This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block ...This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.展开更多
The two-dimensional barrier passage is studied in the framework of Langevin statistical reactive dynamics.The optimal incident angle for a particle diffusing in the dissipative non-orthogonal environment with various ...The two-dimensional barrier passage is studied in the framework of Langevin statistical reactive dynamics.The optimal incident angle for a particle diffusing in the dissipative non-orthogonal environment with various strengthsof coupling between the two degrees of freedom is systematically calculated.The optimal diffusion path of the particlein a non-Ohmic damping system is revealed to have a probability to return to the potential valley under the combinedinfluence of the off-diagonal system tensors.展开更多
The point spectrum and non-degenerate symplectic structure of eigenfunction systems of off-diagonal infinite dimensional Hamiltonian operator H=(■)are studied in this article.The necessary and sufficient conditions f...The point spectrum and non-degenerate symplectic structure of eigenfunction systems of off-diagonal infinite dimensional Hamiltonian operator H=(■)are studied in this article.The necessary and sufficient conditions for the eigenfunction systems of off-diagonal infinite dimensional Hamiltonian operator H to have non-degenerate symplectic structure are given.Further,the necessary and sufficient conditions for point spectrum to be contained in real axis,imaginary axis and other areas are obtained for off-diagonal infinite dimensional Hamiltonian operator H,respectively.As an illustrating example,off-diagonal infinite dimensional Hamiltonian operators derived from the plate bending problem and string vibration problem are used to justify the conclusions.展开更多
A shell-model investigation is performed to show the impact on the structure of ^14C from the off-diagonal cross-shell interaction, pp｜V ｜sdsd, which represents the mixing between the 0 and 2 ω configurations in th...A shell-model investigation is performed to show the impact on the structure of ^14C from the off-diagonal cross-shell interaction, pp｜V ｜sdsd, which represents the mixing between the 0 and 2 ω configurations in the psd model space. The observed levels of the positive states in ^14C can be nicely described in 0-4 ω or a larger model space through the well defined Hamiltonians, YSOX and WBP, with a reduction of the strength of the pp｜V ｜sdsd interaction in the latter. The observed B（GT） values for ^14C can be generally described by YSOX, while WBP and their modifications of the〈 pp｜V｜sdsd〉interaction fail for some values. Further investigation shows the effect of such interactions on the configuration mixing and occupancy. The present work shows examples of how the off-diagonal cross-shell interaction strongly drives the nuclear structure.展开更多
It is shown that in the quantum structural approach to high-Tc superconductivity, the wave function in terms of the alternate molecular bonding geminals possesses off-diagonal long-range order (ODLRO).
Let L = L0 ＋ V be the higher order Schrodiger type operator where L0 is a homogeneous elliptic operator of order 2m in divergence form with bounded coeffi- cients and V is a real measurable function as multiplication...Let L = L0 ＋ V be the higher order Schrodiger type operator where L0 is a homogeneous elliptic operator of order 2m in divergence form with bounded coeffi- cients and V is a real measurable function as multiplication operator （e.g., including （-△）m＋v （m∈N） as special examples）. In this paper, assume that V satisfies a strongly subcritical form condition associated with L0, the authors attempt to establish a the- HL （R） （0 〈 p ≤ 1） associated with the higher order Schrodinger ory of Hardy space P n type operator L. Specifically, we first define the molecular Hardy space Hp （JRn） by the so-called （p, q,ε, M） molecule associated to L and then establish its characterizations by the area integral defined by the heat semigroup e-tL.展开更多
By applying the path-integral formulation and the Feynman theorem, we calculate the off-diagonal superconducting correlation in an ultrasmall metallic grain. Unlike its behavior in the bulk limit, we find that this co...By applying the path-integral formulation and the Feynman theorem, we calculate the off-diagonal superconducting correlation in an ultrasmall metallic grain. Unlike its behavior in the bulk limit, we find that this correlation function is an intensive quantity in this case. Therefore, superconductivity is indeed completely suppressed by quantum fluctuations as the diameter of the grain shrinks to the nanometer scale. This conclusion confirms the previous results by numerical calculations. Furthermore, it also imposes a strong constraint on the delocalizing amplitude of the pair-mixing function, which was recently proposed to characterize superconductivity in the canonical ensemble.PACS numbers: 74.20.Fg, 73.23.Hk, 74.80.展开更多
