Patrick Royall","doi":"arxiv-2409.04603","DOIUrl":"https://doi.org/arxiv-2409.04603","url":null,"abstract":"Colloidoscope is a deep learning pipeline employing a 3D residual Unet\u0000architecture, designed to enhance the tracking of dense colloidal suspensions\u0000through confocal microscopy. This methodology uses a simulated training dataset\u0000that reflects a wide array of real-world imaging conditions, specifically\u0000targeting high colloid volume fraction and low-contrast scenarios where\u0000traditional detection methods struggle. Central to our approach is the use of\u0000experimental signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and\u0000point-spread-functions (PSFs) to accurately quantify and simulate the\u0000experimental data. Our findings reveal that Colloidoscope achieves superior\u0000recall in particle detection (finds more particles) compared to conventional\u0000heuristic methods. Simultaneously, high precision is maintained (high fraction\u0000of true positives.) The model demonstrates a notable robustness to\u0000photobleached samples, thereby prolonging the imaging time and number of frames\u0000than may be acquired. Furthermore, Colloidoscope maintains small scale\u0000resolution sufficient to classify local structural motifs. Evaluated across\u0000both simulated and experimental datasets, Colloidoscope brings the advancements\u0000in computer vision offered by deep learning to particle tracking at high volume\u0000fractions. We offer a promising tool for researchers in the soft matter\u0000community, this model is deployed and available to use pretrained:\u0000https://github.com/wahabk/colloidoscope.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Highly efficient path-integral molecular dynamics simulations with GPUMD using neuroevolution potentials: Case studies on thermal properties of materials 使用神经进化势的 GPUMD 高效路径积分分子动力学模拟:材料热特性案例研究
arXiv - PHYS - Statistical Mechanics Pub Date : 2024-09-06 DOI: arxiv-2409.04430
Penghua Ying, Wenjiang Zhou, Lucas Svensson, Erik Fransson, Fredrik Eriksson, Ke Xu, Ting Liang, Bai Song, Shunda Chen, Paul Erhart, Zheyong Fan
{"title":"Highly efficient path-integral molecular dynamics simulations with GPUMD using neuroevolution potentials: Case studies on thermal properties of materials","authors":"Penghua Ying, Wenjiang Zhou, Lucas Svensson, Erik Fransson, Fredrik Eriksson, Ke Xu, Ting Liang, Bai Song, Shunda Chen, Paul Erhart, Zheyong Fan","doi":"arxiv-2409.04430","DOIUrl":"https://doi.org/arxiv-2409.04430","url":null,"abstract":"Path-integral molecular dynamics (PIMD) simulations are crucial for\u0000accurately capturing nuclear quantum effects in materials. However, their\u0000computational intensity and reliance on multiple software packages often limit\u0000their applicability at large scales. Here, we present an integration of PIMD\u0000methods, including thermostatted ring-polymer molecular dynamics (TRPMD), into\u0000the open-source GPUMD package, combined with highly accurate and efficient\u0000machine-learned neuroevolution potential (NEP) models. This approach achieves\u0000almost the accuracy of first-principles calculations with the computational\u0000efficiency of empirical potentials, enabling large-scale atomistic simulations\u0000that incorporate nuclear quantum effects. We demonstrate the efficacy of the\u0000combined NEP-PIMD approach by examining various thermal properties of diverse\u0000materials, including lithium hydride (LiH), three porous metal-organic\u0000frameworks (MOFs), and elemental aluminum. For LiH, our NEP-PIMD simulations\u0000successfully capture the isotope effect, reproducing the experimentally\u0000observed dependence of the lattice parameter on the reduced mass. For MOFs, our\u0000results reveal that achieving good agreement with experimental data requires\u0000consideration of both nuclear quantum effects and dispersive interactions. For\u0000aluminum, the TRPMD method effectively captures thermal expansion and phonon\u0000properties, aligning well with quantum mechanical predictions. This efficient\u0000NEP-PIMD approach opens new avenues for exploring complex material properties\u0000influenced by nuclear quantum effects, with potential applications across a\u0000broad range of materials.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dimensional crossover via confinement in the lattice Lorentz gas 通过晶格洛伦兹气体中的约束实现维度交叉
arXiv - PHYS - Statistical Mechanics Pub Date : 2024-09-06 DOI: arxiv-2409.04289
A. Squarcini, A. Tinti, P. Illien, O. Bénichou, T. Franosch
