The possible exotic nuclear properties in the neutron-rich Ca,Ni,Zr,and Sn isotopes are examined with the continuum Skyrme Hartree-Fock-Bogoliubov theory in the framework of the Green’s function method.The pairing co...The possible exotic nuclear properties in the neutron-rich Ca,Ni,Zr,and Sn isotopes are examined with the continuum Skyrme Hartree-Fock-Bogoliubov theory in the framework of the Green’s function method.The pairing correlation,the couplings with the continuum,and the blocking effects for the unpaired nucleon in odd-A nuclei are properly treated.The Skyrme interaction SLy4 is adopted for the ph channel and the density-dependentinteraction is adopted for the pp chan-nel,which well reproduce the experimental two-neutron separation energies S_(2n)and one-neutron separation energies Sn.It is found that the criterion S_(n)>0 predicts a neutron drip line with neutron numbers much smaller than those for S_(2n)>0.Owing to the unpaired odd neutron,the neutron pairing energies−E_(pair)in odd-A nuclei are much lower than those in the neighbor-ing even-even nuclei.By investigating the single-particle structures,the possible halo structures in the neutron-rich Ca,Ni,and Sn isotopes are predicted,where sharp increases in the root-mean-square(rms)radii with significant deviations from the traditional rA^(1∕3)rule and diffuse spatial density distributions are observed.Analyzing the contributions of various partial waves to the total neutron densityρlj(r)∕ρ(r)reveals that the orbitals located around the Fermi surface-particularly those with small angular momenta-significantly affect the extended nuclear density and large rms radii.The number of neutrons Nλ(N_(0))occupying above the Fermi surfacen(continuum threshold)is discussed,whose evolution as a function of the mass number A in each isotope is consistent with that of the pairing energy,supporting the key role of the pairing correlation in halo phenomena.展开更多
Single-particle resonances in the continuum are crucial for studies of exotic nuclei.In this study,the Green’s function approach is employed to search for single-particle resonances based on the relativistic-mean-fie...Single-particle resonances in the continuum are crucial for studies of exotic nuclei.In this study,the Green’s function approach is employed to search for single-particle resonances based on the relativistic-mean-field model.Taking^(120)Sn as an example,we identify singleparticle resonances and determine the energies and widths directly by probing the extrema of the Green’s functions.In contrast to the results found by exploring for the extremum of the density of states proposed in our recent study[Chin.Phys.C,44:084105(2020)],which has proven to be very successful,the same resonances as well as very close energies and widths are obtained.By comparing the Green’s functions plotted in different coordinate space sizes,we also found that the results very slightly depend on the space size.These findings demonstrate that the approach by exploring for the extremum of the Green’s function is also very reliable and effective for identifying resonant states,regardless of whether they are wide or narrow.展开更多
A method of combining Green’s function retrieval theory and ultrasonic array imaging using Lamb waves is presented to solve near filed defects in thin aluminum plates.The defects are close to the ultrasonic phased ar...A method of combining Green’s function retrieval theory and ultrasonic array imaging using Lamb waves is presented to solve near filed defects in thin aluminum plates.The defects are close to the ultrasonic phased array and satisfy the near field calculation formula.Near field acoustic information of defects is obscured by the nonlinear effects of initial wave signal in a directly acquired response using the full matrix capture mode.A reconstructed full matrix of inter-element responses is produced from cross-correlation of directly received ultrasonic signals between sensor pairs.This new matrix eliminates the nonlinear interference and restores the near-field defect information.The topological imaging method that was developed in recent ultrasonic inspection is used for displaying the scatterers.The experiments are conducted on both thin aluminum plates containing two and four defects, respectively.The results show that these defects are clearly identified when using a reconstructed full matrix.The spatial resolution is equal to about one wavelength of the selectively excited mode and the identifiable defect is about one fifth of the wavelength.However, in a conventional directly captured image,the images of defects overlap together and cannot be distinguished.The proposed method reduces the background noise and allows for effective topological imaging of near field defects.展开更多
This paper introduces a hybrid approach combining Green’s function Monte Carlo(GFMC)method with projected entangled pair state(PEPS)ansatz.This hybrid method regards PEPS as a trial state and a guiding wave function ...This paper introduces a hybrid approach combining Green’s function Monte Carlo(GFMC)method with projected entangled pair state(PEPS)ansatz.This hybrid method regards PEPS as a trial state and a guiding wave function in GFMC.By leveraging PEPS’s proficiency in capturing quantum state entanglement and GFMC’s efficient parallel architecture,the hybrid method is well-suited for the accurate and efficient treatment of frustrated quantum spin systems.As a benchmark,we applied this approach to study the frustrated J_(1)–J_(2) Heisenberg model on a square lattice with periodic boundary conditions(PBCs).Compared with other numerical methods,our approach integrating PEPS and GFMC shows competitive accuracy in the performance of ground-state energy.This paper provides systematic and comprehensive discussion of the approach of our previous work[Phys.Rev.B 109235133(2024)].展开更多
