The x-ray energies and transition rates associated with single and double electron radiative transitions from the double K hole state 2s2p to the 1s2s and 1s^2 configurations of 11 selected He-like ions(10 ≤ Z ≤ 47)...The x-ray energies and transition rates associated with single and double electron radiative transitions from the double K hole state 2s2p to the 1s2s and 1s^2 configurations of 11 selected He-like ions(10 ≤ Z ≤ 47) are calculated using the fully relativistic multi-configuration Dirac–Fock method(MCDF). An appropriate electron correlation model is constructed with the aid of the active space method, which allows the electron correlation effects to be studied efficiently. The contributions of the electron correlation and the Breit interaction to the transition properties are analyzed in detail. It is found that the two-electron one-photon(TEOP) transition is correlation sensitive. The Breit interaction and electron correlation both contribute significantly to the radiative transition properties of the double K hole state of the He-like ions. Good agreement between the present calculation and previous work is achieved. The calculated data will be helpful to future investigations on double K hole decay processes of He-like ions.展开更多
The Wigner-Seitz unit cell (rhombus) for a honeycomb lattice fails to establish a k-vector in the 2D space, which is required for the Bloch electron dynamics. Phonon motion cannot be discussed in the triangular coordi...The Wigner-Seitz unit cell (rhombus) for a honeycomb lattice fails to establish a k-vector in the 2D space, which is required for the Bloch electron dynamics. Phonon motion cannot be discussed in the triangular coordinates, either. In this paper, we propose a rectangular 4-atom unit cell model, which allows us to discuss the electron and phonon (wave packets) motion in the k-space. The present paper discusses the band structure of graphene based on the rectangular 4-atom unit cell model to establish an appropriate k-vector for the Bloch electron dynamics. To obtain the band energy of a Bloch electron in graphene, we extend the tight-binding calculations for the Wigner-Seitz (2-atom unit cell) model of Reich et al. (Physical Review B, 66, Article ID: 035412 (2002)) to the rectangular 4-atom unit cell model. It is shown that the graphene band structure based on the rectangular 4-atom unit cell model reveals the same band structure of the graphene based on the Wigner-Seitz 2-atom unit cell model;the π-band energy holds a linear dispersion (ε−k ) relations near the Fermi energy (crossing points of the valence and the conduction bands) in the first Brillouin zone of the rectangular reciprocal lattice. We then confirm the suitability of the proposed rectangular (orthogonal) unit cell model for graphene in order to establish a 2D k-vector responsible for the Bloch electron (wave packet) dynamics in graphene.展开更多
Following Ashcroft and Mermin, the conduction electrons (“electrons” or “holes”) are assumed to move as wave packets. Dirac’s theorem states that the quantum wave packets representing massive particles always mov...Following Ashcroft and Mermin, the conduction electrons (“electrons” or “holes”) are assumed to move as wave packets. Dirac’s theorem states that the quantum wave packets representing massive particles always move, following the classical mechanical laws of motion. It is shown here that the conduction electron in an orthorhombic crystal moves classical mechanically if the primitive rectangular-box unit cell is chosen as the wave packet, the condition requiring that the particle density is constant within the cell. All crystal systems except the triclinic system have k-vectors and energy bands. Materials are conducting if the Fermi energy falls on the energy bands. Energy bands and gaps are calculated by using the Kronig-Penny model and its 3D extension. The metal-insulator transition in VO2 is a transition between conductors having three-dimensional and one-dimensional k-vectors.展开更多
This paper studies the properties of Nambu-Poisson geometry from the(n-l,k)-Dirac structure on a smooth manifold M.Firstly,we examine the automorphism group and infinitesimal on higher order Courant algebroid,to prove...This paper studies the properties of Nambu-Poisson geometry from the(n-l,k)-Dirac structure on a smooth manifold M.Firstly,we examine the automorphism group and infinitesimal on higher order Courant algebroid,to prove the integrability of infinitesimal Courant automorphism.Under the transversal smooth morphismΦ:N-→M and anchor mapping of M on(n-1,k)-Dirac structure,it's holds that the pullback(n-1,k)-Dirac structure on M turns out an(n-1,k)-Dirac structure on N.Then,given that the graph of Nambu-Poisson structure takes the form of(n-1,n-2)-Dirac structure,it follows that the single parameter variety of Nambu-Poisson structure is related to one variety closed n-symplectic form under gauge transformation.WhenΦ:N-→M is taken as the immersion mapping of(n-1)-cosymplectic submanifold,the pullback Nambu-Poisson structure on M turns out the Nambu-Poisson structure on N.Finally,we discuss the(n-1,O)-Dirac structure on M can be integrated into a problem of(n-1)-presymplectic groupoid.Under the mapping II:M-→M/H,the corresponding(n-1,O)-Dirac structure is F and E respectively.If E can be integrated into(n-1)-presymplectic groupoid(g,2),then there exists the only,such that the corresponding integral of F is(n-1)-presymplectic groupoid(g,).展开更多
In this paper, we consider the unitary representations of equal rank exceptional groups of type E with a regular lambda-lowest K-type and classify those unitary representations with the nonzero Dirac cohomology.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.U1832126 and 11874051)the National Key Research and Development Program of China(Grant No.2017YFA0402300)。
文摘The x-ray energies and transition rates associated with single and double electron radiative transitions from the double K hole state 2s2p to the 1s2s and 1s^2 configurations of 11 selected He-like ions(10 ≤ Z ≤ 47) are calculated using the fully relativistic multi-configuration Dirac–Fock method(MCDF). An appropriate electron correlation model is constructed with the aid of the active space method, which allows the electron correlation effects to be studied efficiently. The contributions of the electron correlation and the Breit interaction to the transition properties are analyzed in detail. It is found that the two-electron one-photon(TEOP) transition is correlation sensitive. The Breit interaction and electron correlation both contribute significantly to the radiative transition properties of the double K hole state of the He-like ions. Good agreement between the present calculation and previous work is achieved. The calculated data will be helpful to future investigations on double K hole decay processes of He-like ions.
