“Proper Time” Method Calculation of the “One Loop” Thermodynamical Potential for QED in External Electromagnetic Field

The extension of the “proper time” method to the statistical field theory is obtained. The procedure is used to calculate the “one loop” contribution to the thermodynamical potential in electrodynamics, when the electron positron gas is located in a combination of an inhomogeneous electrostatic field and an uniform magnetic one. Also, a “proper time” representation of the temperature Green function for this problem is given.     

The photon two-point function in unitary approximation

The photon two-point function is calculated using the exponential representation for the time-evolution operator taking into account terms up to second order ine in the exponent. The limiting case of vanishing electron mass is examined and it is shown that mass singularities cancel by means of unitarity. Near mass shell the causal Green function exhibits in the limit of vanishing electron mass the expected cut behaviour, off mass shell we recover the result of the usual perturbation theory.     

The influence of solid bodies on low Mach number vortex sound

The mechanisms of sound generation by unsteady, subsonic flows in the presence of solid boundaries are investigated. For this purpose an alternative integral representation for the radiated pressure field is applied which is different from the generally used integral representation introduced by Lighthill and Curle. The main advantage of the method is that there is a linear dependence of the integrand on the time derivative of the vorticity fluctuations in the hydrodynamic near field; instead of the ordinary Green function a “vector Green function” is used. This vector Green function can be chosen for a given flow field in such a way that surface integrals do not appear. Finally, the theory is illustrated by two- and three-dimensional model flows. Analytical solutions are determined by applying the method of matched asymptotic expansions.     

Heating and thermoelectric transport in a molecular junction

The energy dissipation and heat flows associated with the particle current in a system with a molecular junction are considered. In this connection, we determine the effective temperature of the molecular oscillator that is compatible with the existence of a steady state. The calculations based on the Kadanoff-Baym nonequilibrium Green function formalism are carried out supposing a strong coupling of the dot electrons with the molecular vibrations. Accordingly, the representation given by the Lang-Firsov polaron transformation is used and the dependence of results on the electron–phonon interaction strength is investigated.     

An Integral Transform of Coulomb Green’s Function via Sturmian Representation and Off-Shell Scattering

By exploiting the term by term separability of the Sturmian function representation of the Coulomb Green’s function an integral transform of the corresponding outgoing wave Green’s function, that plays a crucial role in the studies of off-shell properties of the Coulomb and Coulomb-like interactions, is derived. Working in the representation space the off-shell Jost solutions and T-matrices for motion in Coulomb and Coulomb-modified nuclear potentials are expressed in terms of simple expressions involving hypergeometric functions. The effectiveness of our constructed expressions for the T-matrices is examined through a model calculation.     

On Recent Analytical Results for Solution of the Scattering Problem for the Sharply Screened Coulomb Potential

Exact representations for the wave function and for the Green function of the Hamiltonian with the sharply screened Coulomb potential are given. The representations are obtained by summing up the partial wave series. The final form of the wave function and the Green function in the region of the coordinate space where the potential is not zero are given in terms of the Coulomb wave function and the Coulomb Green function, respectively. The exact representation has been obtained for the transition operator in the configuration space.     

Understanding of surface states in a correlated electron system

The aim of this work is to find a simple analytic model to explain some principal aspects of the behavior of surface states in correlated electron systems. We start from the analytic expression for the Green function of the semi-infinite tight binding linear chain. This Green function in case of modification of the center of gravity of the first atom and the change in coupling between the first and the second atom is evaluated as an exact analytic expression. Conditions for the existence and classification of surface states are given. The spectral weight of surface states and the local density of states are evaluated. The method is applied to a s.c. (100) surface of a local moment crystal. Conditions for the existence of surface states are derived and their locations in the Brillouin zone are predicted. It is shown that it is possible to include correlation effects within the framework of the discussed model. The comparison with former numerical results is performed. Received 8 March 2000     

Propagation of a short pulse in a medium with a resonance relaxation: The exact solution

A new analytical representation is obtained for the fundamental solution (Green’s function) to the problem of the propagation of a short pulse in an arbitrary medium with a single resonance relaxation process. The analytical representation is based on the generalized function of the local response of a linear medium [1] and includes the well-known Debye and Lorentz relaxation models as particular cases. The representation is used to determine the complete set of possible types of behavior for a short pulse propagating in the medium.     

Dyson equation for Heisenberg ferromagnet

An exact representation for the self-energy operator of the two-time Green function for the transverse spin components for the Heisenberg ferromagnet is obtained.     

Ferromagnetism in Hubbard model in many-electron operator representation

The Hubbard model for a metal with strong correlations is considered in the representation of many-electron X-operators. General self-consistent expressions are obtained for the one-particle Green function taking into account fluctuation corrections. The stability regions of the saturated and unsaturated ferromagnetism in the ground state on the n-U plane (n is the electron concentration and U is the Coulomb interaction parameter) are determined for various bare densities of states (semi-elliptic band and the square, cubic, and hypercubic lattices).     