The pointwise space-time behaviors of the Green’s function and the global solution to the Vlasov-Poisson-Fokker-Planck(VPFP)system in three dimensional space are studied in this paper.It is shown that the Green’s fu...The pointwise space-time behaviors of the Green’s function and the global solution to the Vlasov-Poisson-Fokker-Planck(VPFP)system in three dimensional space are studied in this paper.It is shown that the Green’s function consists of the diffusion waves decaying exponentially in time but algebraically in space,and the singular kinetic waves which become smooth for all(t,x,v)when t>0.Furthermore,we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green’s function.展开更多
Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions(Fan et al., Phys. Rev. B 97, 165140(2018)). In that approximation, the precision of results d...Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions(Fan et al., Phys. Rev. B 97, 165140(2018)). In that approximation, the precision of results depends on the selection of operator basis. Here, for three successively larger operator bases, we calculate the local static averages and the impurity density of states of the single-band Anderson impurity model. The results converge systematically towards those of numerical renormalization group as the basis size is enlarged. We also propose a quantitative gauge of the truncation error within this method and demonstrate its usefulness using the Hubbard-I basis. We thus confirm that the projective truncation approximation is a method of controllable precision for quantum many-body systems.展开更多
Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investi...Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investigated within the framework of linearized water wave theory. The effect of surface tension at the surface below the ice-cover is neglected. There exists only one wave number propagating at just below the ice-cover. A perturbation analysis is employed to solve the boundary value problem governed by Laplace＇s equation by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function and thereby evaluating the reflection and transmission coefficients approximately up to first order. A patch of sinusoidal ripples is considered as an example and the related coefficients are determined.展开更多
In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green's function for this problem and show that it satisfies certain propertie...In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green's function for this problem and show that it satisfies certain properties. Some existence results are obtained by means of nonlinear alternative of Leray-Schauder type theorem and Krasnosel-skii's fixed point theorem.展开更多
In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α＋u（t）＋f（t,u（t）,u＇（t）,…,u^（n-3）（5）,u^（n-2）（t））=0,u^（i）（0）=0,0≤i≤n-2,u^（n-...In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α＋u（t）＋f（t,u（t）,u＇（t）,…,u^（n-3）（5）,u^（n-2）（t））=0,u^（i）（0）=0,0≤i≤n-2,u^（n-2）（1）-βu^（n-2）（ξ）=0,where 0〈t〈1,n-1〈α≤n,n≥2,ξ Е（0,1）,βξ^a-n〈1. We first transform it into another equivalent boundary value problem. Then, we derive the Green＇s function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result.展开更多
The present study deals with the scattering of oblique surface water waves by small undulation on the bottom in the presence of a thin vertical barrier. Here, three different configurations of vertical barriers are in...The present study deals with the scattering of oblique surface water waves by small undulation on the bottom in the presence of a thin vertical barrier. Here, three different configurations of vertical barriers are investigated. Perturbation analysis is employed to determine the physical quantities, namely, the reflection and transmission coefficients. In this analysis, many different Boundary Value Problems (BVPs) are obtained out of which the first two bvps are considered. The zeroth order bvp is solved with the aid of eigenfunction expansion method. The first order reflection and transmission coefficients are derived in terms of the integrals by the method of the Green's integral theorem. The variation of these coefficients is plotted and analyzed for different physical parameters. Furthermore, the energy balance relation, an important relation in the study of water wave scattering, is derived and checked for assuring the correctness of the numerical results for the present problem.展开更多
The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence ...The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the L^p convergence rate of the solution is obtained.展开更多
We present a semi-analytic method to study the electronic conductance of a lengthy armchair honeycomb nanoribbon in the presence of vacancies, defects, or impurities located at a small part of it. For this purpose, we...We present a semi-analytic method to study the electronic conductance of a lengthy armchair honeycomb nanoribbon in the presence of vacancies, defects, or impurities located at a small part of it. For this purpose, we employ the Green's function technique within the nearest neighbor tight-binding approach. We first convert the Hamiltonian of an ideal semiinfinite nanoribbon to the Hamiltonian of some independent polyacetylene-like chains. Then, we derive an exact formula for the self-energy of the perturbed part due to the existence of ideal parts. The method gives a fully analytical formalism for some cases such as an infinite ideal nanoribbon and the one including linear symmetric defects. We calculate the transmission coefficient for some different configurations of a nanoribbon with special width including a vacancy, edge geometrical defects, and two electrical impurities.展开更多
