Electronic Green scattering with n-fold symmetry axis from block circulant matrices

The electronic scattering Green function formalism is applied to a system processing a n-fold symmetry axis. A suitable discretization of the Lippmann-Schwinger equations leads to the inversion of block circulant matrices. This calculation is carried out by using a specialized algorithm, also described, which fully exploits the formal consequences of symmetry.

[1]  Leonard S. Rodberg,et al.  Introduction to the Quantum Theory of Scattering , 1968 .

[2]  Laurens Jansen,et al.  Theory of finite groups : applications in physics, symmetry groups of quantum mechanical systems , 1967 .

[3]  T. Kailath,et al.  Generalized Displacement Structure for Block-Toeplitz,Toeplitz-Block, and Toeplitz-Derived Matrices , 1994 .

[4]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[5]  G. Arfken Mathematical Methods for Physicists , 1967 .

[6]  Henry,et al.  Scattering-theoretic approach to elastic one-electron tunneling through localized barriers: Application to scanning tunneling microscopy. , 1988, Physical review. B, Condensed matter.

[7]  Eleftherios N. Economou,et al.  Green's functions in quantum physics , 1979 .

[8]  Fink,et al.  Holography with low-energy electrons. , 1990, Physical review letters.

[9]  Girard,et al.  Generalized Field Propagator for Electromagnetic Scattering and Light Confinement. , 1995, Physical review letters.

[10]  Gene H. Golub,et al.  Matrix computations , 1983 .

[11]  H. Akaike Block Toeplitz Matrix Inversion , 1973 .

[12]  Alexei A. Maradudin,et al.  Space groups for solid state scientists , 1979 .

[13]  V. Binh,et al.  Nanometric observations at low energy by Fresnel projection microscopy: carbon and polymer fibres , 1995 .

[14]  Heinz Schmid,et al.  In‐line holography using low‐energy electrons and photons: Applications for manipulation on a nanometer scale , 1995 .

[15]  Bayesian Rcvr,et al.  I I I I I I I I I , 1972 .