Terms Of Green Function Research Articles

Analytical Solution of Generalized Space-Time Fractional Cable Equation

In this paper, we consider generalized space-time fractional cable equation in presence of external source. By using the Fourier-Laplace transform we obtain the Green function in terms of infinite series in H-functions. The fractional moments of the fundamental solution are derived and their asymptotic behavior in the short and long time limit is analyzed. Some previously obtained results are compared with those presented in this paper. By using the Bernstein characterization theorem we find the conditions under which the even moments are non-negative.

Frequency-dependent impedance of a strip foundation group and its representation in time domain

A semi-analytical procedure is presented to study the dynamic cross-interference among a group of long strip foundations on an elastic half-space, which is simplified as a two-dimensional problem. In addition to analytical solutions in terms of Green functions, a discretization method is applied to determine the lateral/rocking dynamic impedances of a foundation group. To determine the unknown contact stresses between the foundations and the supporting medium, the soil-foundation interfaces are discretized into a series of strip elements which are only subjected to constant lateral and vertical tractions. Multiple foundations with different widths and separation distances are considered in the formulations. For the time history analysis of those strongly frequency-dependent impedances of a foundation group through a substructure approach, complex Chebyshev polynomials are used to fit the lumped-parameter (L-P) model in the domain-transformation. Numerical results over a wide range of vibration frequencies for impedance calculation are verified with the existing methods. The effects of cross-interference on contact stress distributions and impedances for a group of two and three rigid foundations are discussed in detail. Finally, the accuracy and the validity of the L-P model are rigorously studied by simulating adjacent foundations on an elastic half-space within a close distance.

THE GREEN FUNCTION AND THE SZEGŐ KERNEL FUNCTION

In this paper, we express the Green function in terms of the classical kernel functions in potential theory. In particular, we obtain a formula relating the Green function and the Szegő kernel function which consists of only the Szegő kernel function in a <TEX>$C^{\infty}$</TEX> smoothly bounded finitely connected domain in the complex plane.

KINEMATIC SPIN-FLUCTUATION MECHANISM OF HIGH-TEMPERATURE SUPERCONDUCTIVITY

We study d-wave superconductivity in the extended Hubbard model in the strong correlation limit for a large intersite Coulomb repulsion V. We argue that in the Mott-Hubbard regime with two Hubbard subbands there emerges a new energy scale for the spin-fluctuation coupling of electrons of the order of the electronic kinetic energy W much larger than the exchange energy J. This coupling is induced by the kinematic interaction for the Hubbard operators which results in the kinematic spin-fluctuation pairing mechanism for V < W . The theory is based on the Mori projection technique in the equation of motion method for the Green functions in terms of the Hubbard operators. The doping dependence of superconductivity temperature Tc is calculated for various values of U and V.

Force traction microscopy: An inverse problem with pointwise observations

Force traction microscopy is an inversion method that allows one to obtain the stress field applied by a living cell on the environment on the basis of a pointwise knowledge of the displacement produced by the cell itself. This classical biophysical problem, usually addressed in terms of Green functions, can be alternatively tackled using a variational framework and then a finite elements discretization. In such a case, a variation of the error functional under suitable regularization is operated in view of its minimization. This setting naturally suggests the introduction of a new equation, based on the adjoint operator of the elasticity problem. In this paper we illustrate the rigorous theory of the two-dimensional and three-dimensional problems, involving in the former case a distributed control and in the latter case a surface control. The pointwise observations require one to exploit the theory of elasticity extended to forcing terms that are Borel measures.

Weak localization with nonlinear bosonic matter waves

We investigate the coherent propagation of dilute atomic Bose-Einstein condensates through irregularly shaped billiard geometries that are attached to uniform incoming and outgoing waveguides. Using the mean-field description based on the nonlinear Gross–Pitaevskii equation, we develop a diagrammatic theory for the self-consistent stationary scattering state of the interacting condensate, which is combined with the semiclassical representation of the single-particle Green function in terms of chaotic classical trajectories within the billiard. This analytical approach predicts a universal dephasing of weak localization in the presence of a small interaction strength between the atoms, which is found to be in good agreement with the numerically computed reflection and transmission probabilities of the propagating condensate. The numerical simulation of this quasi-stationary scattering process indicates that this interaction-induced dephasing mechanism may give rise to a signature of weak antilocalization, which we attribute to the influence of non-universal short-path contributions.