It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or...It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or three dimensional rectangular coordinate systems. Firstly, according to the coordinate transformation, the condition that the line integral is the path independent in the polar coordinate system is obtained easily from the Green's theorem in two-dimensional rectangular coordinate system and the condition is extended to arbitrary two-dimension orthogonal curvilinear coordinates. Secondly, through the coordinate transformation relationship and the area projection method, the Stokes formula in three-dimensional rectangular coordinate system is promoted to the spherical coordinate system and cylindrical coordinate system, and the condition that the line integral is a path independent is obtained. Furthermore, the condition is extended to arbitrary three-dimension orthogonal curvilinear coordinates. Lastly, the conclusions are made.展开更多
Very recently,experimental evidence showed that the hydrogen is retained in dithiol-terminated single-molecule junction under the widely adopted preparation conditions,which is in contrast to the accepted view[Nat.Che...Very recently,experimental evidence showed that the hydrogen is retained in dithiol-terminated single-molecule junction under the widely adopted preparation conditions,which is in contrast to the accepted view[Nat.Chem.11351(2019)].However,the hydrogen is generally assumed to be lost in the previous physical models of single-molecule junctions.Whether the retention of the hydrogen at the gold-sulfur interface exerts a significant effect on the theoretical prediction of spin transport properties is an open question.Therefore,here in this paper we carry out a comparative study of spin transport in M-tetraphenylporphyrin-based(M=V,Cr,Mn,Fe,and Co;M-TPP)single-molecule junction through Au-SR and Au-S(H)R bondings.The results show that the hydrogen at the gold-sulfur interface may dramatically affect the spin-filtering efficiency of M-TPP-based single-molecule junction,depending on the type of transition metal ions embedded into porphyrin ring.Moreover,we find that for the Co-TPP-based molecular junction,the hydrogen at the gold-sulfur interface has no obvious effect on transmission at the Fermi level,but it has a significant effect on the spin-dependent transmission dip induced by the quantum interference on the occupied side.Thus the fate of hydrogen should be concerned in the physical model according to the actual preparation condition,which is important for our fundamental understanding of spin transport in the single-molecule junctions.Our work also provides guidance in how to experimentally identify the nature of gold-sulfur interface in the single-molecule junction with spin-polarized transport.展开更多
The spin transport properties are theoretically investigated when a quantum dot(QD)is side-coupled to Majorana bound states(MBSs)driven by a symmetric dipolar spin battery.It is found that MBSs have a great effect on ...The spin transport properties are theoretically investigated when a quantum dot(QD)is side-coupled to Majorana bound states(MBSs)driven by a symmetric dipolar spin battery.It is found that MBSs have a great effect on spin transport properties.The peak-to-valley ratio of the spin current decreases as the coupling strength between the MBS and the QD increases.Moreover,a non-zero charge current with two resonance peaks appears in the system.In the extreme case where the dot-MBS coupling strength is strong enough,the spin current and the charge current are both constants in the non-resonance peak range.When considering the effect of the Zeeman energy,it is interesting that the resonance peak at the higher energy appears one shoulder.And the shoulder turns into a peak when the Zeeman energy is big enough.In addition,the coupling strength between the two MBSs weakens their effects on the currents of the system.These results are helpful for understanding the MBSs signature in the transport spectra.展开更多
Designing tunable molecular devices with different charge carriers in single-molecule junctions is crucial to the nextgeneration electronic technology.Recently,it has been demonstrated that the type of charge carriers...Designing tunable molecular devices with different charge carriers in single-molecule junctions is crucial to the nextgeneration electronic technology.Recently,it has been demonstrated that the type of charge carriers depends on and can be tuned by controlling the molecular length and the number of interfacial covalent bonds.In this study,we show that the type of charge carriers can also be tuned by controlling the material and shape of electrodes.N-heterocyclic carbenes(NHCs)have attracted attention because of their ability to form strong,substitutional inert bonds in a variety of metals.Also,NHCs are more stable than the widely used thiol group.Therefore,we use electrodes to tune the type of charge carriers in a series of NHCs with different side groups.The ab initio calculations based on non-equilibrium Green’s formalism combined with density functional theory show that the dominant charge carrier switches from electrons to holes when gold electrodes are changed into platinum ones.The nature of the charge carriers can be identified by variations in the transport spectra at the Fermi level(EF),which are caused by the side groups.The projections of transport spectra onto the central molecules further validate our inferences.In addition,the transmission coefficient at EF is found to be dependent on the atomic interface structure.In particular,for the NHC without methyl or ethyl side groups,connecting a protruding atom on the electrode surface significantly enhances the transportability of both electrode materials.Overall,this study presents an effective approach to modifying transport properties,which has potential applications in designing functional molecular devices based on NHCs.展开更多
