A Computational Non-commutative Geometry Program for Disordered Topological Insulators. SpringerBriefs in Mathematical Physics; volume 23.

Prodan, Emil:

ISBN 10: 3319550225 / ISBN 13: 9783319550220

Published by Cham, Springer, 2017

About this Item

X, 118 p. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-01312 9783319550220 Sprache: Englisch Gewicht in Gramm: 550.

Seller Inventory # 2485172

Bibliographic Details

• Title: A Computational Non-commutative Geometry Program for Disordered Topological Insulators. SpringerBriefs in Mathematical Physics; volume 23.
• Publisher: Cham, Springer
• Publication Date: 2017
• Language: English
• ISBN 10: 3319550225
• ISBN 13: 9783319550220
• Binding: Softcover
• Weight: 550 grams
• Seller catalogs:
  • SA MATHEMATIK

About this title

Synopsis

This work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators. Noncommutative geometry has been originally proposed by Jean Bellissard as a theoretical framework for the investigation of homogeneous condensed matter systems. Recently, this approach has been successfully applied to topological insulators, where it facilitated many rigorous results concerning the stability of the topological invariants against disorder.

In the first part of the book the notion of a homogeneous material is introduced and the class of disordered crystals defined together with the classification table, which conjectures all topological phases from this class. The manuscript continues with a discussion of electrons’ dynamics in disordered crystals and the theory of topological invariants in the presence of strong disorder is briefly reviewed. It is shown how all this can be captured in the language of noncommutative geometry using the concept of non-commutative Brillouin torus, and a list of known formulas for various physical response functions is presented. 

In the second part, auxiliary algebras are introduced and a canonical finite-volume approximation of the non-commutative Brillouin torus is developed. Explicit numerical algorithms for computing generic correlation functions are discussed. 

In the third part upper bounds on the numerical errors are derived and it is proved that the canonical-finite volume approximation converges extremely fast to the thermodynamic limit. Convergence tests and various applications concludes the presentation.

The book is intended for graduate students and researchers in numerical and mathematical physics.