jb538

Jean Bellissard
Professor
Education

Ph.D., Universite de Provence, Marseille, France 1974

Research Interests

Mathematical Theory of Aperiodic Solids

Mathematical Theory of Aperiodic Solids:

  • Structure: the Hull, transversal, equilibrium Gibbs state, diffraction measure.
  • Application to: Bloch electrons in magnetic field, quasycrystals, semiconductors at low temperature.
  • Noncommutative Geometry: the noncommutative Brillouin zone, electrons & phonons.
  • Topological invariants:K-theory and Gap Labeling theorem
  • Electronic and spectral properties of aperiodic media: Cantor and Singular spectra for electron or phonons. Anderson localization, weak localization and Random Matrix Theory.
  • Coherent transport: spectral and transport exponents
  • Dissipative transport: the Greene-Kubo formulae, models for dissipation, Mott's variable range hopping.
  • Noncommutative Geometry: cyclic cohomology, application to the theory of the Quantum Hall effect.
Other Publications:
  1. "Noncommutative Geometry of Aperiodic Solids ", in "Geometric and Topological Methods for Quantum Field Theory", (Villa de Leyva, 2001), pp. 86-156, World Sci. Publishing, River Edge, NJ, (2003).
  2. "Coherent and dissipative transport in aperiodic solids", Published in Dynamics of Dissipation P. Garbaczewski, R. Olkiewicz (Eds.), Lecture Notes in Physics, 597, Springer (2003), pp. 413-486.
    Proceedings of the 38th Winter School of Theoretical Physics, Ladek, Poland, 6-15 Feb 2002.
  3. "Spaces of Tilings, Finite Telescopic Approximations and Gap-labelling", with R. Benedetti, J.-M. Gambaudo, to appear in Commun. Math. Phys., (2004).
  4. "A Kinetic Model for Quantum Jumps", with D. Spehner, J. Stat. Phys., 104, 525-572, (2001).
  5. "Hull of Aperiodic Solids and Gap Labelling Theorems", with D. Hermmann, M. Zarrouati, in "Directions in Mathematical Quasicrystals", CRM Monograph Series, Volume 13, 207-259, (2000),
    M.B. Baake and R.V. Moody Eds., AMS Providence.
  6. "A Kinetic Theory for Quantum Transport in Aperiodic Media", with H. Schulz-Baldes, J. Stat. Phys., 91, 991-1026, (1998).
  7. "de Haas-van Alphen oscillations and magnetic breakdown: semiclassical calculation of multi-band orbits", with Jean-Yves Fortin, Miguel Gusmao, Timothy Ziman, Phys. Rev., B57, (3), 1484-1497, (1998).
  8. "The Non Commutative Geometry of the Quantum Hall Effect" with H. Schulz-Baldes, A. van Elst, J. Math. Phys., 35, 5373-5471, (1994).
  9. "Non Commutative Methods in Semiclassical Analysis", a course given at the CIME (1991). Published in "Transition to Chaos in Classical and Quantum Mechanics", Lecture Notes in Mathematics, 1589, Springer, (1994).
  10. "Gap Labelling Theorems for Schr?dinger's Operators", in "From Number Theory to Physics" pp.538-630, Les Houches March 89, Springer, J.M. Luck, P. Moussa, M. Waldschmidt Eds., (1993).
  11. "Renormalization Group Analysis and Quasicrystals", in "Ideas and Methods in Analysis, Stochastics, and Applications (in memory of Raphael H?egh-Krohn)", S. Albeverio, J. E. Fenstad, H. Holden, T. Lindstr?m, editors, Cambridge University Press, Cambridge, 1992.
  12. "Spectral Properties of a tight binding Hamiltonian with Period Doubling Potential'' with A. Bovier, J.M. Ghez, Comm. Math. Phys., 135, (1991), 379-399.
  13. "Heisenberg's Picture and Non Commutative Geometry of the Semiclassical Limit'' with M. Vittot, Ann. Inst. H. Poincare, 52, (1990),175-235.
  14. "An Algebraic Semi-Classical Approach to Bloch Electrons in a Magnetic Field'', with R. Rammal, J. de Phys. (France), 51, (1990), 1803-1830.
  15. "Spectral Properties of One-Dimensional Quasicrystals'' with B. Iochum, E. Scoppola, D. Testard, Comm. Math. Phys., 125,(1989), 527-543.
  16. "K-Theory of C*-algebras in Solid State Physics'' in "Statistical Mechanics and Field Theory, Mathematical Aspects'', T.C. Dorlas, M.N. Hugenholtz and M. Winnink, Lecture Notes in Physics, 257, (1986), 99-156.
  17. "Stability and Instability in Quantum Mechanics'' in "Trends and developments in the Eighties", S. Albeverio \& Ph. Blanchard Eds, World Scientific Pub. Co., Singapore (1985).
  18. "Cantor Spectrum for the Almost Mathieu Equation'' with B. Simon, J.Funct. Anal., 48, 408-419, (1982).