Based on density functional theory and non-equilibrium Green’s function method,we studied noncollinear magnetism and spin transport in a 180°domain wall made of zigzag graphene nanoribbon(ZGNR)with different non...Based on density functional theory and non-equilibrium Green’s function method,we studied noncollinear magnetism and spin transport in a 180°domain wall made of zigzag graphene nanoribbon(ZGNR)with different noncollinear magnetic profiles on the top and bottom edges.Our results show that a helical domain wall on the top(bottom)edge and an abrupt domain wall on the bottom(top)edge can survive in the ZGNR.This indicates that such characteristic magnetization distribution can be obtained by some means,e.g.,the introduction of impurity on one edge.Compared to a wide ZGNR,a narrow ZGNR presents obvious coupling between the two edges which changes the magnetization and transmission greatly.As for the above-mentioned distinct magnetic profile,the spin transport is blocked in the abrupt domain wall due to strong spin flip scattering while remains unaffected in the helical domain wall due to the spin mixing effect.We deduce a formula of the transmission for various magnetic profiles of the ZGNRs.A new result based on this formula is that the transmission at the Fermi level can be zero,one,and two by tuning the edge magnetization.Our results provide insights into the noncollinear spin transport of the ZGNR-based devices.展开更多
The idea of replacing traditional silicon-based electronic components with the ones assembled by organic molecules to further scale down the electric circuits has been attracting extensive research focuses.Among the m...The idea of replacing traditional silicon-based electronic components with the ones assembled by organic molecules to further scale down the electric circuits has been attracting extensive research focuses.Among the molecularly assembled components,the design of molecular logic gates with simple structure and high Boolean computing speed remains a great challenge.Here,by using the state-of-the-art nonequilibrium Green’s function theory in conjugation with first-principles method,the spin transport properties of single-molecule junctions comprised of two serially connected transition metal dibenzotetraaza[14]annulenes(TM(DBTAA),TM=Fe,Co)sandwiched between two single-walled carbon nanotube electrodes are theoretically investigated.The numerical results show a close dependence of the spin-resolved current-voltage characteristics on spin configurations between the left and right molecular kernels and the kind of TM atom in TM(DBTAA)molecule.By taking advantage of spin degree of freedom of electrons,NOR or XNOR Boolean logic gates can be realized in Fe(DBTAA)and Co(DBTAA)junctions depending on the definitions of input and output signals.This work proposes a new kind of molecular logic gates and hence is helpful for further miniaturization of the electric circuits.展开更多
The atomistic Green’s function method is improved to compute the polarization resolved phonon transport in a multiterminal system. Based on the recent developments in literature, the algorithm is simplified. The comp...The atomistic Green’s function method is improved to compute the polarization resolved phonon transport in a multiterminal system. Based on the recent developments in literature, the algorithm is simplified. The complex phonon band structure of a semi-infinite periodic terminal is obtained by the generalized eigenvalue equation. Then both the surface Green’s function and phonon group velocity in the terminal are determined from the wave modes propagating away from the scattering region along the terminal. With these key ingredients, the individual phonon mode transmittance between the terminals can be calculated. The feasibility and validity of the method are demonstrated by the chain example compared with the wave packet method, and an example of graphene nanojunction with three terminals.展开更多
For real-time inversion and fast reconstruction of formation true resistivity, the forward modeling of electromagnetic wave logging while drilling is usually based on the transversely isotropic formation model with ve...For real-time inversion and fast reconstruction of formation true resistivity, the forward modeling of electromagnetic wave logging while drilling is usually based on the transversely isotropic formation model with vertical symmetry axis(VTI medium), but it only considers the horizontal and vertical resistivity. It has certain limitation during practical application. This paper presents a forward calculation method of electromagnetic wave logging while drilling in transversely isotropic(TTI) strata with inclined symmetry axis based on the Dyadic Green’s function. Anisotropic angle and azimuth are used to characterize TTI formation. The proposed algorithm is verified by numerical examples, the half-space electromagnetic wave reflection and transmission characteristics with different media are analyzed, and the necessity to use the new algorithm is pointed out. Numerical simulation also shows that there exist a critical borehole dip and critical anisotropic angle in TTI formation. Electromagnetic wave logging while drilling responses follows opposite rule before and after these two critical angles. Besides, the 'horns' at the interface are not only related to well deviation, resistivity contrast, but also related to anisotropic angle and anisotropic azimuth.展开更多
基金the National Natural Science Foundation of China(No.U2032141)the Open Project of Guangxi Key Laboratory of Nuclear Physics and Nuclear Technology(No.NLK2022-02)+4 种基金the Central Government Guidance Funds for Local Scientific and Technological Development,China(Guike ZY22096024)the Natural Science Foundation of Henan Province(No.202300410479)the Guizhou Provincial Science and Technology Projects(No.ZK[2022]203)the Foundation of Fundamental Research for Young Teachers of Zhengzhou University(No.JC202041041)the Physics Research and Development Program of Zhengzhou University(No.32410217).
