Publications (since 1991) (prior to 1991 see )

This material is based upon work supported by the National Science Foundation
 under Grant No. 0300398, No. 0600956, No 0901514,  and No. DMS-1160962 since 2003 until 2016.

Since May 2016, this material is supported by SFB 878,: Groups,Geometry & Actions,
Fachbereich 10 Mathematik und Informatik,
Westfälische Wilhelms-Universität, Münster, Germany

It has been supported by the CRC 701: Spectral Structures and Topological Methods in Mathematics,
Mathematik Universität, Bielefeld, Germany,
since May 2007 each Summer until 2014, and between May 2011-July 2012, during a sabbatical year.

It has been supported by the French Ministère de l'Education Nationale
                        

through the Université Paul Sabatier, Toulouse III 1991-2002

Publication list (1971-2005) (ps) (pdf)

  Jean V. Bellissard
     Structure of Delone Sets (pdf)
     Invited paper to the special issue in memory of Jean Bourgain,
     Journal of Mathematical Physics (submitted on 6 Feb. 2021).

  Siegfried Beckus, Jean V. Bellissard & Giuseppe De Nittis
     Spectral Continuity for Aperiodic Quantum Systems: Applications of a Folklore Theorem (pdf)
     arXiv: 1803.03099 , (March 8, 2018),
     Journal of Mathematical Physics (pdf), 61(12), 123505, (2020)
     (online since December 23rd 2020).

  Siegfried Beckus, Jean V. Bellissard & Horia Cornean
     Hölder Continuity of the Spectra for Aperiodic Hamiltonians (pdf)
     arXiv: 1901.07789, (January 23, 2019),
     Annales Henri Poincaré (pdf), 20(11), 3603-3631, (2019).

  Jean V. Bellissard & Takeshi Egami
     A Simple Theory of Viscosity in Liquids (pdf)
     Phys. Rev. E 98, 063005 pp. 1-9, (2018),

  Siegfried Beckus, Jean V. Bellissard & Giuseppe De Nittis
     Spectral Continuity for Aperiodic Quantum Systems II. Periodic Approximation in 1D (pdf)
     arXiv: 1803.03099, (March 8, 2018),
     Accepted for publication in J. Math. Phys. (Nov. 17, 2020)

  Siegfried Beckus, Jean V. Bellissard & Giuseppe De Nittis
     Spectral Continuity for Aperiodic Quantum Systems I. General Theory (pdf)
     arXiv: 1709.00975, (Aug. 30, 2017),
     J. Funct. Anal., 275, 2917-2977, 2018.
     Corrigendum, J. Funct. Anal., (Available online 17 June 2019).

  Jean V. Bellissard
     Anankeon theory and viscosity of liquids: a toy model (pdf)
     arXiv: 1708.06624v1, (Aug. 19, 2017),

  Emil Prodan & Jean Bellissard
     Mapping the Current-Current Correlation
     Function Near a Quantum Critical Point. (pdf)
     arXiv: 1512.02476, (Dec. 8, 2015),
     Ann. of Phys., 368, 1-15, (2016)   

  Siegfried Beckus & Jean Bellissard
     Continuity of the Spectrum of a Field of Self-Adjoint Operators. (pdf)
     arXiv: 1507.04641 (Jul 16, 2015),
     Ann. Henri Poincaré, 17, 2016, 3425-3442.   

  Jean Bellissard
     Delone Sets and Material Science: a Program (pdf)
    in  Mathematics of Aperiodic Order,  J. Kellendonk, D. Lenz, J. Savinien, Eds.
     "Progress in Mathematics" series, 309, Birkhäuser, 2015.

