Computer Algebra and Materials Physics

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).
Thebook 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.

Offers a practical guide for physicists and students interested in group theory in quantum physics Presents a modernization of the union of "group theory and quantum physics" through effective contemporary computational techniques (computer algebra and quantum simulation), to build a bridge over the ever-deepening chasm between mathematics and physics Includes numerous examples of the group theoretical computations available on desktop PCs, which cooperate with massive and quantitative simulations of quantum dynamics in materials

Autorentext

Akihito Kikuchi received his degrees of B. Sc, M.S. and Ph. D in physics in 1991, 1993, and 1996 from the University of Tokyo. Subsequently he worked as postdoctoral fellow and research associate at the institute for solid state physics in University of Tokyo. Today he works with a private company in Japan as a researcher. His research interests cover condensed matter physics, quantitative electronic structure theory, pseudopotential theory, molecular simulation, elementary excitation in solids, computational chemistry, and the application of symbolic computations (by means of group theory, algebraic geometry, and other modern theory of mathematics) in theororetical material science.

Inhalt
Dedication.- Preface.- Introduction.- Computation of Group Theoretical Properties Using "GAP".- Some Preliminaries.- Application 1: Identification of Wave Functions to Irreducible Representations.- Application 2: A Systematic Way of the Material Designing.- Technical Details.- Symmetry in C60.- Analysis of Vibrational Mode in C60.- Final Remarks.- Appendices A-J.