Publication list:

Preprints:

• Localization for the random displacement model
  In collaboration with M. Loss, S. Nakamura, G. Stolz.
  
• Spectral statistics for the discrete Anderson model in the localized regime
  In collaboration with F. Germinet.
  
• Decorrelation estimates for the eigenlevels of the discrete Anderson model in the localized regime.
  


• The Gross-Pitaevskii functional with a random background potential and condensation in the single particle ground state.
  In collaboration with B. Metzger.

To appear:

• Lifshitz tails for alloy type models in a constant magnetic field
  To appear in J. Phys. A. Volume dedicated to the memory of Pierre Duclos.
  
• An exact renormalization formula for Gaussian exponential sums and applications.
  In collaboration with A. Fedotov.
  To appear in Amer. Math. Jour.
  
• Lifshitz tails for generalized alloy type random Schrödinger operators.
  In collaboration with S. Nakamura.
  To appear in Analysis & PDE.
  

Published:

1. Localization for the random displacement model at weak disorder.
   In collaboration with F. Ghribi.
   Annales Henri Poincaré, Vol. 11, Issue 1, pp. 127-149 (2010).
2. Absolute continuity of the spectrum of a Landau Hamiltonian perturbed by a generic periodic potential.
   Math. Annalen, Volume 347, Number 3, pp. 675-687 (2010).
   
3. Lifshitz tails for alloy type random models in constant magnetic fields: a short review.
   Proceedings of the Conference Spectral and Scattering Theory for Quantum Magnetic Systems
   CIRM, Marseille, France, July 7 - 11, 2008.
   Eds: P. Briet, F. Germinet, G. Raikov.
   Contemporary Mathematics, vol. 500, pp. 153-158 (2009).
   
4. The Fate of the Landau Levels under Perturbations of Constant Sign
   In collaboration with G. Raikov.
   Int. Math. Res. Not. IMRN 2009, no. 24, 4726--4734.
   
5. The integrated density of states for an interacting multiparticle homogeneous model and applications to the Anderson model
   In collaboration with H. Zenk.
   Advances in Mathematical Physics. Vol. 2009, Article ID 679827, 15 pages, 2009.
   
6. Localization on quantum graphs with random edge lengths
   En collaboration avec K. Pankrashkin.
   Letters in Mathematical Physics, Volume 87, pp 99--114 (2009)
   
7. Spectral extrema and Lifshitz tails for non monotonous alloy type models.
   In collaboration with S. Nakamura.
   Comm. Math. Phys. Volume 287, Issue3 (2009), Page 1133
   
8. Pointwise existence of the Lyapunov exponent for a quasi-periodic equation.
   En collaboration avec A. Fedotov.
   ``Mathematical Results in Quantum Mechanics'': Proceedings of the Qmath10 Conference, 10-15 September 2007
   Editors: Ingrid Beltita, Gheorghe Nenciu, Radu Purice
   World Scientific, 2008
   
9. Appendix to ``An invitation to random Schrödinger operators'' by W. Kirsch
   "Random Schrödinger Operators", Panoramas et Synthèses, nb 25, Soc. Math. France (2008).
   
10. Lifshitz tails for some non monotonous random models.
    En collaboration avec S. Nakamura.
    Proceedings of the Séminaire "Équations aux Dérivées Partielles" de l'École Polytechnique. (2007-2008). Talk 14.
    
11. Localization on quantum graphs with random vertex couplings
    In collaboration with K. Pankrashkin
    Jour. Stat. Phys. vol 131, pp 651--673 (2008).
    
12. Localization for Schrödinger operators with random vector potentials
    In collaboration with F. Ghribi and P. D. Hislop.
    Contemporary Mathematics, vol. 447, ``Adventures in mathematical physics'', proceedings of the internationl conference in honor of Jean-Michel Combes, Sept. 4-6, 2006, Eds Germinet, Hislop, pp. 123-138.
    
13. An optimal Wegner estimate and its application to the global continuity of the integrated density of states for random Schrödinger operators
    In collaboration with JM. Combes and P. D. Hislop.
    Duke Math. Journal, vol 140, pp 469-498 (2007).
14. Some new estimates on the spectral shift function associated with random Schrödinger operators
    In collaboration with JM. Combes and P. D. Hislop.
    CRM Proceedings and Lecture Notes, vol. 42, "Probability and Mathematical Physics, Proceeding of the conference celebrating 65th birthday of Stanislav Molchanov", Eds Dawson, Jaksic, Vainberg, pp. 85-96.
    
