A Computational Non-commutative Geometry Program for Disordered Topological Insulators

• Κύριος συγγραφέας: Prodan, Emil (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Σειρά: SpringerBriefs in Mathematical Physics, 23
• Θέματα: Physics.; K-theory.; Functional analysis.; Mathematical physics.; Condensed matter.; Mathematical Methods in Physics.; Mathematical Physics.; Condensed Matter Physics.; K-Theory.; Functional Analysis.

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 condens...

Πίνακας περιεχομένων:

• Disordered Topological Insulators: A Brief Introduction
• Homogeneous Materials
• Homogeneous Disordered Crystals
• Classification of Homogenous Disordered Crystals
• Electron Dynamics: Concrete Physical Models
• Notations and Conventions
• Physical Models
• Disorder Regimes
• Topological Invariants
• The Non-Commutative Brillouin Torus
• Disorder Configurations and Associated Dynamical Systems
• The Algebra of Covariant Physical Observables
• Fourier Calculus
• Differential Calculus
• Smooth Sub-Algebra
• Sobolev Spaces
• Magnetic Derivations
• Physics Formulas
• The Auxiliary C*-Algebras
• Periodic Disorder Configurations
• The Periodic Approximating Algebra
• Finite-Volume Disorder Configurations
• The Finite-Volume Approximating Algebra
• Approximate Differential Calculus
• Bloch Algebras
• Canonical Finite-Volume Algorithm
• General Picture
• Explicit Computer Implementation
• Error Bounds for Smooth Correlations
• Assumptions
• First Round of Approximations
• Second Round of Approximations
• Overall Error Bounds
• Applications: Transport Coefficients at Finite Temperature
• The Non-Commutative Kubo Formula
• The Integer Quantum Hall Effect
• Chern Insulators
• Error Bounds for Non-Smooth Correlations
• The Aizenman-Molchanov Bound
• Assumptions
• Derivation of Error Bounds
• Applications II: Topological Invariants
• Class AIII in d = 1
• Class A in d = 2
• Class AIII in d = 3
• References.