Transformation of Gorkov's equation for type II superconductors into transport-like equations

The stationary behavior of type II superconductors is completely described by Gorkov's equations for a set of four Green's functions, supplemented by two self-consistency equations for gap parameterΔ(r) and vector potentialA(r). Expanding all quantities as usual at the Fermi surface and averaging over impurity positions, this set of equations is transformed into a simpler set for integrated Green's functions (which still contain much more information than is needed in most cases). The resulting equations, when linearized, yield essentially Lüders' transport equation for de Gennes' correlation function. The full equations contain all the known results and provide a promising starting point for numerical calculations. The thermodynamic potential is constructed as a functional of the integrated Green's functions and the mean fieldsΔ andA and a variational principle is formulated which uses this functional. Finally, paramagnetic scatterers are included (in Born approximation) as an example for possible generalizations of the new equations.     

The lattice dynamics of an anharmonic crystal

The theory of the physical properties of an anharmonic crystal is discussed by using the thermodynamic Green's functions for the phonons. A perturbation procedure is developed to obtain the Green's functions and it is shown that for some purposes a quasi-harmonic approximation is useful, in which the frequencies of the normal modes are those determined by infra-red or neutron spectrometry. The thermodynamic, elastic, dielectric and scattering properties of an anharmonic crystal are discussed in terms of the Green's functions, and detailed expressions are given for the more important contributions. Detailed numerical calculations are presented of the thermal expansion, dielectric properties and shapes of some of the inelastically scattered neutron groups, for sodium iodide and potassium bromide. The calculations, which give reasonable agreement with experiment, show that even at quite low temperatures, the lifetimes of some of the normal modes can be quite short. By using the quasi-harmonic approximation it is shown that the large temperature dependence of the normal modes in a ferroelectric crystal can be treated adequately.     

Slave bosons in radial gauge: A bridge between path integral and Hamiltonian language

We establish a correspondence between the resummation of world lines and the diagonalization of the Hamiltonian for a strongly correlated electronic system. For this purpose, we analyze the functional integrals for the partition function and the correlation functions invoking a slave boson representation in the radial gauge. We show in the spinless case that the Green's function of the physical electron and the projected Green's function of the pseudofermion coincide. Correlation and Green's functions in the spinful case involve a complex entanglement of the world lines which, however, can be obtained through a strikingly simple extension of the spinless scheme. As a toy model we investigate the two-site cluster of the single impurity Anderson model which yields analytical results. All expectation values and dynamical correlation functions are obtained from the exact calculation of the relevant functional integrals. The hole density, the hole auto-correlation function and the Green's function are computed, and a comparison between spinless and spin 1/2 systems provides insight into the role of the radial slave boson field. In particular, the exact expectation value of the radial slave boson field is finite in both cases, and it is not related to a Bose condensate.     

Electromagnetic volume scattering in the half-space: a moment-method analysis without Sommerfeld integrals or their approximations

Abstract

Traditionally, in moment-method analyses of electromagnetic scattering, the elements of the impedance matrix are calculated as convolutions of the basis elements with the appropriate dyadic Green's function. However, for scattering in the half-space, the vertical and azimuthal copolar terms of the Green's function require evaluation of Sommerfeld integrals which are computationally burdensome. In this paper, it is shown that, in populating the impedance matrix for the half-space problem, evaluation of Sommerfeld integrals is, in fact, not necessary. For monochromatic excitation, the plane-wave expansion of the scattered field constitutes a Fourier transform, in the horizontal plane, of a vector spectral function. This vector function results from the convolution, in the vertical dimension, of the respective angular spectra of the Green's function and the equivalent current. On application of the moment method, through the Weyl identity, the impedance-matrix elements corresponding to the singular terms of the Green's function are convolutions in the horizontal plane of spherical potentials, and Fourier transforms of scalar spectral functions. These scalar functions are derived from the basis elements and, with a judicious choice of basis, they are well behaved and of compact support, and consequently their Fourier transforms can be computed as FFTs.     

