Linked e-resources
Details
Table of Contents
Acknowledgements; Contents; 1 Introduction; 2 Setting, Hypotheses and Main Results; 2.1 Description of the Abstract Setting; 2.2 The Perturbed Dynamics: Bridge to Analysis; 2.3 Linear Response and the Kubo Formula; 2.4 The Adiabatic Limit and the Kubo
Strěda Formula; 2.5 Zero Temperature Limit and Topological Interpretation; 2.6 The Tight-Binding Type Simplification; 3 Mathematical Framework; 3.1 Algebra of Observables; 3.1.1 The von Neumann Algebra of Observables; 3.1.2 The Algebra of Affiliated Operators; 3.1.3 Finite Versus Semi-finite von Neumann Algebras
3.2 Non-commutative mathfrakLp-Spaces3.2.1 F.n.s Trace State; 3.2.2 Convergence in Measure and Measurable Operators; 3.2.3 Integration and mathfrakLp-Spaces; 3.2.4 Isospectral Transformations and Induced Isometries; 3.3 Generalized Commutators; 3.3.1 Commutators Between mathcalT-Measurable Operators; 3.3.2 Commutators Between mathcalT-Measurable and Affiliated Operators; 3.3.3 Commutators Between Unbounded Operators; 3.4 Non-commutative Sobolev Spaces; 3.4.1 mathcalT-Compatible Spatial Derivations; 3.4.2 Non-commutative Gradient and Sobolev Spaces
4 A Unified Framework for Common Physical Systems4.1 Von Neumann Algebra Associated to Ergodic Topological Dynamical Systems; 4.1.1 Projective Representations of mathbbG; 4.1.2 Randomly Weighted Hilbert Spaces; 4.1.3 Direct Integral of Hilbert Spaces; 4.1.4 The Algebra of Covariant Random Operators; 4.2 The Trace per Unit Volume; 4.3 Generators Compatible with the Trace per Unit Volume; 4.4 Reduction to the Non-random Case; 5 Studying the Dynamics; 5.1 Unperturbed Dynamics; 5.1.1 The Generator of the Unperturbed Dynamics; 5.1.2 A Formula for the Projection in Theorem 2.4.1
6.2.2 Proof of the Kubo Formula6.3 The Adiabatic Limit of the Conductivity Tensor; 7 Applications; 7.1 Linear Response Theory for Periodic and Random Light Conductors; 7.1.1 Schrödinger Formalism of Electromagnetism; 7.1.2 Random Media; 7.1.3 Open Questions; 7.2 Quantum Hall Effect in Solid State Physics; 7.2.1 Continuum Models; 7.2.2 Discrete Models; References; Index
Strěda Formula; 2.5 Zero Temperature Limit and Topological Interpretation; 2.6 The Tight-Binding Type Simplification; 3 Mathematical Framework; 3.1 Algebra of Observables; 3.1.1 The von Neumann Algebra of Observables; 3.1.2 The Algebra of Affiliated Operators; 3.1.3 Finite Versus Semi-finite von Neumann Algebras
3.2 Non-commutative mathfrakLp-Spaces3.2.1 F.n.s Trace State; 3.2.2 Convergence in Measure and Measurable Operators; 3.2.3 Integration and mathfrakLp-Spaces; 3.2.4 Isospectral Transformations and Induced Isometries; 3.3 Generalized Commutators; 3.3.1 Commutators Between mathcalT-Measurable Operators; 3.3.2 Commutators Between mathcalT-Measurable and Affiliated Operators; 3.3.3 Commutators Between Unbounded Operators; 3.4 Non-commutative Sobolev Spaces; 3.4.1 mathcalT-Compatible Spatial Derivations; 3.4.2 Non-commutative Gradient and Sobolev Spaces
4 A Unified Framework for Common Physical Systems4.1 Von Neumann Algebra Associated to Ergodic Topological Dynamical Systems; 4.1.1 Projective Representations of mathbbG; 4.1.2 Randomly Weighted Hilbert Spaces; 4.1.3 Direct Integral of Hilbert Spaces; 4.1.4 The Algebra of Covariant Random Operators; 4.2 The Trace per Unit Volume; 4.3 Generators Compatible with the Trace per Unit Volume; 4.4 Reduction to the Non-random Case; 5 Studying the Dynamics; 5.1 Unperturbed Dynamics; 5.1.1 The Generator of the Unperturbed Dynamics; 5.1.2 A Formula for the Projection in Theorem 2.4.1
6.2.2 Proof of the Kubo Formula6.3 The Adiabatic Limit of the Conductivity Tensor; 7 Applications; 7.1 Linear Response Theory for Periodic and Random Light Conductors; 7.1.1 Schrödinger Formalism of Electromagnetism; 7.1.2 Random Media; 7.1.3 Open Questions; 7.2 Quantum Hall Effect in Solid State Physics; 7.2.1 Continuum Models; 7.2.2 Discrete Models; References; Index