15. The width of resonances for slowly varying perturbations of one-dimensional periodic Schrödinger operators
    In collaboration with M. Marx.
    Exposé IV. Proceedings of the Séminaire "Équations aux Dérivées Partielles" de l'École Polytechnique (2005-2006), Exp. No. IV, 18 pp.
    
16. Lifshitz Tails in Constant Magnetic Fields.
    In collaboration with G. Raikov.
    Comm. Math. Phys. vol 267, pp 669-701 (2006).
    
17. Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators.
    In collaboration with A. Fedotov.
    Ann. Scient. ENS, vol 38, pp. 889-950 (2005).
    A few animations showing the effects of level repulsion:
    
    • &tau large
      
    • &rho small
      
    • &tau small and &rho large
      
    
    
18. Continuity with respect to Disorder of the Integrated Density of States.
    In collaboration with P. Hislop et J. Schenker.
    Ill. Math. Jour., vol 49, pp. 893-904 (2005).
    
19. Weakly resonant tunneling interactions for adiabatic quasi-periodic Schrödinger operators.
    In collaboration with A. Fedotov.
    Mémoires Soc. Math. France, vol 104 (2005).
    
20. The band-edge behavior of the density of surfacic states.
    In collaboration with W. Kirsch.
    Mathematical Physics, Analysis and Geometry, vol 8, pp. 315 - 360 (2006).
    
21. Renormalization of exponential sums and matrix cocycles.
    In collaboration with A. Fedotov.
    Exposé XVI. Proceedings of the Séminaire "Equations aux Dérivées Partielles" de l'École Polytechnique (2004-2005).
    A few animations showing the graphs of the exponential sums (the consecutive values of the sum are linearly interpolated):
    
    • k=2 and a=&pi/10 (~38 MB)
      
    • k=3/2 and a=&pi/10 (~48 MB)
      
    • k=8/5 and a=&pi/10 (~4 MB)
      
    • k=3/2 and a=1 (~21 MB)
      
    
    
22. Absolutely continuous spectrum for the isotropic Maxwell operator with coefficients that are periodic in some directions and decay in others.
    In collaboration with N. Filonov.
    Comm. Math. Phys. vol. 258 , pp. 75--85, (2005).
    
23. On the absolutely continuous spectrum of one dimensional quasi-periodic Schrödinger operators in the adiabatic limit.
    In collaboration with A. Fedotov.
    Transactions A.M.S. vol. 357, pp. 4481-4516 (2005).
    
24. Global Continuity of the Integrated Density of States for Random Landau Hamiltonians
    In collaboration with J.M. Combes, P. Hislop and G. Raykov.
    Comm. Partial Differential Equations, vol. 29, pp. 1187--1213 (2004).
    
25. Opérateurs de Schrödinger quasi-périodiques adiabatiques : Interactions entre les bandes spectrales d'un opérateur périodique.
    In collaboration with A. Fedotov.
    Exposé VIII. Proceedings of the Séminaire "Equations aux Dérivées Partielles" de l'École Polytechnique (2003-2004).
    
26. On the singular spectrum for adiabatic quasi-periodic Schrödinger operators on the real line.
    In collaboration with A. Fedotov.
    Annales H. Poincaré, vol. 5, pp. 929--978 (2004).
    
27. Geometric tools of the adiabatic complex WKB method.
    In collaboration with A. Fedotov.
    Asymptotic Analysis, vol. 39(3,4), pp. 309--357 (2004).
    
28. Absolute continuity of the spectrum of a Schrödinger operator with a potential which is periodic in some directions and decays in others
    In collaboration with N. Filonov.
    Documenta Mathematica, vol. 9, pp. 107--121 (2004). Erratum in the same volume.
    
29. A note on Anderson localization for the random hopping model.
    In collaboration with S. Nakamura.
    Jour. Math. Phys., vol 44, pp. 4975--4980 (2003)
    
30. The spectral theory of adiabatic quasi-periodic operators on the real line.
    In collaboration with A. Fedotov.
    Markov Processes and Related Fields, vol. 9, pp. 579 -- 615 (2003).
    
31. Regularity properties for the density of states of random Schrödinger operators.
    In collaboration with J.M. Combes et P. Hislop.
    Contemporary Mathematics, Vol. 339, pp. 15 -- 25 (2003).
    
32. Anderson localization for 2D discrete Schrödinger operator with random vector potential.
    In collaboration with S. Nakamura, F. Nakano, Y. Nomura.
    Annales Henri Poincaré, vol. 4, pp. 795--811 (2003).
    