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

Abstract

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.     

Constrained Correlation Dynamics of QED in Canonical Form(Ⅱ)Equal Time Limit and Two-Body Correlation Dynamics

The equations of motion for multi-time correlation Green's functions are transformed into those for equal-time correlation Green's functions,which include the equations of motion for electron's and photon's density matrices as well as vertex functions.In two-body correlation truncation approximation,we present the explicit expressions for the equations of motion,Gauss law and Ward identities explicitly.     

Two-particle Green's functions in non-equilibrium matter

The method of derivation of two-particle Green's functions in the non-equilibrium matter has been developed. The closed set of equations for the vertex functions, as well as for the two-particle Green's functions, is obtained by means of the summation of the series of indecomposable diagrams. The solution of such equations completely determines the two-particle Green's functions in the matter.     

Approximation of Green's functions

Special symmetries of the Green's functions of a non-relativistic many fermion-system and conservation laws, expressible by hermitian generators, are formulated as relations for a Green's function operator. Approximations for the Green's functions, defined as partial summations of the perturbation expansion, and consistent with the symmetries and conservation laws are presented.     

A Green's Function Approach to the Shift of Spectral Lines in Dense Plasmas

Variations of the spectral lines in high dense ion plasmas with temperature and pressure may be characterized by the broadening as well as by the shift of spectral lines. For dense hydrogen- and alkali-plasmas (free carrier density larger than 10¹⁶/cm³) one of the possible mechanisms responsible for line profiles is considered to be the Coulomb interaction with free charged carriers. Using thermodynamic Green's functions, a systematic approach to the theory of spectral lines starting from the complex dielectric function is outlined. The line shift is derived from a perturbative treatment of the two-particle Green's function in the surrounding plasma. The shift of several lines proportional to the carrier density is evaluated as a function of the temperature and compared with experimental results.     

Mixing of meson, hybrid, and glueball states

An effective QCD Hamiltonian is constructed with the aid of the background perturbation theory and relativistic Feynman-Schwinger path integrals for Green's functions. The resulting spectrum displays mass gaps of about 1 GeV when an additional valence gluon is added to the bound state. The mixing of meson, hybrid, and glueball states is defined in two ways—through generalized Green's functions and through a modified Feynman diagram technique—giving similar answers. Results for mixing matrix elements are numerically not large (around 0.1 GeV) and agree with earlier analytic estimates and lattice simulations.     

Quantum Electrodynamics at High Temperature: (I). One Spatial Dimension

The photon sector of Quantum Electrodynamics (QED) in one spatial dimension is analyzed at high temperature to all orders of perturbation theory. The imaginary-time formalism is used. The photon self-energy and propagator at finite temperature with vanishing frequency are given to second order of perturbation theory. Based upon them, an improved perturbation theory which incorporates Debye screening if formulated. In the infinite-temperature limit, the photon sector becomes equivalent to a massive scalar boson field plus a masslees pure gauge field and both are decoupled: all connected Green's functions with given external momenta much smaller than the temperature and containing, at least, one closed fermion loop with four or more vertices vanish. An approximate generating functional yielding all leading high-temperature corrections to all connected Green's functions is preaented. The Iast result leads to establish for one spatial dimension a conjecture of Gross, Pisarski and Yaffe regarding the reduction of QED to a sort of ϕ⁴ theory at high temperature. The leading high temperature contribution to the thermodynamic potential to all perturbativc orders: i) is given in terms of the dominant high temperature contribution to the two-point photon Green's function for zero frequency, ii) is shown to be both ultraviolet and infrared finite.     

