# A Computational Non-commutative Geometry Program for Disordered Topological InsulatorsAuxiliary \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^*$$\end{document}-Algebras

A Computational Non-commutative Geometry Program for Disordered Topological Insulators: Auxiliary... [This Chapter introduces and characterizes the approximating algebras used later to define the canonical finite-volume approximations and to analyze the numerical errors. In particular, the approximating finite algebra generates the ordinary finite super-cell models with periodic boundary conditions, which are commonly used in the numerical investigations. Formalizing them in an algebraic setting will enable us to bridge more naturally with the thermodynamic limit, to put forward a canonical finite-volume approximation and to ultimately resolve the error estimates with minimal effort. Several key ideas of the Chapter already appeared in [3] but other are reported here for the first time.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# A Computational Non-commutative Geometry Program for Disordered Topological InsulatorsAuxiliary \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^*$$\end{document}-Algebras

Part of the SpringerBriefs in Mathematical Physics Book Series (volume 23)
12 pages

/lp/springer-journals/a-computational-non-commutative-geometry-program-for-disordered-JBkylTGEOc
Publisher
Springer International Publishing
ISBN
978-3-319-55022-0
Pages
49 –61
DOI
10.1007/978-3-319-55023-7_4
Publisher site
See Chapter on Publisher Site

### Abstract

[This Chapter introduces and characterizes the approximating algebras used later to define the canonical finite-volume approximations and to analyze the numerical errors. In particular, the approximating finite algebra generates the ordinary finite super-cell models with periodic boundary conditions, which are commonly used in the numerical investigations. Formalizing them in an algebraic setting will enable us to bridge more naturally with the thermodynamic limit, to put forward a canonical finite-volume approximation and to ultimately resolve the error estimates with minimal effort. Several key ideas of the Chapter already appeared in [3] but other are reported here for the first time.]

Published: Mar 18, 2017

Keywords: Commutation Relation; Position Operator; Generic Element; Differential Calculus; Invariant Probability Measure