Green functions in stochastic field theory

Functional representations are reviewed for the generating function of Green functions of stochastic problems stated either with the use of the Fokker-Planck equation or the master equation. Both cases are treated in a unified manner based on the operator approach similar to quantum mechanics. Solution of a second-order stochastic differential equation in the framework of stochastic field theory is constructed. Ambiguities in the mathematical formulation of stochastic field theory are discussed. The Schwinger-Keldysh representation is constructed for the Green functions of the stochastic field theory which yields a functional-integral representation with local action but without the explicit functional Jacobi determinant or ghost fields.     

Faddeev–Jackiw canonical path integral quantization for a general scenario,its proper vertices and generating functionals

We generalize the Faddeev–Jackiw canonical path integral quantization for the scenario of a Jacobian with J=1 to that for the general scenario of non-unit Jacobian, give the representation of the quantum transition amplitude with symplectic variables and obtain the generating functionals of the Green function and connected Green function. We deduce the unified expression of the symplectic field variable functions in terms of the Green function or the connected Green function with external sources. Furthermore, we generally get generating functionals of the general proper vertices of any n-points cases under the conditions of considering and not considering Grassmann variables, respectively; they are regular and are the simplest forms relative to the usual field theory.     

硅中Jahn-Teller畸变的磷-空位复合缺陷的电子结构

本文采用扩展的缺陷势,利用一个紧束缚的Koster-Slater格林函数方法,确定了磷-空位缺陷的波函数为深能级E的函数,以深能级的实验值为输入参数,得到的波函数定量地描述了EPR和ENDOR实验资料,特别是,理论给出空位的四个近邻原子上的超精细相互作用常数α和b,同实验符合得很好。 关键词：     

Conserving approximations for response functions of the Fermi gas in a random potential

One- and two-electron Green functions are simultaneously needed to determine the responsefunctions of the electron gas in a random potential. Reliable approximations must retainconsistency between the two types of Green functions expressed via Ward identities so thattheir output is compliant with macroscopic symmetries and conservation laws. Such aconsistency is not directly guaranteed when summing nonlocal corrections to the local(dynamical) mean field. We analyze the reasons for this failure and show how the full Wardidentity can generically be implemented in the diagrammatic approach to the vertexfunctions without breaking the analytic properties of the self-energy. We use thelow-energy asymptotics of the conserving two-particle vertex determining the singular partof response and correlation functions to derive an exact representation of the diffusionconstant in terms of Green functions of the perturbation theory. We then calculateexplicitly the leading vertex corrections to the mean-field diffusion constant due tomaximally-crossed diagrams.     

A simple approach to the evaluation of the hall conductivity in impure metals within the green function formalism

A simple method of dealing with the Hall effect in metals with short-ranged impurities in a weak magnetic field is proposed. The method is based on a Schwinger representation for the electron Green function in the magnetic field. The efficacy of the method is demonstrated on a calculation of the antisymmetric components of the conductivity tensor at finite wave vector. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 2, 141–145 (25 January 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Green函数及δ函数的三方向球函数展开式

将1/R及δ函数的积分表达式分离径向与角向变量得到了用三个分矢的球函数及冪级数表达的展开式。     

Green functions in a super self-dual Yang-Mills background

In euclidean supersymmetric theories of chiral superfields and vector superfields coupled to a super-self-dual Yang-Mills background, we define Green functions for the Laplace-type differential operators which are obtained from the quadratic part of the action. These Green functions are expressed in terms of the Green function on the space of right chiral superfields, and an explicit expression for the right chiral Green function in the fundamental representation of an SU(n) gauge group is presented using the supersymmetric version of the ADHM formalism. The superfield kernels associated with the Laplace-type operators are used to obtain the one-loop quantum corrections to the super-self-dual Yang-Mills action, and also to provide a superfield version of the super-index theorems for the components of chiral superfields in a self-dual background.     

Magnetic and electric phase transitions in the Hubbard model

Within the Hubbard model, two boson Green’s functions that describe the propagation of collective excitations of the electronic system—magnons (states with a single electron spin flip) and doublons (states with two electrons at one site of the crystal lattice)—are calculated for a Coulomb interaction of arbitrary strength and for an arbitrary electron concentration by applying a decoupling procedure to the double-time X-operator Green’s functions. It is found that the magnon and doublon Green’s functions are similar in structure and there is a close analogy between them. Instability of the paramagnetic phase with respect to spin ordering is investigated using the magnon Green’s function, and instability of the metallic phase to charge ordering is analyzed with the help of the doublon Green’s function. Criteria for the paramagnet-ferromagnet and metal-insulator phase transitions are found.     

The O(2.1) algebra and the electron green function in a Coulomb field

An integral representation for the Green function of a charged particle moving in a Coulomb field is obtained, with the help of the O(2.1) algebra, in a form convenient for applications.