The Schrodinger equation for a particle in the V-shaped potential decorated by a repulsive or attractive Dirac delta function interaction at the center is solved, demonstrating the crucial influence of point interacti...The Schrodinger equation for a particle in the V-shaped potential decorated by a repulsive or attractive Dirac delta function interaction at the center is solved, demonstrating the crucial influence of point interaction on the even-parity states of the original system without decoration. As strength of the attraction increases, the ground state energy falls down without limit; and in limit of infinitely large attraction, the ground state approaches a singular state. Our analysis and conclusion can be readily generalized to any one-dimensional system a particle interacts with symmetrical potential plus the Dirac delta function interaction at the center.展开更多
A novel method of deriving the electromagnetic dyadic Green＇s functions in an unbounded, lossless, reciprocal and homogeneous chiral media described by the constitutive relations D = εE ＋ jγB and H = jγE ＋ μ^-1...A novel method of deriving the electromagnetic dyadic Green＇s functions in an unbounded, lossless, reciprocal and homogeneous chiral media described by the constitutive relations D = εE ＋ jγB and H = jγE ＋ μ^-1B - （ωε）^-1γJ is given. The divergenceless and irrotational splitting of dyadic Dirac 8 function and Fourier transformation are used to directly obtain the divergenceless and irrotational component of spectral-domain dyadic Green＇s functions in chiral media. This method avoids using the dyadic Green＇s function eigenfunction expansion technique. The method given here can be generalized to a source-free region and an achiral case.展开更多
In this paper, the properties of the exponential Radon transform and its dual are discussed. Furthermore, the analytical reconstruction formulas of exponential Radon transform with two different methods are developed.
It is well known that the macroscopic Maxwell’s equations can be obtained from the corresponding microscopic or atomic equations by a proper averaging process. The purpose of this paper is to present the macroscopic ...It is well known that the macroscopic Maxwell’s equations can be obtained from the corresponding microscopic or atomic equations by a proper averaging process. The purpose of this paper is to present the macroscopic Maxwell’s equations which are valid in all regions of space, including an interface between two different media; and the boundary conditions can naturally emerge from the macroscopic equations as an effect of average of the microscopic Maxwell’s equations. In addition, the application of the unit step functions and the Dirac delta function to our discussion not only permits great mathematical simplicity but also gives rise to convenient physical concepts for the description and representation of the actual fields in the vicinity of the interface.展开更多
The two-dimensional Dirac equation for a fermion moving under Kratzer potential in the presence of an external magnetic field is analytically being solved for the energy eigenvalues and eigenfunctions. Subsequently, w...The two-dimensional Dirac equation for a fermion moving under Kratzer potential in the presence of an external magnetic field is analytically being solved for the energy eigenvalues and eigenfunctions. Subsequently, we have obtained the Wigner function corresponding to the eigenfunctions.展开更多
This paper is concerned with the distribution of normalized zero-sets of random meromorphic functions.The normalization of the zero-set plays the same role as the counting function for a meromorphic function in Nevanl...This paper is concerned with the distribution of normalized zero-sets of random meromorphic functions.The normalization of the zero-set plays the same role as the counting function for a meromorphic function in Nevanlinna theory.The results generalize the theory of Shiffman and Zelditch on the distribution of the zeroes of random holomorphic sections of powers of positive Hermitian holomorphic line bundles.As in a very special case,our paper resembles a form of First Main Theorem in classical Nevanlinna Theory.展开更多
The Riemann Zeta functionζ(s)has many different representations.In this paper,we derive several new integral representations of the Zeta function using the inverse Mellin transform and a hyperbolic cosecant identity....The Riemann Zeta functionζ(s)has many different representations.In this paper,we derive several new integral representations of the Zeta function using the inverse Mellin transform and a hyperbolic cosecant identity.We also derive a general integral transformation similar to the Dirac delta function and propose a few new avenues for solving Riemann’s Hypothesis.展开更多