文摘The possible exotic nuclear properties in the neutron-rich Ca,Ni,Zr,and Sn isotopes are examined with the continuum Skyrme Hartree-Fock-Bogoliubov theory in the framework of the Green’s function method.The pairing correlation,the couplings with the continuum,and the blocking effects for the unpaired nucleon in odd-A nuclei are properly treated.The Skyrme interaction SLy4 is adopted for the ph channel and the density-dependentinteraction is adopted for the pp chan-nel,which well reproduce the experimental two-neutron separation energies S_(2n)and one-neutron separation energies Sn.It is found that the criterion S_(n)>0 predicts a neutron drip line with neutron numbers much smaller than those for S_(2n)>0.Owing to the unpaired odd neutron,the neutron pairing energies−E_(pair)in odd-A nuclei are much lower than those in the neighbor-ing even-even nuclei.By investigating the single-particle structures,the possible halo structures in the neutron-rich Ca,Ni,and Sn isotopes are predicted,where sharp increases in the root-mean-square(rms)radii with significant deviations from the traditional rA^(1∕3)rule and diffuse spatial density distributions are observed.Analyzing the contributions of various partial waves to the total neutron densityρlj(r)∕ρ(r)reveals that the orbitals located around the Fermi surface-particularly those with small angular momenta-significantly affect the extended nuclear density and large rms radii.The number of neutrons Nλ(N_(0))occupying above the Fermi surfacen(continuum threshold)is discussed,whose evolution as a function of the mass number A in each isotope is consistent with that of the pairing energy,supporting the key role of the pairing correlation in halo phenomena.
基金supported by the National Natural Science Foundation of China(No.U2032141)the Natural Science Foundation of Henan Province(No.202300410479,No.202300410480)+1 种基金the Foundation of Fundamental Research for Young Teachers of Zhengzhou University(No.JC202041041)the Physics Research and Development Program of Zhengzhou University(No.32410217).
文摘Single-particle resonances in the continuum are crucial for studies of exotic nuclei.In this study,the Green’s function approach is employed to search for single-particle resonances based on the relativistic-mean-field model.Taking^(120)Sn as an example,we identify singleparticle resonances and determine the energies and widths directly by probing the extrema of the Green’s functions.In contrast to the results found by exploring for the extremum of the density of states proposed in our recent study[Chin.Phys.C,44:084105(2020)],which has proven to be very successful,the same resonances as well as very close energies and widths are obtained.By comparing the Green’s functions plotted in different coordinate space sizes,we also found that the results very slightly depend on the space size.These findings demonstrate that the approach by exploring for the extremum of the Green’s function is also very reliable and effective for identifying resonant states,regardless of whether they are wide or narrow.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674214 and 11874255)
文摘A method of combining Green’s function retrieval theory and ultrasonic array imaging using Lamb waves is presented to solve near filed defects in thin aluminum plates.The defects are close to the ultrasonic phased array and satisfy the near field calculation formula.Near field acoustic information of defects is obscured by the nonlinear effects of initial wave signal in a directly acquired response using the full matrix capture mode.A reconstructed full matrix of inter-element responses is produced from cross-correlation of directly received ultrasonic signals between sensor pairs.This new matrix eliminates the nonlinear interference and restores the near-field defect information.The topological imaging method that was developed in recent ultrasonic inspection is used for displaying the scatterers.The experiments are conducted on both thin aluminum plates containing two and four defects, respectively.The results show that these defects are clearly identified when using a reconstructed full matrix.The spatial resolution is equal to about one wavelength of the selectively excited mode and the identifiable defect is about one fifth of the wavelength.However, in a conventional directly captured image,the images of defects overlap together and cannot be distinguished.The proposed method reduces the background noise and allows for effective topological imaging of near field defects.
基金Project supported by the National Natural Science Foundation of China(Grant No.11934020)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0302402).
文摘This paper introduces a hybrid approach combining Green’s function Monte Carlo(GFMC)method with projected entangled pair state(PEPS)ansatz.This hybrid method regards PEPS as a trial state and a guiding wave function in GFMC.By leveraging PEPS’s proficiency in capturing quantum state entanglement and GFMC’s efficient parallel architecture,the hybrid method is well-suited for the accurate and efficient treatment of frustrated quantum spin systems.As a benchmark,we applied this approach to study the frustrated J_(1)–J_(2) Heisenberg model on a square lattice with periodic boundary conditions(PBCs).Compared with other numerical methods,our approach integrating PEPS and GFMC shows competitive accuracy in the performance of ground-state energy.This paper provides systematic and comprehensive discussion of the approach of our previous work[Phys.Rev.B 109235133(2024)].
