Multichannel Green's functions and perturbation theory for multichannel problems

Theoretical and Mathematical Physics -     

On the problem of the ergodic constant in the theory of classical Green's functions

Moscow Institute of Electronic Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 84, No. 3, pp. 459–473, September, 1990.     

On the operator representation of the Green's functions of the dynamic theory of elasticity

Starting from the operator notation for the dyadic Green's function for elastic displacement of the nonstationary theory of elasticity, we propose a method of factoring the mutually orthogonal components of the Green's function in the form of tensor products of operators acting respectively on the coordinates of the points of observation and the source. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 78–80.     

Green's functions for polynomials in the Laplacian

A Green's function is constructed for an arbitrary polynomial in theN-dimensional Laplacian operator, subject only to the condition that no root of the polynomial may be real and negative.     

Two-time temperature Green's functions in kinetic theory and molecular hydrodynamics: I. The chain of equations for the irreducible functions

We develop a scheme for constructing chains of equations for the irreducible Green's functions. The structure of the equations allows going beyond the usual perturbation theory in solving specific problems. We obtain general relations that allow any correlation function to be expressed through solutions of an infinite chain of equations for the irreducible functions. Translated from Teoreticheskaya i Matematischeskaya Fizika, Vol. 118, No. 1, pp. 105–125, January, 1999.     

Quasiparticle treatment of quantum-mechanical perturbation theory in the free electron gas

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 82, No. 3, pp. 410–427, March, 1990.     

Three-dimensional Green's functions in anisotropic magneto-electro-elastic bimaterials

In this paper, we derive three-dimensional Green's functions in anisotropic magneto-electro-elastic full space, half space, and bimaterials based on the extended Stroh formalism. While in the full space, the Green's functions are obtained in an explicit form, those in the half space and bimaterials are expressed as a sum of the full-space Green's function and a Mindlin- type complementary part, with the latter being evaluated in terms of a regular line integral over [0, p][0, \pi]. Despite the complexity involved, the current Green's function expressions are surprisingly simple. Furthermore, the piezoelectric, piezomagnetic, and purely elastic Green's functions can all be obtained from the current Green's functions by setting simply the appropriate material coefficients to zero. A special material case, to which the extended Stroh formalism cannot be applied directly, has also been identified.¶Simple numerical examples are presented for Green's functions in full space, half space, and bimaterials with fully coupled and uncoupled anisotropic magneto-electro-elastic material properties.For given material properties and fixed source and field points, the effect of magneto-electro-elastic coupling on the Green's function is discussed. In particular, we observed that magneto-electro-elastic coupling could significantly alter the magnitude of certain Green's displacement and stress components, with difference as high as 45% being noticed. This result is remarkable and should be of great interest in the material analysis and design.