Localization due to disorder has been one of the most intriguing theoretical concepts that evolved in condensed matter physics.Here,we expand the theory of localization by considering two types of disorders at the sam...Localization due to disorder has been one of the most intriguing theoretical concepts that evolved in condensed matter physics.Here,we expand the theory of localization by considering two types of disorders at the same time,namely,the original Anderson’s disorder and the structural defect disorder,which has been suggested to be a key component in recently discovered two-dimensional amorphous materials.While increasing the degree of both disorders could induce localization of wavefunction in real space,we find that a small degree of structural defect disorder can significantly enhance the localization.As the degree of structural defect disorder increases,localized states quickly appear within the extended phase to enter a broad crossover region with mixed phases.We establish two-dimensional diagrams for the wavefunction localization and conductivity to highlight the interplay between the two types of disorders.Our theoretical model provides a comprehensive understanding of localization in two-dimensional amorphous materials and highlights the promising tunability of their transport properties.展开更多
Anderson acceleration(AA)is an extrapolation technique designed to speed up fixed-point iterations.For optimization problems,we propose a novel algorithm by combining the AA with the energy adaptive gradient method(AE...Anderson acceleration(AA)is an extrapolation technique designed to speed up fixed-point iterations.For optimization problems,we propose a novel algorithm by combining the AA with the energy adaptive gradient method(AEGD)[arXiv:2010.05109].The feasibility of our algorithm is ensured in light of the convergence theory for AEGD,though it is not a fixed-point iteration.We provide rigorous convergence rates of AA for gradient descent(GD)by an acceleration factor of the gain at each implementation of AA-GD.Our experimental results show that the proposed AA-AEGD algorithm requires little tuning of hyperparameters and exhibits superior fast convergence.展开更多
The aim of this study of the spatial dispersion of tin, niobium and tantalum mineralization associated with the Mayo Darlé granitoids was to produce prospecting guides through predictive maps of Sn, Nb and Ta in ...The aim of this study of the spatial dispersion of tin, niobium and tantalum mineralization associated with the Mayo Darlé granitoids was to produce prospecting guides through predictive maps of Sn, Nb and Ta in the region. It was based on a database (in appendix) obtained after analysis of rock samples (greisens and quartz veins) collected in the field, using a portable X-ray fluorescence (XRF) spectrometer. Two approaches were used: 1) structural studies in the field using the directions of veins and fractures 2) the use of variographic maps, an essential element in geostatistics for determining directional anisotropies. A joint synthesis of the modelling results shows that tin, tantalum and niobium mineralization at Mayo Darlé is concentrated along strike intervals N315E to N320E, with mineralization also occurring along strike N35E for high-grade Sn, medium-grade Ta and low-grade Nb. In short, mineral concentrations disperse progressively in space: positively from east to west for tantalum and niobium, and inversely for tin.展开更多
Three women,as far as is known,captured Denis Thatcher’sheart:the famous Margaret,his first wife Margot,and his daugh-ter Carol.Of these,Carol must be the most doting.This is notto say anything against Margare,a duti...Three women,as far as is known,captured Denis Thatcher’sheart:the famous Margaret,his first wife Margot,and his daugh-ter Carol.Of these,Carol must be the most doting.This is notto say anything against Margare,a dutiful wife who no doubtseverely scolded the likes of Alan Clark or anyone else who展开更多
Anderson localization of phonons is a kind of phonon wave effect,which has been proved to occur in many structures with disorders.In this work,we introduced aperiodicity to boron nitride/carbon nanotube superlattices(...Anderson localization of phonons is a kind of phonon wave effect,which has been proved to occur in many structures with disorders.In this work,we introduced aperiodicity to boron nitride/carbon nanotube superlattices(BN/C NT SLs),and used molecular dynamics to calculate the thermal conductivity and the phonon transmission spectrum of the models.The existence of phonon Anderson localization was proved in this quasi one-dimensional structure by analyzing the phonon transmission spectra.Moreover,we introduced interfacial mixing to the aperiodic BN/C NT SLs and found that the coexistence of the two disorder entities(aperiodicity and interfacial mixing)can further decrease the thermal conductivity.In addition,we also showed that anharmonicity can destroy phonon localization at high temperatures.This work provides a reference for designing thermoelectric materials with low thermal conductivity by taking advantage of phonon localization.展开更多
Based on the algebraic equation of motion(AEOM)approach,we have studied the single-impurity Anderson model by analytically solving the AEOM of the f-electron one-particle Green function in the Kondo limit.The related ...Based on the algebraic equation of motion(AEOM)approach,we have studied the single-impurity Anderson model by analytically solving the AEOM of the f-electron one-particle Green function in the Kondo limit.The related spectral function satisfies the sum rule and shows that there is a well-known three-peak structure at zero temperature.In the low energy limit,we obtain the analytical formula of the Kondo temperature that is the same as the exact solution in form except for a prefactor.We also show that the shape of the Kondo resonance is the Lorentzian form and the corresponding weight is proportional to the spin-flip correlation function.展开更多
In this paper, we consider the continuous parabolic Anderson model with a logcorrelated Gaussian field, and obtain the precise quenched long-time asymptotics and spatial asymptotics. To overcome the difficulties arisi...In this paper, we consider the continuous parabolic Anderson model with a logcorrelated Gaussian field, and obtain the precise quenched long-time asymptotics and spatial asymptotics. To overcome the difficulties arising from the log-correlated Gaussian field in the proof of the lower bound of the spatial asymptotics, we first establish the relation between quenched long-time asymptotics and spatial asymptotics, and then get the lower bound of the spatial asymptotics through the lower bound of the quenched long-time asymptotics.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.92165101)the National Key R&D Program of China(Grant No.2021YFA1400500)+1 种基金the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB33000000)the Beijing Natural Science Foundation(Grant No.JQ22001).We are grateful for computational resources supported by High-performance Computing Platform of Peking University.