基金supported by National Natural Science Foundation of China(11671100 and 12171104)the National Science Fund for Excellent Young Scholars(11922107)Guangxi Natural Science Foundation(2018GXNSFAA138210 and 2019JJG110010)。
文摘The pointwise space-time behaviors of the Green’s function and the global solution to the Vlasov-Poisson-Fokker-Planck(VPFP)system in three dimensional space are studied in this paper.It is shown that the Green’s function consists of the diffusion waves decaying exponentially in time but algebraically in space,and the singular kinetic waves which become smooth for all(t,x,v)when t>0.Furthermore,we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green’s function.
基金Project supported by the National Key Basic Research Program of China(Grant No.2012CB921704)the National Natural Science Foundation of China(Grant No.11374362)+1 种基金the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No.15XNLQ03)
文摘Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions(Fan et al., Phys. Rev. B 97, 165140(2018)). In that approximation, the precision of results depends on the selection of operator basis. Here, for three successively larger operator bases, we calculate the local static averages and the impurity density of states of the single-band Anderson impurity model. The results converge systematically towards those of numerical renormalization group as the basis size is enlarged. We also propose a quantitative gauge of the truncation error within this method and demonstrate its usefulness using the Hubbard-I basis. We thus confirm that the projective truncation approximation is a method of controllable precision for quantum many-body systems.
文摘Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investigated within the framework of linearized water wave theory. The effect of surface tension at the surface below the ice-cover is neglected. There exists only one wave number propagating at just below the ice-cover. A perturbation analysis is employed to solve the boundary value problem governed by Laplace＇s equation by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function and thereby evaluating the reflection and transmission coefficients approximately up to first order. A patch of sinusoidal ripples is considered as an example and the related coefficients are determined.
基金Supported by the National Natural Science Foundation of China（11161049）
文摘In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green's function for this problem and show that it satisfies certain properties. Some existence results are obtained by means of nonlinear alternative of Leray-Schauder type theorem and Krasnosel-skii's fixed point theorem.
基金Supported by the National Nature Science Foundation of China(11071001)Supported by the Key Program of Ministry of Education of China(205068)
文摘In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α＋u（t）＋f（t,u（t）,u＇（t）,…,u^（n-3）（5）,u^（n-2）（t））=0,u^（i）（0）=0,0≤i≤n-2,u^（n-2）（1）-βu^（n-2）（ξ）=0,where 0〈t〈1,n-1〈α≤n,n≥2,ξ Е（0,1）,βξ^a-n〈1. We first transform it into another equivalent boundary value problem. Then, we derive the Green＇s function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result.
基金Supported by SERB-DST Grant(No.SB/FTP/MS-034/2013)
文摘The present study deals with the scattering of oblique surface water waves by small undulation on the bottom in the presence of a thin vertical barrier. Here, three different configurations of vertical barriers are investigated. Perturbation analysis is employed to determine the physical quantities, namely, the reflection and transmission coefficients. In this analysis, many different Boundary Value Problems (BVPs) are obtained out of which the first two bvps are considered. The zeroth order bvp is solved with the aid of eigenfunction expansion method. The first order reflection and transmission coefficients are derived in terms of the integrals by the method of the Green's integral theorem. The variation of these coefficients is plotted and analyzed for different physical parameters. Furthermore, the energy balance relation, an important relation in the study of water wave scattering, is derived and checked for assuring the correctness of the numerical results for the present problem.
基金supported by the National Natural Science Foundation of China(11271141)Chongqing Science&Technology Commission(cstc2018jcyjAX0787)
文摘The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multidimensions(n ≥ 3) is considered. Based on Green's function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the L^p convergence rate of the solution is obtained.
文摘We present a semi-analytic method to study the electronic conductance of a lengthy armchair honeycomb nanoribbon in the presence of vacancies, defects, or impurities located at a small part of it. For this purpose, we employ the Green's function technique within the nearest neighbor tight-binding approach. We first convert the Hamiltonian of an ideal semiinfinite nanoribbon to the Hamiltonian of some independent polyacetylene-like chains. Then, we derive an exact formula for the self-energy of the perturbed part due to the existence of ideal parts. The method gives a fully analytical formalism for some cases such as an infinite ideal nanoribbon and the one including linear symmetric defects. We calculate the transmission coefficient for some different configurations of a nanoribbon with special width including a vacancy, edge geometrical defects, and two electrical impurities.