文摘The Wigner-Seitz unit cell (rhombus) for a honeycomb lattice fails to establish a k-vector in the 2D space, which is required for the Bloch electron dynamics. Phonon motion cannot be discussed in the triangular coordinates, either. In this paper, we propose a rectangular 4-atom unit cell model, which allows us to discuss the electron and phonon (wave packets) motion in the k-space. The present paper discusses the band structure of graphene based on the rectangular 4-atom unit cell model to establish an appropriate k-vector for the Bloch electron dynamics. To obtain the band energy of a Bloch electron in graphene, we extend the tight-binding calculations for the Wigner-Seitz (2-atom unit cell) model of Reich et al. (Physical Review B, 66, Article ID: 035412 (2002)) to the rectangular 4-atom unit cell model. It is shown that the graphene band structure based on the rectangular 4-atom unit cell model reveals the same band structure of the graphene based on the Wigner-Seitz 2-atom unit cell model;the π-band energy holds a linear dispersion (ε−k ) relations near the Fermi energy (crossing points of the valence and the conduction bands) in the first Brillouin zone of the rectangular reciprocal lattice. We then confirm the suitability of the proposed rectangular (orthogonal) unit cell model for graphene in order to establish a 2D k-vector responsible for the Bloch electron (wave packet) dynamics in graphene.
文摘Following Ashcroft and Mermin, the conduction electrons (“electrons” or “holes”) are assumed to move as wave packets. Dirac’s theorem states that the quantum wave packets representing massive particles always move, following the classical mechanical laws of motion. It is shown here that the conduction electron in an orthorhombic crystal moves classical mechanically if the primitive rectangular-box unit cell is chosen as the wave packet, the condition requiring that the particle density is constant within the cell. All crystal systems except the triclinic system have k-vectors and energy bands. Materials are conducting if the Fermi energy falls on the energy bands. Energy bands and gaps are calculated by using the Kronig-Penny model and its 3D extension. The metal-insulator transition in VO2 is a transition between conductors having three-dimensional and one-dimensional k-vectors.
文摘This paper studies the properties of Nambu-Poisson geometry from the(n-l,k)-Dirac structure on a smooth manifold M.Firstly,we examine the automorphism group and infinitesimal on higher order Courant algebroid,to prove the integrability of infinitesimal Courant automorphism.Under the transversal smooth morphismΦ:N-→M and anchor mapping of M on(n-1,k)-Dirac structure,it's holds that the pullback(n-1,k)-Dirac structure on M turns out an(n-1,k)-Dirac structure on N.Then,given that the graph of Nambu-Poisson structure takes the form of(n-1,n-2)-Dirac structure,it follows that the single parameter variety of Nambu-Poisson structure is related to one variety closed n-symplectic form under gauge transformation.WhenΦ:N-→M is taken as the immersion mapping of(n-1)-cosymplectic submanifold,the pullback Nambu-Poisson structure on M turns out the Nambu-Poisson structure on N.Finally,we discuss the(n-1,O)-Dirac structure on M can be integrated into a problem of(n-1)-presymplectic groupoid.Under the mapping II:M-→M/H,the corresponding(n-1,O)-Dirac structure is F and E respectively.If E can be integrated into(n-1)-presymplectic groupoid(g,2),then there exists the only,such that the corresponding integral of F is(n-1)-presymplectic groupoid(g,).
基金This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10501025 and 10431040)
文摘In this paper, we consider the unitary representations of equal rank exceptional groups of type E with a regular lambda-lowest K-type and classify those unitary representations with the nonzero Dirac cohomology.
