The Non-commutative Geometry of
Aperiodic Solids
Abstract
Index
1. APERIODIC SOLIDS
a) Examples, physical properties, structure, electronic properties,
phonons, transport
b) Bloch theory for perfect crystals
c) Atomic structure: the hull as a dynamical system. Construction of the non-commutative
Brillouin zone
d) Quasicrystals
2. THERMODYNAMICS
a) Gibbs states, their hull
b) Diffraction measure
c) Electronic density of states
d) Phonon density of modes
3. TRANSPORT
a) Introduction to transport theory
b) Kinetic models for transport
c) Establishing Green-Kubo's formula for the electric conductivity
4. ONE EXAMPLE: THE INTEGER QUANTUM HALL EFFECT
a) The physics of the IQHE
b) Heuristic approach
c) The quantization of the Hall conductivity: non-commutative Chern classes
d) Localization and existence of "plateaux": the Dixmier trace and localization
estimates
5. ANOMALOUS TRANSPORT
a) Spectral and transport exponents: definitions
b) Properties of the exponents: the Guarneri bound
c) The anomalous Drude formula
d) Quasicrystals: description, electronic properties, transport properties, relevance of
anomalous transport
6. PROSPECTS AND OPEN PROBLEMS
Lectures
1. lectures
