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.     

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.     

Two and three body equations in quantum field models

In each pure phase of a ?(φ)₂ quantum field model, we establish local regularity of the Green's functions and exponential decay for noncritical models. We establish the existence of two-particle and three-particle Bethe-Salpeter kernels in the Euclidean region.     

Functional Integral Approach to a Many Fermion System with Bound States

The equation of state for a dense system of interacting Fermions is derived using functional integral technique. To investigate the formation of bound states, a Hubbard-Stratonovich transformation is applied which expresses the action as functional of pair fields. The evaluation of the partition function in lowest orders with respect to the pair fields leads to a result which can be interpreted as the contribution of two-particle states, accounting for density corrections as Pauli blocking and self-energy shift. Comparison is performed with results for the equation of state of hot dense matter (plasmas, nuclear matter) obtained within a Green's function approach.     

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.     

Quantum Theory of Solid State Plasma Dielectric Response

We review the quantum mechanical derivation of the random phase approximation (RPA) for solid state plasmas, starting from the Hamilton equations for canonically paired “second quantized” creation and annhilation field operators of interacting quantum many‐body systems. Discussing variational differentiation, the coupled equations of motion for the quantum field operators are derived. The concept of Green's functions is reviewed and interpreted, first for retarded Green's functions, and their equations of motion are developed from the equations of motion for the field operators. Thermodynamic Green's functions are discussed, and their periodicity/antiperiodicity properties in imaginary time are carefully examined with discussion of Matsubara Fourier series and representation in terms of a spectral weight function. The analytic continuation from imaginary time to real time is treated. Finally, we define nonequilibrium Green's functions and discuss the linearized timedependent Hartree approximation leading to the random phase approximation. An interesting application to the case of Graphene in a perpendicular magnetic field is discussed in detail, along with applications to normal systems, in terms of attendant phenomenology involving electron‐hole pair excitations and plasmons (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

A calculation of the odd parity spectrum of16O and40Ca from the interaction between nucleons: Method and first results

In the framework of an exact many-body theory based on the formalism of Green's functions, we rederive an eigenvalue equation capable of describing single particle excitations of a Fermi system. The effective two-particle interaction entering this equation is extracted free of all adjustable parameters from a very simple nucleon-nucleon interaction by solving the corresponding integral equation for nuclear matter and using a local density approximation. We apply our method for describing those states of the doubly magic nuclei¹⁶O and⁴⁰Ca which probably can be understood as one-particle-one-hole excitations from the ground state, i.e. low-lying negative parity levels, and — in view of the simplicity of the interaction assumed — find reasonably good aggreement with experimental evidence.     

Some exact identities connecting one- and two-particle Green's functions in spin–orbit coupling systems

Some exact identities connecting one- and two-particle Green's functions in the presence of spin–orbit coupling have been derived. These identities are similar to the Ward identity in usual quantum transport theory of electrons. A satisfying approximate calculation of the spin transport in spin–orbit coupling system should also preserve these identities, just as the Ward identities should be remained in the usual electronic transport theory.     

Contribution to the theory of bremsstrahlung in scattering media

Bremsstrahlung of particles in matter is investigated on the basis of a method developed for finding the two-particle Green’s functions in nonequilibrium media. A closed system of equations for the exact two-particle Green’s functions in a medium, which completely determined the bremsstrahlung spectrum in matter, is obtained by summing a series of irreducible diagrams. The radiation of fast charged particles undergoing multiple elastic collisions in a static medium is investigated in detail. For quite strong scattering in matter, the spectrum found differs substantially from the spectrum found previously by A. B. Migdal [Dokl. Akad. Nauk SSSR 96, 49 (1954)] (Landau-Pomeranchuk-Migdal effect).     

Equivalence betweenS-matrix and Green's function approach to the kondo problem

We prove the complete equivalence of Suhl'sS-matrix approach and Nagaoka's Green's functions approach to the Kondo problem. This proof is established quite generally for any density of states function of the electrons. In particular we solve Suhl's equations and show that Nagaoka's equations as well as their solutions can be derived from Suhl's approach. Vice versa it is shown that the solutions of the Nagaoka equations satisfy Suhl's equations uniquely.     

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.     

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.     

Localized magnetic excitations of coupled impurities in a transverse Ising ferromagnet

A Green's function formalism is used to calculate the spectrum of excitations of two neighboring impurities implanted in a semi-infinite ferromagnetic. The equations of motion for the Green's functions are determined in the framework of the Ising model in a transverse field and results are given for the effect of the exchange coupling, position and orientation of the impurities on the spectra of localized spin wave modes.     

On Green's function for cylindrically symmetric fields of polarized radiation

Analytic expressions for Green's function describing the process of transfer of polarized radiation in homogeneous isotropic infinite medium in case of cylindrical symmetry and nonconservative scattering are obtained. The solution is based on the set of systems of Abel integral equations of the first kind obtained using the principle of superposition, and the known expression of Green's function for radiation fields with plane-parallel symmetry. Eigenvalue decompositions for the corresponding matrices of generalized spherical functions are found. Using this result the systems of Abel integral equations are diagonalized, and the final solution is obtained.     

The (d,p)-reaction treated by the formalism of Green's functions

The full energy dependence of the two-particle Green's function is taken into account in deriving theS-matrix for a (d, p)-reaction leading from an even-even nucleus in the ground state to a single-particle residual state in the even-odd nucleus. The resultingT-vertex of many-body theory is discussed with the Bethe-Salpeter equation in the particle-particle channel, which allows for a renormalization in the same sense as for bound state problems but now in a different range of energy. Special attention is paid to the problems arising in expanding the deuteron (two particles in the continuum) into shell model wave functions.     

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 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.     

Quantum transport equations for two-band semiconductor systems

Employing nonequilibrium Green's functions and the equation of motion technique, transport equations for two-band semiconductor systems are derived and their physical significance is discussed.