Hyperbolic shear polaritons(HShPs)emerge with widespread attention as a class of polariton modes with broken symmetry due to shear lattices.We find a mechanism of generating quasi-HShPs(q-HShPs).When utilizing vortex ...Hyperbolic shear polaritons(HShPs)emerge with widespread attention as a class of polariton modes with broken symmetry due to shear lattices.We find a mechanism of generating quasi-HShPs(q-HShPs).When utilizing vortex waves as excitation sources of hyperbolic materials without off-diagonal elements,q-HShPs will appear.In addition,these asymmetric q-HShPs can be recovered as symmetric modes away from the source,with a critical transition mode between the left-skewed and right-skewed q-HShPs,via tuning the magnitude of the off-diagonal imaginary component and controlling the topological charge of the vortex source.It is worth mentioning that we explore the influence of parity of topological charges on the field distribution and demonstrate these exotic phenomena from numerical and analytical perspectives.Our results will promote opportunities for both q-HShPs and vortex waves,widening the horizon for various hyperbolic materials based on vortex sources and offering a degree of freedom to control various kinds of polaritons.展开更多
Matrices and integral operators with off-diagonal decay appear in numerous areas of mathematics including numerical analysis and harmonic analysis, and they also play impor-tant roles in engineering science including ...Matrices and integral operators with off-diagonal decay appear in numerous areas of mathematics including numerical analysis and harmonic analysis, and they also play impor-tant roles in engineering science including signal processing and communication engineering. Wiener’s lemma states that the localization of matrices and integral operators are preserved un-der inversion. In this introductory note, we re-examine several approaches to Wiener’s lemma for matrices. We also review briefly some recent advances on localization preservation of operations including nonlinear inversion, matrix factorization and optimization.展开更多
This paper presents a model to describe alternating current （AC） conductivity of DNA sequences, in which DNA is considered as a one-dimensional （1D） disordered system, and electrons transport via hopping between l...This paper presents a model to describe alternating current （AC） conductivity of DNA sequences, in which DNA is considered as a one-dimensional （1D） disordered system, and electrons transport via hopping between localized states. It finds that AC conductivity in DNA sequences increases as the frequency of the external electric field rises, and it takes the form of σac（ω） - ω2 ln^2（1/ω）. Also AC conductivity of DNA sequences increases with the increase of temperature, this phenomenon presents characteristics of weak temperature-dependence. Meanwhile, the AC conductivity in an offdiagonally correlated case is much larger than that in the uncorrelated case of the Anderson limit in low temperatures, which indicates that the off-diagonal correlations in DNA sequences have a great effect on the AC conductivity, while at high temperature the off-diagonal correlations no longer play a vital role in electric transport. In addition, the proportion of nucleotide pairs p also plays an important role in AC electron transport of DNA sequences. For p 〈 0.5, the conductivity of DNA sequence decreases with the increase of p, while for p ≥ 0.5, the conductivity increases with the increase of p.展开更多
A separable Hamiltonian system of Mindlin plate bending problems is obtained. Using the equivalence between the differen form and integral form of the separable Hamiltonian system, the biorthogonal relationships of th...A separable Hamiltonian system of Mindlin plate bending problems is obtained. Using the equivalence between the differen form and integral form of the separable Hamiltonian system, the biorthogonal relationships of the eigenfunctions are presen! Based on the biorthogonal relationships, a novel complete biorthogonal expansion of the Mindlin plate bending problems x~ two opposite sides simply supported is proposed through the products of operator matrices. The exact solutions to deflections bending moments for the Mindlin plate with fully simply supported sides are obtained. A numerical example is illustrated to ve~ the accuracy and validity of the expansion method.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10962004 and 11061019)the Doctoral Foundation of Inner Mongolia(Grant Nos.2009BS0101 and 2010MS0110)+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20070126002)the Chunhui Program of the Ministry of Education of China(Grant No.Z2009-1-01010)
文摘This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.