文摘Localization due to disorder has been one of the most intriguing theoretical concepts that evolved in condensed matter physics.Here,we expand the theory of localization by considering two types of disorders at the same time,namely,the original Anderson’s disorder and the structural defect disorder,which has been suggested to be a key component in recently discovered two-dimensional amorphous materials.While increasing the degree of both disorders could induce localization of wavefunction in real space,we find that a small degree of structural defect disorder can significantly enhance the localization.As the degree of structural defect disorder increases,localized states quickly appear within the extended phase to enter a broad crossover region with mixed phases.We establish two-dimensional diagrams for the wavefunction localization and conductivity to highlight the interplay between the two types of disorders.Our theoretical model provides a comprehensive understanding of localization in two-dimensional amorphous materials and highlights the promising tunability of their transport properties.
基金partially supported by the National Science Foundation under(Grant DMS No.1812666)。
文摘Anderson acceleration(AA)is an extrapolation technique designed to speed up fixed-point iterations.For optimization problems,we propose a novel algorithm by combining the AA with the energy adaptive gradient method(AEGD)[arXiv:2010.05109].The feasibility of our algorithm is ensured in light of the convergence theory for AEGD,though it is not a fixed-point iteration.We provide rigorous convergence rates of AA for gradient descent(GD)by an acceleration factor of the gain at each implementation of AA-GD.Our experimental results show that the proposed AA-AEGD algorithm requires little tuning of hyperparameters and exhibits superior fast convergence.
文摘The aim of this study of the spatial dispersion of tin, niobium and tantalum mineralization associated with the Mayo Darlé granitoids was to produce prospecting guides through predictive maps of Sn, Nb and Ta in the region. It was based on a database (in appendix) obtained after analysis of rock samples (greisens and quartz veins) collected in the field, using a portable X-ray fluorescence (XRF) spectrometer. Two approaches were used: 1) structural studies in the field using the directions of veins and fractures 2) the use of variographic maps, an essential element in geostatistics for determining directional anisotropies. A joint synthesis of the modelling results shows that tin, tantalum and niobium mineralization at Mayo Darlé is concentrated along strike intervals N315E to N320E, with mineralization also occurring along strike N35E for high-grade Sn, medium-grade Ta and low-grade Nb. In short, mineral concentrations disperse progressively in space: positively from east to west for tantalum and niobium, and inversely for tin.
文摘Three women,as far as is known,captured Denis Thatcher’sheart:the famous Margaret,his first wife Margot,and his daugh-ter Carol.Of these,Carol must be the most doting.This is notto say anything against Margare,a dutiful wife who no doubtseverely scolded the likes of Alan Clark or anyone else who
文摘Anderson localization of phonons is a kind of phonon wave effect,which has been proved to occur in many structures with disorders.In this work,we introduced aperiodicity to boron nitride/carbon nanotube superlattices(BN/C NT SLs),and used molecular dynamics to calculate the thermal conductivity and the phonon transmission spectrum of the models.The existence of phonon Anderson localization was proved in this quasi one-dimensional structure by analyzing the phonon transmission spectra.Moreover,we introduced interfacial mixing to the aperiodic BN/C NT SLs and found that the coexistence of the two disorder entities(aperiodicity and interfacial mixing)can further decrease the thermal conductivity.In addition,we also showed that anharmonicity can destroy phonon localization at high temperatures.This work provides a reference for designing thermoelectric materials with low thermal conductivity by taking advantage of phonon localization.
基金Project supported by the National Natural Science Foundation of China(Grant No.11974420)。
文摘Based on the algebraic equation of motion(AEOM)approach,we have studied the single-impurity Anderson model by analytically solving the AEOM of the f-electron one-particle Green function in the Kondo limit.The related spectral function satisfies the sum rule and shows that there is a well-known three-peak structure at zero temperature.In the low energy limit,we obtain the analytical formula of the Kondo temperature that is the same as the exact solution in form except for a prefactor.We also show that the shape of the Kondo resonance is the Lorentzian form and the corresponding weight is proportional to the spin-flip correlation function.
基金supported by the National Natural Science Foundation of China (12201282)the Institute of Meteorological Big Data-Digital Fujian and the Fujian Key Laboratory of Data Science and Statistics (2020L0705)the Education Department of Fujian Province (JAT200325)。
文摘In this paper, we consider the continuous parabolic Anderson model with a logcorrelated Gaussian field, and obtain the precise quenched long-time asymptotics and spatial asymptotics. To overcome the difficulties arising from the log-correlated Gaussian field in the proof of the lower bound of the spatial asymptotics, we first establish the relation between quenched long-time asymptotics and spatial asymptotics, and then get the lower bound of the spatial asymptotics through the lower bound of the quenched long-time asymptotics.