Many‐body Green's function theory for thin ferromagnetic films: exact treatment of the single‐ion anisotropy

A theory for the magnetization of ferromagnetic films is formulated within the framework of many‐body Green's function theory which considers all components of the magnetization. The model Hamiltonian includes a Heisenberg term, an external magnetic field, a second‐ and fourth‐order uniaxial single‐ion anisotropy, and the magnetic dipole‐dipole coupling. The single‐ion anisotropy terms can be treated exactlyby introducing higher‐order Green's functions and subsequently taking advantage of relations between products of spin operators which leads to an automatic closure of the hierarchy of the equations of motion for the Green's functions with respect to the anisotropy terms. This is an improvement on the method of our previous work, which treated the corresponding terms only approximately by decoupling them at the level of the lowest‐order Green's functions. RPA‐like approximations are used to decouple the exchange interaction terms in both the low‐order and higher‐order Green's functions. As a first numerical example we apply the theory to a monolayer for spin S = 1 in order to demonstrate the superiority of the present treatment of the anisotropy terms over the previous approximate decouplings.     

Two-particle Green's functions in non-equilibrium matter

The method of the derivation of two-particle Green's functions in non-equilibrium matter is developed. The closed set of equations for the vertex functions and also for the two-particle Green's functions is obtained by means of the summation of the series of irreducible diagrams. The solution of such equations completely defines the two-particle Green's functions in matter.     

Remarks on a coordinate system for critical fluctuations

The elements of a coordinate system for critical fluctuations are expressed in terms of the correlation functions which characterize the thermodynamic behavior of the system. As well, a k-dependent generalization of Le Chatelier's principle is derived.     

Estimates of general Mayer graphs. I: Construction of upper bounds for a given graph by means of sets of subgraphs

A large number of physical quantities (thermodynamic and correlation functions, scattering amplitudes, intermolecular potentials, etc. ...) can be expressed as sums of an infinite number of multiple integrals of the following type: $$\Gamma \left( {x_1 ,. . . , x_n } \right) = \int {\prod {f_L \left( {x_{i,} x_j } \right)dx_{n + 1} . . . dx_{n + k} } }$$ These are called Mayer graphs in statistical mechanics, Feynman graphs in quantum field theory, and multicenter integrals in quantum chemistry. We call themn-graphs here. In a preceding note [Physics Letters 62A:295 (1977)], we have proposed a new estimation method which provides upper bounds for arbitraryn-graphs. This article is devoted to developing in detail the foundations of this method. As a first application, we prove that all virial coefficients of polar systems are finite. More generally, we show on some examples that our estimation method can givefinite upper bounds forn-graphs occurring in the perturbative developments of thermodynamic functions of neutral, polar, and ionized gases and of Green's functions of Euclidean quantum field theories (thus improving Weinberg's theorem), as also in variational approximations of intermolecular potentials. Our estimation method is based on the Hölder inequality which is an improvement over the mean value estimation method, employed by Riddell, Uhlenbeck, and Groeneveld, except for the hard-sphere gas, where both methods coincide. The method is applied so far only to individual graphs and not to thermodynamic functions.     

Green's electron function in a quantized plane wave field

It is shown that the Green's function of an electron that interacts with a quantized plane wave can be expressed in terms of the corresponding Green's function of a scalar particle. By using the known expression for the Green's function of a scalar particle, an integral representation is found with respect to the intrinsic time for the Green's electron function in a quantized plane wave of arbitrary form.     

Renormalization and Operator Product Expansion in Theories with Massless Particles

Renormalization procedure in theories including massless particles is presented. With the help of counterterm formalizm the operator product expansion for arbitrary composite fields is derived. The coefficient functions are explicitly expressed in terms of certain Green's functions.     

利用海洋环境噪声估计海流流速

为了观测海流在短时间尺度上的变化,基于被动声层析原理,提出了一种利用浅海海洋环境噪声估计海流流速的方法.通过波束形成增加噪声互相关函数的能量积累,从环境噪声互相关函数提取出两个水平阵列间的经验格林函数,利用经验格林函数的时间到达结构反演阵列间的浅海海流流速.海上实验数据处理结果表明,该方法提取了2h时间平均的经验格林函...