{"title":"Dimensional crossover via confinement in the lattice Lorentz gas","authors":"A. Squarcini, A. Tinti, P. Illien, O. Bénichou, T. Franosch","doi":"arxiv-2409.04289","DOIUrl":"https://doi.org/arxiv-2409.04289","url":null,"abstract":"We consider a lattice model in which a tracer particle moves in the presence\u0000of randomly distributed immobile obstacles. The crowding effect due to the\u0000obstacles interplays with the quasi-confinement imposed by wrapping the lattice\u0000onto a cylinder. We compute the velocity autocorrelation function and show that\u0000already in equilibrium the system exhibits a dimensional crossover from two- to\u0000one-dimensional as time progresses. A pulling force is switched on and we\u0000characterize analytically the stationary state in terms of the stationary\u0000velocity and diffusion coefficient. Stochastic simulations are used to discuss\u0000the range of validity of the analytic results. Our calculation, exact to first\u0000order in the obstacle density, holds for arbitrarily large forces and\u0000confinement size.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Boundary dissipative spin chains with partial solvability inherited from system Hamiltonians 从系统哈密顿继承部分可解性的边界耗散自旋链
arXiv - PHYS - Statistical Mechanics Pub Date : 2024-09-05 DOI: arxiv-2409.03208
Chihiro Matsui, Naoto Tsuji
{"title":"Boundary dissipative spin chains with partial solvability inherited from system Hamiltonians","authors":"Chihiro Matsui, Naoto Tsuji","doi":"arxiv-2409.03208","DOIUrl":"https://doi.org/arxiv-2409.03208","url":null,"abstract":"Partial solvability plays an important role in the context of statistical\u0000mechanics, since it has turned out to be closely related to the emergence of\u0000quantum many-body scar states, i.e., exceptional energy eigenstates which do\u0000not obey the strong version of the eigenstate themalization hypothesis. We show\u0000that partial solvability of a quantum many-body system can be maintained even\u0000when the system is coupled to boundary dissipators under certain conditions. We\u0000propose two mechanisms that support partially solvable structures in boundary\u0000dissipative systems: The first one is based on the restricted spectrum\u0000generating algebra, while the second one is based on the Hilbert space\u0000fragmentation. From these structures, we derive exact eigenmodes of the\u0000Gorini-Kossakowski-Sudarshan-Lindblad equation for a family of quantum spin\u0000chain models with boundary dissipators, where we find various intriguing\u0000phenomena arising from the partial solvability of the open quantum systems,\u0000including persistent oscillations (quantum synchronization) and the existence\u0000of the matrix product operator symmetry. We discuss how the presence of\u0000solvable eigenmodes affects long-time behaviors of observables in boundary\u0000dissipative spin chains based on numerical simulations using the quantum\u0000trajectory method.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bayesian inference of wall torques for active Brownian particles 活动布朗粒子壁面力矩的贝叶斯推理
arXiv - PHYS - Statistical Mechanics Pub Date : 2024-09-05 DOI: arxiv-2409.03533
Sascha Lambert, Merle Duchene, Stefan Klumpp
{"title":"Bayesian inference of wall torques for active Brownian particles","authors":"Sascha Lambert, Merle Duchene, Stefan Klumpp","doi":"arxiv-2409.03533","DOIUrl":"https://doi.org/arxiv-2409.03533","url":null,"abstract":"The motility of living things and synthetic self-propelled objects is often\u0000described using Active Brownian particles. To capture the interaction of these\u0000particles with their often complex environment, this model can be augmented\u0000with empirical forces or torques, for example, to describe their alignment with\u0000an obstacle or wall after a collision. Here, we assess the quality of these\u0000empirical models by comparing their output predictions with trajectories of\u0000rod-shaped active particles that scatter sterically at a flat wall. We employ a\u0000classical least-squares method to evaluate the instantaneous torque. In\u0000addition, we lay out a Bayesian inference procedure to construct the posterior\u0000distribution of plausible model parameters. In contrast to the least squares\u0000fit, the Bayesian approach does not require orientational data of the active\u0000particle and can readily be applied to experimental tracking data.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finite time path field theory perturbative methods for local quantum spin chain quenches 局部量子自旋链淬火的有限时间路径场论微扰方法
arXiv - PHYS - Statistical Mechanics Pub Date : 2024-09-05 DOI: arxiv-2409.03832
Domagoj Kuić, Alemka Knapp, Diana Šaponja-Milutinović