An analytical model is proposed to estimate the discontinuous mechanical behavior of an existing shield tunnel above a new tunnel. The existing shield tunnel is regarded as a Timoshenko beam with longitudinal joints. ...An analytical model is proposed to estimate the discontinuous mechanical behavior of an existing shield tunnel above a new tunnel. The existing shield tunnel is regarded as a Timoshenko beam with longitudinal joints. The opening and relative dislocation of the longitudinal joints can be calculated using Dirac delta functions. Compared with other approaches, our method yields results that are consistent with centrifugation test data. The effects of the stiffness reduction at the longitudinal joints (α and β), the shearing stiffness of the Timoshenko beam GA, and different additional pressure profiles on the responses of the shield tunnel are investigated. The results indicate that our proposed method is suitable for simulating the discontinuous mechanical behaviors of existing shield tunnels with longitudinal joints. The deformation and internal forces decrease as α, β, and GA increase. The bending moment and shear force are discontinuous despite slight discontinuities in the deflection, opening, and dislocation. The deflection curve is consistent with the additional pressure profile. Extensive opening, dislocation, and internal forces are induced at the location of mutation pressures. In addition, the joints allow rigid structures to behave flexibly in general, as well as allow flexible structures to exhibit locally rigid characteristics. Owing to the discontinuous characteristics, the internal forces and their abrupt changes at vulnerable sections must be monitored to ensure the structural safety of existing shield tunnels.展开更多
Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewe...Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients—one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum—are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between s and p orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented.展开更多
In this paper the compositions(x^(μ)_(+))_(-)^(-s),(x_(+)^(μ))_(+)^(-s),(|x|^(μ))_(-)^(-s)and(|x|^(μ))_(-)^(-s)of distributions x_(+)^(μ),|x|^(μ)and x^(-s)are considered.They are defined via neutrix calculusfor...In this paper the compositions(x^(μ)_(+))_(-)^(-s),(x_(+)^(μ))_(+)^(-s),(|x|^(μ))_(-)^(-s)and(|x|^(μ))_(-)^(-s)of distributions x_(+)^(μ),|x|^(μ)and x^(-s)are considered.They are defined via neutrix calculusforμ>0,s=1,2,...andμs∈Z^(+).In addition,the composition of x^(-s)ln|x|andis also defined for r,s∈Z^(+).展开更多
基金Supported by the Natural Science Foundation of China under Grant Nos. 50831003, 50571037, and 10774041
文摘The Schrodinger equation for a particle in the V-shaped potential decorated by a repulsive or attractive Dirac delta function interaction at the center is solved, demonstrating the crucial influence of point interaction on the even-parity states of the original system without decoration. As strength of the attraction increases, the ground state energy falls down without limit; and in limit of infinitely large attraction, the ground state approaches a singular state. Our analysis and conclusion can be readily generalized to any one-dimensional system a particle interacts with symmetrical potential plus the Dirac delta function interaction at the center.
基金Sponsored by the Natural Science Foundation of Liaoning Province (Grant No.20092146)
文摘A novel method of deriving the electromagnetic dyadic Green＇s functions in an unbounded, lossless, reciprocal and homogeneous chiral media described by the constitutive relations D = εE ＋ jγB and H = jγE ＋ μ^-1B - （ωε）^-1γJ is given. The divergenceless and irrotational splitting of dyadic Dirac 8 function and Fourier transformation are used to directly obtain the divergenceless and irrotational component of spectral-domain dyadic Green＇s functions in chiral media. This method avoids using the dyadic Green＇s function eigenfunction expansion technique. The method given here can be generalized to a source-free region and an achiral case.
基金Supported by the National Natural Science Foundation of China (61271398)the Ningbo Natural Science Foundation (2011A610170)the Scientific Research Fund of Zhejiang Provincial Education Department(Y201016044)
文摘In this paper, the properties of the exponential Radon transform and its dual are discussed. Furthermore, the analytical reconstruction formulas of exponential Radon transform with two different methods are developed.