基金Funded by the Natural Science Foundation Project of CQCSTC(No.cstc2012jj A50018)the Basic Research of Chongqing Municipal Education Commission(No.KJ120631)the Science Research Foundation Project of CQNU(No.16XYY31)
文摘It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or three dimensional rectangular coordinate systems. Firstly, according to the coordinate transformation, the condition that the line integral is the path independent in the polar coordinate system is obtained easily from the Green's theorem in two-dimensional rectangular coordinate system and the condition is extended to arbitrary two-dimension orthogonal curvilinear coordinates. Secondly, through the coordinate transformation relationship and the area projection method, the Stokes formula in three-dimensional rectangular coordinate system is promoted to the spherical coordinate system and cylindrical coordinate system, and the condition that the line integral is a path independent is obtained. Furthermore, the condition is extended to arbitrary three-dimension orthogonal curvilinear coordinates. Lastly, the conclusions are made.
基金the National Natural Science Foundation of China(Grant Nos.11674092,11804093,and 61764005)the Natural Science Foundation of Hunan Province,China(Grant No.2019JJ40006)+2 种基金the Scientific Research Fund of the Education Department of Hunan Province,China(Grant No.18B368)the Science and Technology Development Plan Project of Hengyang City,China(Grant No.2018KJ121)the Science and Technology Plan Project of Hunan Province,China(Grant No.2016TP1020).
文摘Very recently,experimental evidence showed that the hydrogen is retained in dithiol-terminated single-molecule junction under the widely adopted preparation conditions,which is in contrast to the accepted view[Nat.Chem.11351(2019)].However,the hydrogen is generally assumed to be lost in the previous physical models of single-molecule junctions.Whether the retention of the hydrogen at the gold-sulfur interface exerts a significant effect on the theoretical prediction of spin transport properties is an open question.Therefore,here in this paper we carry out a comparative study of spin transport in M-tetraphenylporphyrin-based(M=V,Cr,Mn,Fe,and Co;M-TPP)single-molecule junction through Au-SR and Au-S(H)R bondings.The results show that the hydrogen at the gold-sulfur interface may dramatically affect the spin-filtering efficiency of M-TPP-based single-molecule junction,depending on the type of transition metal ions embedded into porphyrin ring.Moreover,we find that for the Co-TPP-based molecular junction,the hydrogen at the gold-sulfur interface has no obvious effect on transmission at the Fermi level,but it has a significant effect on the spin-dependent transmission dip induced by the quantum interference on the occupied side.Thus the fate of hydrogen should be concerned in the physical model according to the actual preparation condition,which is important for our fundamental understanding of spin transport in the single-molecule junctions.Our work also provides guidance in how to experimentally identify the nature of gold-sulfur interface in the single-molecule junction with spin-polarized transport.
基金supported by Natural Science Fund for Colleges and Universities in Hebei Province,China(Grant No.ZD2017031)the Doctoral Initial Funding of Hebei University of Science and Technology(Grant No.1181291)。
文摘The spin transport properties are theoretically investigated when a quantum dot(QD)is side-coupled to Majorana bound states(MBSs)driven by a symmetric dipolar spin battery.It is found that MBSs have a great effect on spin transport properties.The peak-to-valley ratio of the spin current decreases as the coupling strength between the MBS and the QD increases.Moreover,a non-zero charge current with two resonance peaks appears in the system.In the extreme case where the dot-MBS coupling strength is strong enough,the spin current and the charge current are both constants in the non-resonance peak range.When considering the effect of the Zeeman energy,it is interesting that the resonance peak at the higher energy appears one shoulder.And the shoulder turns into a peak when the Zeeman energy is big enough.In addition,the coupling strength between the two MBSs weakens their effects on the currents of the system.These results are helpful for understanding the MBSs signature in the transport spectra.
基金Project supported by the National Natural Science Foundation of China(Grants Nos.11874242 and 21933002)the Shandong Provincial Natural Science Foundation,China(Grant No.ZR2019PA022).