  Emil Prodan, Bryan Leung, Jean Bellissard
     The non-commutative n-th Chern number (pdf)
     arXiv: 1305.2425
     J. of Phys. A: Math. Theor., 48, 485202, (2013)

  Bellissard J., A. Julien ,
     Bi-Lipshitz Embedding of Ultrametric Cantor Sets into Euclidean Spaces (pdf)
     arXiv: 1202.4330 (Feb. 20, 2012, Oct. 22 2013), submitted

  Bellissard J., Schulz-Baldes H.,
    Scattering theory for lattice operators in dimension d≥3  (pdf)
    arXiv:1109.5459v1
   Rev. Math. Phys, 24, (2012), no. 8, 1250020 1-51.

  Androulakis G., Bellissard J., Sadel C.
    Dissipative dynamics in semiconductors at low temperature  (pdf)
    arXiv:1107.1248  (July 6 2011),
   J. Stat. Phys., 147, (2012), 448-486.

  Bellissard J., Marcolli M., Reihani K.
    Dynamical Systems on Spectral Metric Spaces  (pdf) 
    arXiv: 1008.4617 (August 30 2010)

J. Bellissard, A. Julien, J. Savinien,
Tiling Groupoids And Bratteli Diagrams,  (pdf)
arXiv: 0911.0080 [math.OA]
Annales Henri Poincaré, 11, 69-99, 2010

Bellissard J., Radin C., Shlosman S.,
The characterization of ground states, (pdf)
J. Phys. A: Math. Theor. 43 (2010) 305001.  (online version)

Palmer I., Bellissard J.,
Uniquely Ergodic Minimal Tiling Spaces with Positive Entropy,  (pdf)
arXiv: 0906.2997,  submitted in

J. Pearson, J. Bellissard,
Noncommutative Riemannian Geometry and Diffusion on Ultrametric Cantor Sets  (pdf)
arXiv: 0802.1336v1 [math.OA]
J.  Noncommut. Geo., 3, (2009), 447-480

S. Garoufalidis, J. Bellissard,
Algebraic G-Functions associated to matrices over a group ring  (pdf)
arXiv: 0708.4234 [math.CO]

J. Bellissard, J. Savinien
A spectral sequence for the K-theory of tiling spaces  (pdf)
arXiv: 0705.2483v1 [math.KT]
Erg. Th. Dyn. Syst., 29, (2009), 997--1031.

J. Bellissard, P. Hislop, G. Stolz
Correlations  Estimates in the Lattice Anderson Model  (pdf)
J. Stat. Phys, 129, (2007), 649-662.
arXiv:math-phys/0703058v1 

J. Bellissard, R. Benedetti, J.-M. Gambaudo,
Spaces of Tilings, Finite Telescopic Approximations and Gap-labelling 

J. Bellissard, J. Geronimo, A. Volberg, P. Yuditskii,
If they are limit periodic ?   (pdf)
in Complex Analysis and Dynamical Systems, pp. 43-53,
Contemp. Math., 382, Amer. Math. Soc., Providence, RI, 2005.

J. Bellissard,
Random Matrix Theory and the Anderson Model   (pdf)
J. Stat. Phys.,  116 (1-4): 739-754, (2004),
(special issue  at the occasion of Elliott Lieb's 70th birthday)

J. Bellissard, J. Magnen, V. Rivasseau
Supersymmetric Analysis of a Simplified Two Dimensional Anderson Model at Small Disorder   (pdf)
In Inhomogeneous Random Systems, (Cergy Pointoise, 2002)
Markov Processes and Related Fields ,

J. Bellissard,
Noncommutative Geometry of Aperiodic Solids   (pdf)
"Geometric and Topological Methods for Quantum Field Theory", (Villa de Leyva, 2001), pp. 86-156,

 J. Bellissard,
Coherent and dissipative transport in aperiodic solids    (pdf)
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.