文摘It is well known that the macroscopic Maxwell’s equations can be obtained from the corresponding microscopic or atomic equations by a proper averaging process. The purpose of this paper is to present the macroscopic Maxwell’s equations which are valid in all regions of space, including an interface between two different media; and the boundary conditions can naturally emerge from the macroscopic equations as an effect of average of the microscopic Maxwell’s equations. In addition, the application of the unit step functions and the Dirac delta function to our discussion not only permits great mathematical simplicity but also gives rise to convenient physical concepts for the description and representation of the actual fields in the vicinity of the interface.
文摘The two-dimensional Dirac equation for a fermion moving under Kratzer potential in the presence of an external magnetic field is analytically being solved for the energy eigenvalues and eigenfunctions. Subsequently, we have obtained the Wigner function corresponding to the eigenfunctions.
文摘This paper is concerned with the distribution of normalized zero-sets of random meromorphic functions.The normalization of the zero-set plays the same role as the counting function for a meromorphic function in Nevanlinna theory.The results generalize the theory of Shiffman and Zelditch on the distribution of the zeroes of random holomorphic sections of powers of positive Hermitian holomorphic line bundles.As in a very special case,our paper resembles a form of First Main Theorem in classical Nevanlinna Theory.
文摘The Riemann Zeta functionζ(s)has many different representations.In this paper,we derive several new integral representations of the Zeta function using the inverse Mellin transform and a hyperbolic cosecant identity.We also derive a general integral transformation similar to the Dirac delta function and propose a few new avenues for solving Riemann’s Hypothesis.
基金supported by the National Natural Science Foundation of China(Grant No.52108363)Postdoctoral Science Foundation of China(No.2021M700654)+2 种基金Fundamental Research Funds for the Central Universities(No.3132022175)Key Laboratory of Urban Underground Engineering of Ministry of Education,Beijing Jiaotong University(No.TUL2022-01)Liaoning Revitalization Talents Program(No.XLYC1905015).
文摘An analytical model is proposed to estimate the discontinuous mechanical behavior of an existing shield tunnel above a new tunnel. The existing shield tunnel is regarded as a Timoshenko beam with longitudinal joints. The opening and relative dislocation of the longitudinal joints can be calculated using Dirac delta functions. Compared with other approaches, our method yields results that are consistent with centrifugation test data. The effects of the stiffness reduction at the longitudinal joints (α and β), the shearing stiffness of the Timoshenko beam GA, and different additional pressure profiles on the responses of the shield tunnel are investigated. The results indicate that our proposed method is suitable for simulating the discontinuous mechanical behaviors of existing shield tunnels with longitudinal joints. The deformation and internal forces decrease as α, β, and GA increase. The bending moment and shear force are discontinuous despite slight discontinuities in the deflection, opening, and dislocation. The deflection curve is consistent with the additional pressure profile. Extensive opening, dislocation, and internal forces are induced at the location of mutation pressures. In addition, the joints allow rigid structures to behave flexibly in general, as well as allow flexible structures to exhibit locally rigid characteristics. Owing to the discontinuous characteristics, the internal forces and their abrupt changes at vulnerable sections must be monitored to ensure the structural safety of existing shield tunnels.
基金supported by the Universidad del Pais Vasco/Euskal Herriko Unibertsitatea (Grant No. UFI 11/55)the Ministerio de Economia y Competitividad (Grant No. FIS2012-36673-C03-03)+2 种基金the Basque Government (Grant No. IT472-10)the Helmholtz Gemeinschaft Deutscher-Young Investigators Group (Grant No. VH-NG-717, Functional Nanoscale Structure and Probe Simulation Laboratory)the Impuls und Vernetzungsfonds der HelmholtzGemeinschaft Postdoc Programme
文摘Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients—one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum—are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between s and p orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented.
基金Tubitak(Scientific and Technological Research Council of Turkey).
文摘In this paper the compositions(x^(μ)_(+))_(-)^(-s),(x_(+)^(μ))_(+)^(-s),(|x|^(μ))_(-)^(-s)and(|x|^(μ))_(-)^(-s)of distributions x_(+)^(μ),|x|^(μ)and x^(-s)are considered.They are defined via neutrix calculusforμ>0,s=1,2,...andμs∈Z^(+).In addition,the composition of x^(-s)ln|x|andis also defined for r,s∈Z^(+).
