**Real Space Green's Function Technique**

### A Brief Description

The key feature of this method is to use a Local Green's Function to study the properties of a complex system with no long range order or posessing partial order. It has been shown, by Wu and his co-workers[K.S. Dy, S.Y. Wu, and T. Spratlin, Phys. Rev. **B20**, 4237 (1979).], that for a block tri-diagonal matrix, one can obtain exact expressions for diagonal and off diagonal elements. The local density of the states is then simply proportional to the imaginary part of the Green's Function at the locality in question. This method has been successfully used to study vibrational properties of the Au(511) surface, Incommensurate Structures, Alloys, etc. Since the calculation of Green's Function involves inverting matrices, we have developed efficient schemes to invert large matrices. Also, we have developed an efficient recursive relation that eliminates the redundancy in the calculation of the Local Green's Function(LGF). This procedure of calculating the LGF does not have any truncation unlike the traditional method of calculating the LGF via the continued fraction method.

### Recent Publications in Real Space Green's Function Technique

- S.Y. Wu, J.A. Cocks and C.S. Jayanthi,
*An Accelerated Inversion Algorithm Using Resolvent Matrix Method*, Computer Physics Communication, 71, 125(1992). - S.Y. Wu, J.A. Cocks and C.S. Jayanthi,
*General Recursive Relation for the Calculation of the Local Green's Function*, S.Y. Wu, J.A. Cocks and C.S. Jayanthi, Physical Review B**49**, 7957 (1994). - S.Y. Wu and C.S. Jayanthi.
*The Local Analysis via the Real Space Green's Function*, Int. J. Modern Physics B Vol. 9, No. 16, p. 1869-1897 (1995) ...**(Invited Review)**. - C.S. Jayanthi and S.Y. Wu,
*Act Locally and Think Globally*, Journal of Computer-Aided Design,**3**(1996). - N. Mingo, L. Jurczyszyn, F.J. Garcia-Vidal, R. Saiz-Pardo, P.L. Andres, F. Flores, S.Y. Wu, and W. More,
*Theory of the Scanning Tunneling Microscope: Xe on Ni and Al*, Phys. Rev.**B54**, 1 (1996).