基金Supported by the Scientific Research Starting Foundation of Qufu Normal University and the National Natural Science Foundation of China under Grant No.10847101
文摘The two-dimensional barrier passage is studied in the framework of Langevin statistical reactive dynamics.The optimal incident angle for a particle diffusing in the dissipative non-orthogonal environment with various strengthsof coupling between the two degrees of freedom is systematically calculated.The optimal diffusion path of the particlein a non-Ohmic damping system is revealed to have a probability to return to the potential valley under the combinedinfluence of the off-diagonal system tensors.
基金Supported by the National Natural Science Foundation of China(Grant No.11961022)the Natural Science Foundation of Inner Mongolia Autonomous Region(Grant Nos.2021MS01017,2021BS01007,2020ZD01)+3 种基金Inner Mongolia Higher Education Scientific Research Project(Grant Nos.NJZY21205,NJZY21208)University Basic Scientific Research Business Funding of Inner Mongolia(Grant No.ZSQN202216)Inner Mongolia“Grassland Talents”Industrial Innovation Talent Team ProjectResearch and Innovation Team Construction Plan of Hohhot Minzu College(Grant No.HM-TD-202005)。
文摘The point spectrum and non-degenerate symplectic structure of eigenfunction systems of off-diagonal infinite dimensional Hamiltonian operator H=(■)are studied in this article.The necessary and sufficient conditions for the eigenfunction systems of off-diagonal infinite dimensional Hamiltonian operator H to have non-degenerate symplectic structure are given.Further,the necessary and sufficient conditions for point spectrum to be contained in real axis,imaginary axis and other areas are obtained for off-diagonal infinite dimensional Hamiltonian operator H,respectively.As an illustrating example,off-diagonal infinite dimensional Hamiltonian operators derived from the plate bending problem and string vibration problem are used to justify the conclusions.
基金Supported by National Natural Science Foundation of China(11305272)Special Program for Applied Research on Super Computation of the NSFC Guangdong Joint Fund(the second phase)+3 种基金the Guangdong Natural Science Foundation(2014A030313217)the Pearl River S&T Nova Program of Guangzhou(201506010060)the Tip-top Scientific and Technical Innovative Youth Talents of Guangdong special support program(2016TQ03N575)the Fundamental Research Funds for the Central Universities(17lgzd34)
文摘A shell-model investigation is performed to show the impact on the structure of ^14C from the off-diagonal cross-shell interaction, pp｜V ｜sdsd, which represents the mixing between the 0 and 2 ω configurations in the psd model space. The observed levels of the positive states in ^14C can be nicely described in 0-4 ω or a larger model space through the well defined Hamiltonians, YSOX and WBP, with a reduction of the strength of the pp｜V ｜sdsd interaction in the latter. The observed B（GT） values for ^14C can be generally described by YSOX, while WBP and their modifications of the〈 pp｜V｜sdsd〉interaction fail for some values. Further investigation shows the effect of such interactions on the configuration mixing and occupancy. The present work shows examples of how the off-diagonal cross-shell interaction strongly drives the nuclear structure.
基金Project (No. 29892168) supported by the National Natural Science Foundation of China.
文摘It is shown that in the quantum structural approach to high-Tc superconductivity, the wave function in terms of the alternate molecular bonding geminals possesses off-diagonal long-range order (ODLRO).
基金supported by NSFC(No.11301203)NSFC(No.11371057,11471033)+5 种基金NSFC(No.11371158)the Fundamental Research Funds for the Central Universities(CCNU-14A05037)the Fundamental Research Funds for the Central Universities(No.2014KJJCA10)SRFDP(No.20130003110003)the program for Changjiang ScholarsInnovative Research Team in University(No.IRT13066)
文摘Let L = L0 ＋ V be the higher order Schrodiger type operator where L0 is a homogeneous elliptic operator of order 2m in divergence form with bounded coeffi- cients and V is a real measurable function as multiplication operator （e.g., including （-△）m＋v （m∈N） as special examples）. In this paper, assume that V satisfies a strongly subcritical form condition associated with L0, the authors attempt to establish a the- HL （R） （0 〈 p ≤ 1） associated with the higher order Schrodinger ory of Hardy space P n type operator L. Specifically, we first define the molecular Hardy space Hp （JRn） by the so-called （p, q,ε, M） molecule associated to L and then establish its characterizations by the area integral defined by the heat semigroup e-tL.