J. Bellissard, R. Rebolledo, D.Spehner, W. von Waldenfels
The Quantum Flow of Electronic transport I: The finite volume case
mp_arc 02-212, (2002)

J. Bellissard, R. Benedetti, J.-M. Gambaudo,
Spaces of Tilings, Finite Telescopic Approximations and Gap-labelling
  accepted in Commun. Math. Phys., March 22nd, 2003,

J. Bellissard, I. Guarneri, H. Schulz-Baldes,
Phase-averaged transport for quasiperiodic Hamiltonians
Commun. Math. Phys., 227 , 515-539 (2002)

D. Spehner, J. Bellissard,
The Quantum Jumps approach for infinitely many states
to be published in Proceedings of the International Conference on Quantum Optics of Santiago,
(August 2000), M. Orszag and J.C. Retamal Eds.,
Lectures Notes in Physics, 575, 355-376, Springer-Verlag, (2001).

J. Bellissard, J. Kellendonk, A. Legrand,
Gap-labelling for three-dimensional aperiodic solids,  (C.R.A.S.),   C. R. Acad. Sci. (Paris), t.332, Série I, p. 521-525, (2001).

D. Spehner, J. Bellissard,
A Kinetic Model for Quantum Jumps,   J. Stat. Phys., 104, 525-572, (2001).

J. Bellissard,
Anomalous Transport: results, conjectures and Applications to Quasicrystals  (pdf)
Materials Science and Engineering, 294-296, 450-457, (2000).

J. Bellissard, D. Herrmann, M. Zarrouati,
Hull of Aperiodic Solids and Gap Labelling Theorems   (pdf)
in Directions in Mathematical Quasicrystals, CRM Monograph Series, Volume 13, 207-259, (2000),
M.B. Baake and R.V. Moody Eds., AMS Providence. 

J. Bellissard, H. Schulz-Baldes,
Subdiffusive quantum transport for 3D-Hamiltonians with absolutely continuous spectra
J. Stat. Phys.  99, 587-594 (2000).

J. Vidal, R. Mosseri, J. Bellissard,
Spectrum and diffusion for a class of tight-binding models on hypercubes
J. Phys., A 32, 2361-67, (1999).

J. Bellissard, E. Contensou, A. Legrand,
K-théorie des quasi-cristaux, image par la trace: le cas du réseau octogonal 

C. R. Acad. Sci. (Paris), t.327, Série I, p. 197-200, (1998).  

A. Barelli, J. Bellissard, F. Claro,
Magnetic field induced directional localization in a 2D rectangular lattice
Phys. Rev. Letters, 83, 5082-5085, (1999).

J. Bellissard, H. Schulz-Baldes,
A Kinetic Theory for Quantum Transport in Aperiodic Media
J. Stat. Phys., 91, 991-1026, (1998).

J. Bellissard, C. Camacho, A. Barelli, F. Claro,
Exact Random Walk Distribution using Noncommutative Geometry
J. Phys. A Math. Gen., 30, L707-L709, (1997).

J. Bellissard, Jean-Yves Fortin, Miguel Gusmao, Timothy Ziman,
de Haas-van Alphen oscillations and magnetic breakdown: semiclassical calculation of multi-band orbits
Phys. Rev., B57, (3), 1484-1497, (1998).

H. Schulz-Baldes, J. Bellissard,
Anomalous transport: a mathematical framework
Rev. Math. Phys., 10, 1-46 (1998).

A. Barelli, J. Bellissard, P. Jacquod, D.L. Shepelyansky,
Two interacting Hofstadter butterflies
Phys. Rev., B55, 9524-9533, (1997).

A. Barelli, J. Bellissard, P. Jacquod, D.L. Shepelyansky,
Double butterfly spectrum for two interacting particles in the Harper model
Phys. Rev. Lett., 77, 4752-4755, (1996). 

J. Bellissard, H. Schulz-Baldes,
Anomalous transport in Quasicrystals
in Proceedings of the 5th International Conference on Quasicrystals, Editors C. Janot, R. Mosseri, World Scientific, Singapore, (1995).

J. Bellissard, J.X. Zhong, R. Mosseri,
Green's function analysis of energy spectra scaling properties
J. Phys: Condens. Matter 7, 3507-3514, (1995).