The absence of QCD β-function factorization property of the generalized Crewther relation in the ʼt Hooft [formula omitted]-based scheme

We apply the ʼt Hooft MS¯-based scheme to study the scheme-dependence of the QCD generalization of Crewther relation for the product of the normalized non-singlet perturbative contributions to the e+e−-annihilation Adler function and to the Bjorken sum rule of the polarized lepton–nucleon deep-inelastic scattering process. We prove that after the transformations from the pure MS¯-scheme to the ʼt Hooft scheme the characteristic MS¯-scheme theoretical property of this relation, namely the factorization of the β-function in its conformal symmetry breaking part, disappears. Another “non-comfortable” theoretical consequence of the application of this prescription in N=1 SUSY QED model is mentioned. It is shown, that within the ʼt Hooft scheme the expansions of Green functions in terms of the Lambert function is simplified in high orders of perturbation theory. This may be considered as the attractive feature of the ʼt Hooft scheme, which manifest itself in high-order perturbative phenomenological applications.

Theory of high-temperature superconductivity in cuprates

A microscopic theory of electronic spectrum and superconducting pairing in the high-temperature cuprate superconductors is presented. The theory is based on consideration of strong electron correlations within the Bogolyubov polar model. The Dyson equation is derived by using the equation of motion method for the thermodynamic Green functions in terms of the Hubbard operators. The self-energy is evaluated in the noncrossing approximation for electron scattering on spin and charge fluctuations induced by kinematic interaction. The theory demonstrates that a strong Coulomb repulsion results in the anomalous electronic spectrum and unconventional (d-wave) superconducting pairing with high T c mediated by the antiferromagnetic exchange and spin fluctuations.

Theory of superconductivity in strongly correlated materials: Application to cuprate superconductors

A microscopic theory of superconductivity in systems with strong electron correlations is considered within the Hubbard model. The Dyson equation for the matrix Green function in terms of the Hubbard operators is derived and solved in the noncrossing approximation for the self-energy. Two channels of superconducting pairing are revealed: mediated by antiferromagnetic (AFM) exchange and spin-fluctuations. It is proved that AFM exchange interaction results in pairing of all electrons in the conduction band and high Tc proportional to the Fermi energy. Tc dependence on lattice constants (or pressure) and an oxygen isotope shift of Tc are explained.

Electronic spectrum and superconductivity in Hubbard model

A microscopic theory of electronic spectrum and superconducting pairing within the Hubbard model is formulated. The Dyson equation for the normal and anomalous Green functions in terms of the Hubbard operators is derived by applying the Mori-type projection technique. The self-energy is evaluated in the noncrossing approximation for electron scattering on spin and charge uctuations induced by kinematic interaction for Hubbard operators. Numerical results for electron dispersion in the strong correlation limit are presented. Superconducting pairing mediated by antiferromagnetic exchange and spin uctuations is discussed.

Mean field solutions to singlet hopping and superconducting pairing within a two-band Hubbard model

The mean field Green function solution of the two-band singlet-hole Hubbard model for high-T c superconductivity in cuprates (N.M. Plakida et al., Phys. Rev. B51, 16599 (1995), JETP 97, 331 (2003)) involves expressions of higher order correlation functions describing respectively the singlet hopping and the superconducting pairing. Rigorous derivation of their values is reported based on the finding that specific invariant classes of polynomial Green functions in terms of the Wannier overlap coefficients v ij exist.

Electronic spectrum in cuprates within p– d Hubbard model

A microscopic theory for electronic spectrum of the CuO 2 plane within an effective p– d Hubbard model is proposed. Dyson equation for the one-electron Green function in terms of the Hubbard operators is derived which is solved self-consistently for the self-energy evaluated in the noncrossing approximation. Electron scattering on spin fluctuations induced by kinematical interaction is described by a model dynamical spin susceptibility. Doping and temperature dependence of electron dispersions, spectral functions, the Fermi surface and the coupling constant λ are studied.

Analysis for an N-stepped Rayleigh bar with sections of complex geometry

In this paper we analyse the vibrations of an N -stepped Rayleigh bar with sections of complex geometry, supported by end lumped masses and springs. Equations of motion and boundary conditions are derived from the Hamilton’s variational principal. The solutions for tapered and exponential sections are given. Two types of orthogonality for the eigenfunctions are obtained. The analytic solution to the N -stepped Rayleigh model is constructed in terms of Green function.

