scholarly journals Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism

2014 ◽  
Vol 90 (20) ◽  
Author(s):  
Aftab Alam ◽  
Suffian N. Khan ◽  
A. V. Smirnov ◽  
D. M. Nicholson ◽  
Duane D. Johnson
Keyword(s):  
Green’S Function ◽  
Multiple Scattering ◽  
Green's Function ◽  
Scattering Theory ◽  
Basis Set ◽  
Multiple Scattering Theory

Multiple-scattering theory with a truncated basis set

1992 ◽  
Vol 46 (12) ◽  
pp. 7433-7447 ◽  
Author(s):  
X.-G. Zhang ◽  
W. H. Butler
Keyword(s):  
Multiple Scattering ◽  
Scattering Theory ◽  
Basis Set ◽  
Multiple Scattering Theory

LOCAL DENSITY CALCULATIONS FOR LARGE SYSTEMS USING MULTIPLE SCATTERING THEORY

1995 ◽  
Vol 02 (01) ◽  
pp. 71-79
Author(s):  
D.M.C. NICHOLSON ◽  
G.M. STOCKS ◽  
Y. WANG ◽  
W.A. SHELTON ◽  
Z. SZOTEK ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Multiple Scattering ◽  
Scattering Theory ◽  
Schrodinger Equation ◽  
Local Density ◽  
Basis Set ◽  
Scattering Method ◽  
Multiple Scattering Theory ◽  
Large Systems ◽  
Multiple Scattering Method

The accuracy of energy differences calculated from first principles within the local density approximation (LDA) has been demonstrated for a large number of systems. Armed with these energy differences researchers are addressing questions of phase stability and structural relaxation. However, these techniques are very computationally intensive and are therefore not being used for the simulation of large complex systems. Many of the methods for solving the Kohn-Sham equations of the LDA rely on basis set methods for solution of the Schrodinger equation. An alternative approach is multiple scattering theory (MST). We feel that the locally exact solutions of the Schrodinger equation which are at the heart of the multiple scattering method give the method an efficiency which cannot be ignored in the search for methods with which to attack large systems. Furthermore, the analytic properties of the Green function which is determined directly in MST result in computational shortcuts.

scholarly journals Unified double- and single-sided homogeneous Green’s function representations

2016 ◽  
Vol 472 (2190) ◽  
pp. 20160162 ◽  
Author(s):  
Kees Wapenaar ◽  
Joost van der Neut ◽  
Evert Slob
Keyword(s):  
Green’S Function ◽  
Multiple Scattering ◽  
Green's Function ◽  
Time Reversal ◽  
Wave Theory ◽  
Boundary Integral ◽  
Open Boundary ◽  
Quantum Mechanical ◽  
Holographic Imaging ◽  
Scattering Time

In wave theory, the homogeneous Green’s function consists of the impulse response to a point source, minus its time-reversal. It can be represented by a closed boundary integral. In many practical situations, the closed boundary integral needs to be approximated by an open boundary integral because the medium of interest is often accessible from one side only. The inherent approximations are acceptable as long as the effects of multiple scattering are negligible. However, in case of strongly inhomogeneous media, the effects of multiple scattering can be severe. We derive double- and single-sided homogeneous Green’s function representations. The single-sided representation applies to situations where the medium can be accessed from one side only. It correctly handles multiple scattering. It employs a focusing function instead of the backward propagating Green’s function in the classical (double-sided) representation. When reflection measurements are available at the accessible boundary of the medium, the focusing function can be retrieved from these measurements. Throughout the paper, we use a unified notation which applies to acoustic, quantum-mechanical, electromagnetic and elastodynamic waves. We foresee many interesting applications of the unified single-sided homogeneous Green’s function representation in holographic imaging and inverse scattering, time-reversed wave field propagation and interferometric Green’s function retrieval.

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