The asymptotic behaviour of the exact and approximative ν = 1/2 Chern-Simons Green's functions

We consider the asymptotic behaviour of the Chern-Simons Green's function of the ν = 1/ system for an infinite area in position-time representation. We calculate explicitly the asymptotic form of the Green's function of the interaction free Chern-Simons system for small times. The calculated Green's function vanishes exponentially with the logarithm of the area. Furthermore, we discuss the form of the divergence for all τ and also for the Coulomb interacting Chern-Simons system. We compare the asymptotics of the exact Chern-Simons Green's function with the asymptotics of the Green's function in the Hartree-Fock as well as the random-phase approximation (RPA). The asymptotics of the Hartree-Fock Green's function correspondence well with the exact Green's function. In the case of the RPA Green's function we do not get the correct asymptotics. At last, we calculate the self consistent Hartree-Fock Green's function. Received 5 July 2001 and Received in final form 30 November 2001     

Construction of the Green's function for the pseudoharmonical oscillator

In the present paper we have constructed the Green's function for the pseudoharmonical potential, which is considered as an intermediate potential between the harmonic and anharmonic potentials. We have used a hybrid method, by combining the Laplace transformation method and the Green's function technique. The Green's function is used for obtaining the density matrix for a quantum-statistical system, in coordinate representation. Even if this is not a new result, the method can be applied to a class of exactly solvable potentials.     

Extracting the Green's function from measurements of the energy flux

Existing methods for Green's function extraction give the Green's function from the correlation of field fluctuations recorded at those points. In this work it is shown that the Green's function for acoustic waves can be retrieved from measurements of the integrated energy flux through a closed surface taken from three experiments where two time-harmonic sources first operate separately, and then simultaneously. This makes it possible to infer the Green's function in acoustics from measurements of the energy flux through an arbitrary closed surface surrounding both sources. The theory is also applicable to quantum mechanics where the Green's function can be retrieved from measurement of the flux of scattered particles through a closed surface.     

Functional integral approach to the single impurity Anderson model

Recently, a functional integral representation was proposed by Weller [1], in which the fermionic fields strictly satisfy the constraint of no double occupancy at each lattice site. This is achieved by introducing spin dependent Bose fields. The functional integral method is applied to the single impurity Anderson model both in the Kondo and mixed-valence regime. Thef-electron Green's function and susceptibility are calculated using an Ising-like representation for the Bose fields. We discuss the difficulty to extract a spectral function from the knowledge of the imaginary time Green's function. The results are compared with NCA calculations.     

On the resistance of an infinite square network of identical resistors – Theoretical and experimental comparison

A review of the theoretical approach for calculating the resistance between two arbitrary lattice points in an infinite square lattice (perfect and perturbed cases) is carried out using the lattice Green's function. We show how to calculate the resistance between the origin and any other site using the lattice Green's function at the origin, G_o (0, 0), and its derivatives. Experimental results are obtained for a finite square network consisting of 30 ×30 identical resistors, and a comparison with those obtained theoretically is presented.     

A boundary integral method to compute Green's functions for the radiative transport equation

The Green's function for the time-independent radiative transport equation in the whole space can be computed as an expansion in plane wave solutions. Plane wave solutions are a general class of solutions for the radiative transport equation. Because plane wave solutions are not known analytically in general, we calculate them numerically using the discrete ordinate method. We use the whole space Green's function to derive boundary integral equations. Through the solution of the boundary integral equations, we compute the Green's function for bounded domains. In particular we compute the Green's function for the half space, the slab, and the two-layered half space. The boundary conditions used here are in their most general form. Hence, this theory can be applied to boundaries with any kind of reflection and transmission law.     