文摘Designing tunable molecular devices with different charge carriers in single-molecule junctions is crucial to the nextgeneration electronic technology.Recently,it has been demonstrated that the type of charge carriers depends on and can be tuned by controlling the molecular length and the number of interfacial covalent bonds.In this study,we show that the type of charge carriers can also be tuned by controlling the material and shape of electrodes.N-heterocyclic carbenes(NHCs)have attracted attention because of their ability to form strong,substitutional inert bonds in a variety of metals.Also,NHCs are more stable than the widely used thiol group.Therefore,we use electrodes to tune the type of charge carriers in a series of NHCs with different side groups.The ab initio calculations based on non-equilibrium Green’s formalism combined with density functional theory show that the dominant charge carrier switches from electrons to holes when gold electrodes are changed into platinum ones.The nature of the charge carriers can be identified by variations in the transport spectra at the Fermi level(EF),which are caused by the side groups.The projections of transport spectra onto the central molecules further validate our inferences.In addition,the transmission coefficient at EF is found to be dependent on the atomic interface structure.In particular,for the NHC without methyl or ethyl side groups,connecting a protruding atom on the electrode surface significantly enhances the transportability of both electrode materials.Overall,this study presents an effective approach to modifying transport properties,which has potential applications in designing functional molecular devices based on NHCs.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.NSFC11804158,NSFC61974067,NSFC91750112,and NSFC11947101)。
文摘Based on density functional theory and non-equilibrium Green’s function method,we studied noncollinear magnetism and spin transport in a 180°domain wall made of zigzag graphene nanoribbon(ZGNR)with different noncollinear magnetic profiles on the top and bottom edges.Our results show that a helical domain wall on the top(bottom)edge and an abrupt domain wall on the bottom(top)edge can survive in the ZGNR.This indicates that such characteristic magnetization distribution can be obtained by some means,e.g.,the introduction of impurity on one edge.Compared to a wide ZGNR,a narrow ZGNR presents obvious coupling between the two edges which changes the magnetization and transmission greatly.As for the above-mentioned distinct magnetic profile,the spin transport is blocked in the abrupt domain wall due to strong spin flip scattering while remains unaffected in the helical domain wall due to the spin mixing effect.We deduce a formula of the transmission for various magnetic profiles of the ZGNRs.A new result based on this formula is that the transmission at the Fermi level can be zero,one,and two by tuning the edge magnetization.Our results provide insights into the noncollinear spin transport of the ZGNR-based devices.
基金National Natural Science Foundation of China(Grant Nos.11874242,21933002,and 11704230)China Postdoctoral Science Foundation(Grant No.2017M612321)the Taishan Scholar Project of Shandong Province of China.
文摘The idea of replacing traditional silicon-based electronic components with the ones assembled by organic molecules to further scale down the electric circuits has been attracting extensive research focuses.Among the molecularly assembled components,the design of molecular logic gates with simple structure and high Boolean computing speed remains a great challenge.Here,by using the state-of-the-art nonequilibrium Green’s function theory in conjugation with first-principles method,the spin transport properties of single-molecule junctions comprised of two serially connected transition metal dibenzotetraaza[14]annulenes(TM(DBTAA),TM=Fe,Co)sandwiched between two single-walled carbon nanotube electrodes are theoretically investigated.The numerical results show a close dependence of the spin-resolved current-voltage characteristics on spin configurations between the left and right molecular kernels and the kind of TM atom in TM(DBTAA)molecule.By taking advantage of spin degree of freedom of electrons,NOR or XNOR Boolean logic gates can be realized in Fe(DBTAA)and Co(DBTAA)junctions depending on the definitions of input and output signals.This work proposes a new kind of molecular logic gates and hence is helpful for further miniaturization of the electric circuits.
基金Project supported by the National Natural Science Foundation of China(Grant No.51376094)Jiangsu Overseas Visiting Scholar Program for University Prominent Young&Middle-aged Teachers and Presidents,China
文摘The atomistic Green’s function method is improved to compute the polarization resolved phonon transport in a multiterminal system. Based on the recent developments in literature, the algorithm is simplified. The complex phonon band structure of a semi-infinite periodic terminal is obtained by the generalized eigenvalue equation. Then both the surface Green’s function and phonon group velocity in the terminal are determined from the wave modes propagating away from the scattering region along the terminal. With these key ingredients, the individual phonon mode transmittance between the terminals can be calculated. The feasibility and validity of the method are demonstrated by the chain example compared with the wave packet method, and an example of graphene nanojunction with three terminals.
基金Supported by the National Natural Science Foundation of China(41474100,41574118)
文摘For real-time inversion and fast reconstruction of formation true resistivity, the forward modeling of electromagnetic wave logging while drilling is usually based on the transversely isotropic formation model with vertical symmetry axis(VTI medium), but it only considers the horizontal and vertical resistivity. It has certain limitation during practical application. This paper presents a forward calculation method of electromagnetic wave logging while drilling in transversely isotropic(TTI) strata with inclined symmetry axis based on the Dyadic Green’s function. Anisotropic angle and azimuth are used to characterize TTI formation. The proposed algorithm is verified by numerical examples, the half-space electromagnetic wave reflection and transmission characteristics with different media are analyzed, and the necessity to use the new algorithm is pointed out. Numerical simulation also shows that there exist a critical borehole dip and critical anisotropic angle in TTI formation. Electromagnetic wave logging while drilling responses follows opposite rule before and after these two critical angles. Besides, the 'horns' at the interface are not only related to well deviation, resistivity contrast, but also related to anisotropic angle and anisotropic azimuth.
