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| Area of Research |
Mathematical Physics, Spectral Theory |
| Degree | Ph.D. 1974, University of Provence
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Current research interests:
- The Theory of Aperiodic Solids:
Applications of C*-algebras to physics, rigorous results
Research Report (ps)
(pdf)
Main topics include:
- Aperiodic media
The Non Commutative Brillouin zone
Bloch electrons in a uniform magnetic field
Quasicrystals
Lightly doped semi-conductors
Hamiltonians periodic in time: the kicked rotor
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Gap Labelling and K-Theory
Hamiltonians with Cantor spectrum
K-theory: the abstract gap labelling theorem
1D Hamiltonians, automatic potentials,
Gap labelling for finite type tilings (including quasicrystals)
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Semi-classical Analysis
Harper like models, Hofstadter butterfly, braiding
Fast rotating molecules
Canonical formalism, the quantum phase space
Arnold-Liouville theorem for quantum integrable systems
Perturbation theory uniform in Planck's constant
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Non Commutative Geometry
The integer quantum Hall effect (IQHE)
Chern numbers in rotation bands
Noncommutative Fermi surfaces (in progress)
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Transport theory
Localization: localization length, pure point spectra, KAM method
Dissipation, random Hamiltonian processes, Kubo's formula
Anomalous diffusion, transport and spectral exponents, anomalous Drude
formula
Variable range hopping, the Mott-Efros-Schklovsky theory, application to
the IQHE (in progress)
Transport in quasicrystals (in progress)
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