Scalar Green's functions in an Euclidean space with a conical-type line singularity

In an Euclidean space with a conical-type line singularity, we determine the Green's function for a charged massive scalar field interacting with a magnetic flux running through the line singularity. We give an integral expression of the Green's function and a local form in the neighbourhood of the point source, where it is the sum of the usual Green's function in Euclidean space and a regular term. As an application, we derive the vacuum energy-momentum tensor in the massless case for an arbitrary magnetic flux.Supported by a grant from CNPq (Brazilian government agency FA)     

SYMMETRY AND WARD IDENTITIES FOR DISORDERED ELECTRON SYSTEMS

We study the field theory approach to Anderson localization in the framework of closed time path Green's function (CTPGF).The theory is found to be invariant under an Sp(2) group. Ward identities related to this symmetry are derived. A non-linear σ model arises as a consequence of the dynamical symmetry breaking caused by the imaginary part of the retarded Green's function.     

多个侧向链对横向量子线传输性质的调制

利用递推格林函数方法，研究了与多个量子点间无相互作用的量子链相耦合的横向量子线的电子输运特性，发现量子链上格点的个数N_U与侧向无限或有限量子链个数N对横向量子线输运性质的不同调制规律.由计算可知，利用格林函数可以方便的对传输构型及传输链中的格点数进行调解，从而得到各种人为量子器件的输运性质. 关键词： 递推格林函数 无限链 有限链 电子输运     

Ingoing and outgoing waves in the non-relativistic theory of photoionization

A well-known formula for the differential cross section for photoionization contains a so-called ‘final state’ wave function which asymptotically behaves as a Coulomb-modified plane wave plus an ingoing Coulomb-modified radial wave. We explain the reason of appearance of that function on the ground of an analysis of an asymptotic form of a relevant outgoing Green's function. The reasoning is carried out without referring to an intuitive argumentation of Breit and Bethe [Phys. Rev. 93 (1954) 888].     

Short-range correlations in nuclear matter using Green's functions within a discrete pole approximation

We treat short-range correlations in nuclear matter, induced by the repulsive core of the nucleon–nucleon potential, within the framework of self-consistent Green's function theory. The effective in-medium interaction sums the ladder diagrams of both the particle–particle and hole–hole type. The demand of self-consistency results in a set of nonlinear equations which must be solved by iteration. We explore the possibility of approximating the single-particle Green's function by a limited number of poles and residues.     

Scattering of a scalar wave from a two-dimensional randomly rough Neumann surface

We present a reciprocity and unitarity preserving formulation of the scattering of a scalar plane wave from a two-dimensional, randomly rough surface on which the Neumann boundary condition is satisfied. The theory is formulated on the basis of the Rayleigh hypothesis in terms of a single-particle Green's function G(q_‖|k_‖) for the surface electromagnetic waves that exist at the surface due to its roughness, where k_‖ and q_‖ are the projections on the mean scattering plane of the wave vectors of the incident and scattered waves, respectively. The specular scattering is expressed in terms of the average of this Green's function over the ensemble of realizations of the surface profile function (G(q_‖|k_‖)). The Dyson equation satisfied by (G(q_‖|k_‖)) is presented, and the properties of the solution are discussed, with particular attention to the proper self-energy in terms of which the averaged Green's function is expressed. The diffuse scattering is expressed in terms of the ensemble average of a two-particle Green's function, which is the product of two single-particle Green's functions. The Bethe-Salpeter equation satisfied by the averaged two-particle Green's function is presented, and properties of its solution are discussed. In the small roughness limit, and with the irreducible vertex function approximated by the sum of the contribution from the maximally-crossed diagrams, which represent the coherent interference between all time-reversed scattering sequences, the solution of the Bethe-Salpeter equation predicts the presence of enhanced backscattering in the angular dependence of the intensity of the waves scattered diffusely.     