J. Bellissard,
The Non Commutative Geometry of the Quantum Hall Effect
Published in the Proceedings of the International Conference of Mathematic (Zürich 94), Birkhäuser (1995).

J. Bellissard, H. Schulz-Baldes, A. van Elst,
The Non Commutative Geometry of the Quantum Hall Effect
J. Math. Phys., 35, 5373-5471, (1994).

J. Bellissard,
Lipshitz Continuity of Gaps Boundaries for Hofstadter-like Spectra
Comm. Math. Phys., 160, 599-614, (1994).

D. Poilblanc, T. Ziman, J. Bellissard, F. Mila, G. Montambaux,
Poisson versus GOE statistics in integrable and non-integrable quantum Hamiltonians
Europhys. Lett., 22, 537-542, (1993). 

A. Barelli, J. Bellissard,
Semiclassical Methods in Solid State Physics: two examples
J. de Physique I (France), 3, 471-500, (1993). 

J. Bellissard,
Non Commutative Methods in Semiclassical Analysis
course given at the CIME (1991). Published in Transition to Chaos in Classical and Quantum Mechanics,
Lecture Notes in Mathematics, 1589, Springer, (1994).

J. Bellissard, G. Montambaux, D. Poilblanc, C. Sire,
Quantum Chaos in Strongly Correlated Fermions
Phys. Rev. Letters., 70 , 497, (1993).

J. Bellissard,
The Gap Labelling Theorem: the case of automatic sequences   (pdf)
in Quantum and non-commutative analysis (Kyoto, 1992), pp. 179-181,
Math. Phys. Stud., 16, Kluwer Acad. Publ., Dordrecht, (1993).

J. Bellissard,
Gap Labelling Theorems for Schrödinger's Operators   (pdf) 
in From Number Theory to Physics pp.538-630, Les Houches March 89, Springer, J.M. Luck, P. Moussa, M. Waldschmidt Eds., (1993).

J. Bellissard,
Le Papillon de Hofstadter, d'après B. Helffer et J. Sjöstrand
Séminaire Bourbaki, 44ème année, 1991-92, # 745, (novembre 1991). In Astérisque, 206, 7-40, (1992).

J. Bellissard, A. Barelli,
Dynamical localization: a Mathematical Framework   (pdf) 
in Quantum Chaos, Quantum Measurements P. Cvitanovic, I.C. Percival & A. Wirzba Eds., Kluwer Publ., pp. 105-129, (1992).

J. Bellissard, A. Bovier, J.M. Ghez,
Gap labelling Theorems for One Dimensional Discrete Schrödinger Operators
Rev. of Math. Phys., 4, 1-37, (1992).

J. Bellissard,
Renormalization Group Analysis and Quasicrystals
In Ideas and Methods in Analysis, Stochastics, and Applications (in memory of Raphael Høegh-Krohn)
S. Albeverio, J. E. Fenstad, H. Holden, T. Lindstrøm, editors, Cambridge University Press, Cambridge, 1992

J. Bellissard, S. Vaienti,
Rigorous diffusion properties for the sawtooth map
Commun. Math. Phys., 144, 521-536, (1992).

J. Bellissard, A. Bovier, J.M. Ghez,
Spectral Properties of a Tight Binding Hamiltonian with Period Doubling Potential
Commun. Math. Phys., 137, 379-399, (1991).

J. Bellissard, B. Iochum, D. Testard,
Continuity properties of electronic spectrum of 1D quasicrystals
Commun. Math. Phys., 141, 353-380, (1991).

J. Bellissard, Ch. Kreft, R. Seiler,
Analysis of the Spectrum of a Particle on a Triangular Lattice
with two MagneticFluxes by Algebraic and Numerical Methods,
J.  of Phys. A 24, 2329-2353, (1991).<

(publications prior to 1991 see )