{"title":"Finite time path field theory perturbative methods for local quantum spin chain quenches","authors":"Domagoj Kuić, Alemka Knapp, Diana Šaponja-Milutinović","doi":"arxiv-2409.03832","DOIUrl":"https://doi.org/arxiv-2409.03832","url":null,"abstract":"We discuss local magnetic field quenches using perturbative methods of finite\u0000time path field theory in the following spin chains: Ising and XY in a\u0000transverse magnetic field. Their common characteristics are: i) they are\u0000integrable via mapping to second quantized noninteracting fermion problem; ii)\u0000when the ground state is nondegenerate (true for finite chains except in\u0000special cases) it can be represented as a vacuum of Bogoliubov fermions. By\u0000switching on a local magnetic field perturbation at finite time, the problem\u0000becomes nonintegrable and must be approached via numeric or perturbative\u0000methods. Using the formalism of finite time path field theory based on Wigner\u0000transforms of projected functions, we show how to: i) calculate the basic\u0000\"bubble\" diagram in the Loschmidt echo of a quenched chain to any order in the\u0000perturbation; ii) resum the generalized Schwinger-Dyson equation for the\u0000fermion two point retarded functions in the \"bubble\" diagram, hence achieving\u0000the resummation of perturbative expansion of Loschmidt echo for a wide range of\u0000perturbation strengths under certain analiticity assumptions. Limitations of\u0000the assumptions and possible generalizations beyond it and also for other spin\u0000chains are further discussed.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"66 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamics and kinetic theory of hard spheres under strong confinement 强约束下硬球的动力学和动力学理论
arXiv - PHYS - Statistical Mechanics Pub Date : 2024-09-05 DOI: arxiv-2409.03452
J. Javier Brey, M. I. García de Soria, P. Maynar
{"title":"Dynamics and kinetic theory of hard spheres under strong confinement","authors":"J. Javier Brey, M. I. García de Soria, P. Maynar","doi":"arxiv-2409.03452","DOIUrl":"https://doi.org/arxiv-2409.03452","url":null,"abstract":"The kinetic theory description of a low density gas of hard spheres or disks,\u0000confined between two parallel plates separated a distance smaller than twice\u0000the diameter of the particles, is addressed starting from the Liouville\u0000equation of the system. The associated BBGKY hierarchy of equations for the\u0000reduced distribution functions is expanded in powers of a parameter measuring\u0000the density of the system in the appropriate dimensionless units. The Boltzmann\u0000level of description is obtained by keeping only the two lowest orders in the\u0000parameter. In particular, the one-particle distribution function obeys a couple\u0000of equations. Contrary to what happens with a Boltzmann-like kinetic equation\u0000that has been proposed for the same system on a heuristic basis, the kinetic\u0000theory formulated here admits stationary solutions that are consistent with\u0000equilibrium statistical mechanics, both in absence and presence of external\u0000fields. In the latter case, the density profile is rather complex due to the\u0000coupling between the inhomogeneities generated by the confinement and by the\u0000external fields. The general theory formulated provides a solid basis for the\u0000study of the properties of strongly confined dilute gases.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"66 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Efficient Enumeration of Flat-Foldings : Study on Random Single Vertex Origami 平面折纸的高效枚举:随机单顶点折纸研究
arXiv - PHYS - Statistical Mechanics Pub Date : 2024-09-05 DOI: arxiv-2409.03240
Chihiro Nakajima
{"title":"An Efficient Enumeration of Flat-Foldings : Study on Random Single Vertex Origami","authors":"Chihiro Nakajima","doi":"arxiv-2409.03240","DOIUrl":"https://doi.org/arxiv-2409.03240","url":null,"abstract":"This paper deals with themes such as approximate counting/evaluation of the\u0000total number of flat-foldings for random origami diagrams, evaluation of the\u0000values averaged over various instances, obtaining forcing sets for general\u0000origami diagrams, and evaluation of average computational complexity. An\u0000approach to the above problems using a physical model and an efficient size\u0000reduction method for them is proposed. Using a statistical mechanics model and\u0000a numerical method of approximate enumeration based on it, we give the result\u0000of approximate enumeration of the total number of flat-foldings of\u0000single-vertex origami diagram with random width of angles gathering around the\u0000central vertex, and obtain its size dependence for an asymptotic prediction\u0000towards the limit of infinite size. In addition, an outlook with respect to the\u0000chained determination of local stacking orders of facets caused by the\u0000constraint that prohibits the penetration of them is also provided from the\u0000viewpoint of organizing the terms included in the physical model. A method to\u0000efficiently solve the problem of the determination or enumeration of\u0000flat-foldings is discussed based on the above perspectives. This is thought to\u0000be closely related to forcing sets.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"76 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信