Expressions of the Green function in terms of reflection coefficients

We study the one-dimensional Schrodinger equation and derive exact expressions for the Green function in terms of reflection coefficients which are defined for semi-infinite intervals. We also discuss the relation between our results and the WKB approximation.

Nonequlibrium Green-function-based resonance system

The Tani transformation is used for the representation of the Hamiltonian to a decaying system with bound states. We considered the Liouvillean Green function and self-energy for a system far from equilibrium. Then we express the many-body Green function in terms of expectation values of decaying system operators. Next we considered that the solutions obtained from the variational stabilization process with functional derivative correspond to the resonant poles for the decaying system. This adapted variation of the procedure is applied to our model potential of three-dimensional $\ensuremath{\delta}$ barriers. We evaluated the poles for $S$ states and the corresponding initial-state wave functions for this potential.

Ab initioelectron propagator theory of molecular wires. II. Multiorbital terminal description

Correlated, ab initio electron propagator methodology may be applied to the calculation of electrical current through a molecular wire. A new theoretical formalism is developed for the calculation of retarded and advanced Green functions in terms of the electron propagator matrix for a bridge molecule. The calculation of the current requires integration in a complex half-plane for a trace that involves terminal and Green function matrices that may have any rank. Because the latter arrays have poles represented by matrices, an alternative expression is developed in terms of ordinary poles which are (n-1)-fold degenerate or nondegenerate. For an arbitrary number of terminal orbitals, the analytical expression for the current is given in terms of pole strengths, poles, and terminal matrix elements of the electron propagator, i.e., the parameters that are found in the output of numerical calculations.

On the spectral relations for multitime correlation functions

A general approach for derivation of the spectral relations for the multitime correlation functions is presented. A special attention is paid to the consideration of the non-ergodic (conserving) contributions and it is shown that such contributions can be treated in a rigorous way using multitime temperature Green functions. Representation of the multitime Green functions in terms of the spectral densities and solution of the reverse problem -- finding of the spectral densities from the known Green functions are given for the case of the three-time correlation functions.

Antiferromagnetic exchange and spin-fluctuation pairing in cuprate superconductors

Abstract A microscopic theory of superconductivity is formulated within an effective p - d Hubbard model for a CuO 2 plane. By applying the Mori-type projection technique, the Dyson equation is derived for the Green functions in terms of Hubbard operators. The antiferromagnetic exchange caused by interband hopping results in pairing of all carries in the conduction subband and high T c proportional to the Fermi energy. Kinematic interaction in intraband hopping is responsible for the conventional spin-fluctuation pairing. Numerical solution of the gap equation proves the d -wave gap symmetry and defines T c doping dependence. Oxygen isotope shift and pressure dependence of T c are also discussed.

Ab initioelectron propagator theory of molecular wires: I. Formalism

Ab initio electron propagator methodology may be applied to the calculation of electrical current through a molecular wire. A new theoretical approach is developed for the calculation of the retarded and advanced Green functions in terms of the electron propagator matrix for the bridge molecule. The calculation of the current requires integration in a complex half plane for a trace that involves terminal and Green's-function matrices. Because the Green's-function matrices have complex poles represented by matrices, a special scheme is developed to express these "matrix poles" in terms of ordinary poles. An expression for the current is derived for a terminal matrix of arbitrary rank. For a single terminal orbital, the analytical expression for the current is given in terms of pole strengths, poles, and terminal matrix elements of the electron propagator. It is shown that Dyson orbitals with high pole strengths and overlaps with terminal orbitals are most responsible for the conduction of electrical current.

Energy Spectrum of Ground State and Excitation Spectrum of Quasi-particle forHard-Core Boson in Optical Lattices**The project supported by NationalFundamental Research Programof China under Grant No. 2001CB309307, the Knowledge Innovation Program ofthe Chinese Academy of Sciences, and National Natural Science Foundationof China under Grant Nos. 10334050 and 10474105

We investigate the energy spectrum of ground state andquasi-particle excitation spectrum of hard-core bosons, whichbehave very much like spinless noninteracting fermions, in opticallattices by means of the perturbation expansion and Bogoliubovapproach. The results show that the energy spectrum has a singleband structure, and the energy is lower near zero momentum; theexcitation spectrum gives corresponding energy gap, and the systemis in Mott-insulating state at Tonks limit. The analytic result ofenergy spectrum is in good agreement with that calculated in termsof Green's function at strong correlation limit.