文摘By applying the path-integral formulation and the Feynman theorem, we calculate the off-diagonal superconducting correlation in an ultrasmall metallic grain. Unlike its behavior in the bulk limit, we find that this correlation function is an intensive quantity in this case. Therefore, superconductivity is indeed completely suppressed by quantum fluctuations as the diameter of the grain shrinks to the nanometer scale. This conclusion confirms the previous results by numerical calculations. Furthermore, it also imposes a strong constraint on the delocalizing amplitude of the pair-mixing function, which was recently proposed to characterize superconductivity in the canonical ensemble.PACS numbers: 74.20.Fg, 73.23.Hk, 74.80.
基金supported by the National Natural Science Foundation of China(Grant Nos.92050102 and 11904006)The National Key Research and Development Program of China(Grant No.2020YFA0710100)+2 种基金Jiangxi Provincial Natural Science Foundation(Grant Nos.20224ACB201005)Shenzhen Science and Technology Program(Grant Nos.JCYJ20210324121610028)the Fundamental Research Funds for the Central Universities(Grant Nos.20720200074,20720220134,and 20720220033).
文摘Hyperbolic shear polaritons(HShPs)emerge with widespread attention as a class of polariton modes with broken symmetry due to shear lattices.We find a mechanism of generating quasi-HShPs(q-HShPs).When utilizing vortex waves as excitation sources of hyperbolic materials without off-diagonal elements,q-HShPs will appear.In addition,these asymmetric q-HShPs can be recovered as symmetric modes away from the source,with a critical transition mode between the left-skewed and right-skewed q-HShPs,via tuning the magnitude of the off-diagonal imaginary component and controlling the topological charge of the vortex source.It is worth mentioning that we explore the influence of parity of topological charges on the field distribution and demonstrate these exotic phenomena from numerical and analytical perspectives.Our results will promote opportunities for both q-HShPs and vortex waves,widening the horizon for various hyperbolic materials based on vortex sources and offering a degree of freedom to control various kinds of polaritons.
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education,Science and Technology(2013R1A1A2005402)National Science Foundation(DMS-1109063)
文摘Matrices and integral operators with off-diagonal decay appear in numerous areas of mathematics including numerical analysis and harmonic analysis, and they also play impor-tant roles in engineering science including signal processing and communication engineering. Wiener’s lemma states that the localization of matrices and integral operators are preserved un-der inversion. In this introductory note, we re-examine several approaches to Wiener’s lemma for matrices. We also review briefly some recent advances on localization preservation of operations including nonlinear inversion, matrix factorization and optimization.
基金supported by the Doctoral Program Foundation of Institutions of Higher Education,China (Grant No 20070533075)
文摘This paper presents a model to describe alternating current （AC） conductivity of DNA sequences, in which DNA is considered as a one-dimensional （1D） disordered system, and electrons transport via hopping between localized states. It finds that AC conductivity in DNA sequences increases as the frequency of the external electric field rises, and it takes the form of σac（ω） - ω2 ln^2（1/ω）. Also AC conductivity of DNA sequences increases with the increase of temperature, this phenomenon presents characteristics of weak temperature-dependence. Meanwhile, the AC conductivity in an offdiagonally correlated case is much larger than that in the uncorrelated case of the Anderson limit in low temperatures, which indicates that the off-diagonal correlations in DNA sequences have a great effect on the AC conductivity, while at high temperature the off-diagonal correlations no longer play a vital role in electric transport. In addition, the proportion of nucleotide pairs p also plays an important role in AC electron transport of DNA sequences. For p 〈 0.5, the conductivity of DNA sequence decreases with the increase of p, while for p ≥ 0.5, the conductivity increases with the increase of p.
基金supported by the National Natural Science Foundation of China (Grant No. 10962004)the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant No. 2012MS0105)
文摘A separable Hamiltonian system of Mindlin plate bending problems is obtained. Using the equivalence between the differen form and integral form of the separable Hamiltonian system, the biorthogonal relationships of the eigenfunctions are presen! Based on the biorthogonal relationships, a novel complete biorthogonal expansion of the Mindlin plate bending problems x~ two opposite sides simply supported is proposed through the products of operator matrices. The exact solutions to deflections bending moments for the Mindlin plate with fully simply supported sides are obtained. A numerical example is illustrated to ve~ the accuracy and validity of the expansion method.
