Computer Algebra and Materials Physics

Description

This book is intended as an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The first part explains how to use computer algebra for applications in solid-state simulation, based on the GAP computer algebra package. Computer algebra enables us to easily obtain various group theoretical properties, such as the representations, character tables, and subgroups. Furthermore it offers a new perspective on material design, which could be executed in a mathematically rigorous and systematic way. The second part then analyzes the relation between the structural symmetry and the electronic structure in C60 (as an example of a system without periodicity). The principal object of the study was to illustrate the hierarchical change in the quantum-physical properties of the molecule, which correlates to the reduction in the symmetry (as it descends down in the ladder of subgroups). The book also presents the computation of the vibrational modes of the C60 by means of the computer algebra. In order to serve the common interests of researchers, the details of the computations (the required initial data and the small programs developed for the purpose) are explained in as much detail as possible. Front Matter ....Pages i-xi Introduction (Akihito Kikuchi)....Pages 1-5 Computation of Group Theoretical Properties Using “GAP” (Akihito Kikuchi)....Pages 7-12 Some Preliminaries (Akihito Kikuchi)....Pages 13-17 Application 1: Identification of Wavefunctions to Irreducible Representations (Akihito Kikuchi)....Pages 19-27 Application 2: A Systematic Way of the Material Designing (Akihito Kikuchi)....Pages 29-38 Technical Details (Akihito Kikuchi)....Pages 39-71 Symmetry in C\(_{60}\) (Akihito Kikuchi)....Pages 73-102 Analysis of Vibrational Mode in C\(_{60}\) (Akihito Kikuchi)....Pages 103-118 Final Remarks (Akihito Kikuchi)....Pages 119-121 Back Matter ....Pages 123-159