Si4团簇电子输运性质的第一性原理计算

采用密度泛函理论和非平衡格林函数相结合的方法对Si₄ 团簇与Au(100)电极空位相连的纳米结点的电子输运性质进行了理论模拟计算, 得到了纳米结点在不同距离下的几何结构、电子结构、电导、透射谱、电荷转移量; 讨论了当距离d_z=12.004 Å时纳米结点的电导、电流随电压的变化关系. 关键词： 密度泛函理论 非平衡格林函数 4团簇')" href="#">Si₄团簇 电子输运     

Finite temperature contributions to the renormalized energy-momentum tensor for an arbitrary curved space-time

The finite temperature contributions to the effective Lagrangian and energy-momentum tensor in the cases of scalar and spinor fields are evaluated by means of the Green's function method. The results are obtained in an arbitrary curved space-time by adiabatic expansions of the Green's functions.We would like to thank professor D. Ivanenko for support of our work and many stimulating discussions.     

Simulating biochemical networks at the particle level and in time and space: Green's function reaction dynamics

We present a technique, called Green's function reaction dynamics (GFRD), for particle-based simulations of reaction-diffusion systems. GFRD uses a maximum time step such that only single particles or pairs of particles have to be considered. For these particles, the Smoluchowski equations are solved analytically using Green's functions, which are used to set up an event-driven algorithm. We apply the technique to a model of gene expression. Under biologically relevant conditions, GFRD is up to 5 orders of magnitude faster than conventional particle-based schemes.     

Some fermi surface properties of double-exchange interaction systems

We study the photoemission spectrum of the double-exchange (DE) interaction systems. The DE Hamiltonian can be transformed into a simple form consisting of fermions and Schwinger bosons. We apply the gauge-field model and calculate the Green's function of the gauge field, fermions, and bosons. The imaginary part of the Green's function of an electron has an asymmetrical peak with strong temperature dependence. This can explain why the shape of the angle-resolved photoemission spectra of manganites near the Fermi surface is very different from that of Fermi liquid. We also show why the position of the Fermi surface is not sensitive to temperature.     

Anisotropy of the energy gap in the insulating phase of the U-t-t' Hubbard model

We apply a diagrammatic expansion method around the atomic limit () for the U-t-t ' Hubbard model at half filling and finite temperature by means of a continued fraction representation of the one-particle Green's function. From the analysis of the spectral function we find an energy dispersion relation with a modulation of the energy gap in the insulating phase. This anisotropy is compared with experimental ARPES results on insulating cuprates. Received 18 May 2000 and Received in final form 9 August 2000     

Green's functions for Maxwell's equations: application to spontaneous emission

We present a new formalism for calculating the Green's function for Maxwell's equations. As our aim is to apply our formalism to light scattering at surfaces of arbitrary materials, we derive the Green's function in a surface representation. The only requirement on the material is that it should have periodicity parallel to the surface. We calculate this Green's function for light of a specific frequency and a specific incident direction and distance with respect to the surface. The material properties entering the Green's function are the reflection coefficients for plane waves at the surface. Using the close relationship between the Green's function and the density of states (DOS), we apply our method to calculate the spontaneous emission rate as a function of the distance to a material surface. The spontaneous emission rate can be calculated using Fermi's Golden Rule, which can be expressed in terms of the DOS of the optical modes available to the emitted photon. We present calculations for a finite slab of cylindrical rods, embedded in air on a square lattice. It is shown that the enhancement or suppression of spontaneous emission strongly depends on the frequency of the light. This revised version was published online in November 2006 with corrections to the Cover Date.     

An approach to the nonequilibrium theory of highly excited semiconductors

We present an investigation of the optical properties of semiconductors, which are excited by a strong laser pulse. On the basis of a nonequilibrium Green's function technique (Keldysh formalism) we study the system of electrons and holes, interacting among themselves and with the exciting pulse. A set of coupled equations for the one-particle Green's function and the transverse and longitudinal polarizability is derived, which is valid for arbitrary excitation conditions. For an initially prepared state, which is not too far from a quasiequilibrium state of the excited system, the theory is elaborated in detail, using a screened Hartree-Fock approximation scheme. Within this approximation earlier results of various theoretical approaches are found to be special cases of the equilibrium limit of the present theory.