33. Local and Global Continuity of the Integrated Density of States
    In collaboration with J.M. Combes and P. Hislop.
    Contemp. Math., vol. 327, pp. 61--74 (2003).
    
34. Hölder continuity of the integrated density of states for some random operators at all energies.
    In collaboration with J.M. Combes and P. Hislop.
    I.M.R.N., vol 2003 [4], pp. 179--209 (2003).
    
35. Lifshitz tails for 2-dimensional random Schrödinger operators
    In collaboration with T. Wolff.
    Journal d'Analyse Mathématique, vol. 88, pp. 63--147 (2002)
    
36. Weak disorder localization and Lifshitz tails.
    Comm. Math. Phys., vol. 232, pp 125-155 (2002).
    
37. The Integrated Density Of States For Some Random Operators With Nonsign Definite Potentials
    In collaboration with P. Hislop.
    Jour. Func. Anal., vol. 195, pp 12--47 (2002).
    
38. Weak disorder localization and Lifshitz tails : continuous Hamiltonians.
    Ann. I.H.P. vol. 3, pp 711--737 (2002).
    
39. Une remarque à propos des asymptotiques de Lifshitz internes.
    C.R.A.S Série I vol. 335 pp 87--92 (2002).
    
40. Anderson transitions for a family of almost periodic Schrödinger equations in the adiabatic case
    In collaboration with A. Fedotov.
    Commun. Math. Phys. vol. 227, pp. 1--92 (2002).
    
41. Mathematical Analysis of the Photoelectric Effect.
    In collaboration with V. Bach et H. Zenk.
    Advances in Theoretical and Mathematical Physics vol 5, pp 969--999 (2002).
    
42. Internal Lifshitz tails for Schrödinger operators with random potentials
    Jour. Math. Phys. vol. 43 pp 2948--2958 (2002)
    
43. Asymptotiques de Lifshitz.
    Exposé IV. Proceedings of the Séminaire "Equations aux Dérivées Partielles", École Polytechnique (2001-2002).
    
44. Internal Lifshitz tails for random Schrödinger operators
    In collaboration with T. Wolff.
    Proceedings of the I.C.M.P. 2000, Imperial College, London.
    Eds A. Fokas, A. Grigoryan, T. Kibble, B. Zegarlinski.
    International Press, 2002
    
45. The Wegner estimate and the integrated density of states for some random operators
    In collaboration with J.-M. Combes, P. D. Hislop and S. Nakamura.
    Proceedings of the ``Spectral and Inverse Spectral theories of Schrödinger Operators'', 14-20/12/2000, Goa (Inde).
    Proceedings of the Indian Academy of Sciences, Mathematical Sciences, vol. 112 (1), pp. 31-55 (2002).
    
46. Lifshitz tails for random perturbations of periodic Schrödinger operators
    Proceedings of the ``Spectral and Inverse Spectral theories of Schrödinger Operators'', 14-20/12/2000, Goa (Inde).
    Proceedings of the Indian Academy of Sciences, Mathematical Sciences, vol. 112 (1), pp. 147-163 (2002).
    
47. A complex WKB method for adiabatic problems
    In collaboration with A. Fedotov.
    Asymptotic Analysis, vol. 27 pp. 219--264 (2001).
    
48. Endpoints of the spectrum of periodic operators are generically simple
    In collaboration with J. Ralston.
    Meth. Appl. Anal., volume 7 dedicated to C. Morawetz, pp 459-464 (2000).
    
49. Precise high energy asymptotics for the integrated density of states of an unbounded random Jacobi matrix.
    Rev. Math. Phys. vol. 12 [4], pp 575-620 (2000).
    
50. Lifshitz tails for random Schrödinger operators with negative singular Poisson potential.
    In collaboration with L. Pastur.
    Comm. Math. Phys. vol. 206, pp 57-103 (1999).
    
51. Internal Lifshits tails for random perturbations of periodic Schrödinger operators.
    Duke Math. Jour. vol 98, pp 335-396 (1999).
    
52. Transitions d'Anderson pour des opérateurs de Schrödinger quasi-périodiques en dimension 1.
    In collaboration with A. Fedotov.
    Exposé IV. Proceedings of the Séminaire "Equations aux Dérivées Partielles", École Polytechnique (1998-1999).
    
53. Coexistence of different spectral types for almost periodic Schrödinger equations in dimension one.
    In collaboration with A. Fedotov.
    Proceedings of the conference ``Mathematical Results in Quantum Mechanics (QMath7)'', Prague, 22-26 June 1998 Operator Theory: Advances and Applications, vol 108, pp 243-251.
    
54. A short introduction to the theory of random Schrödinger operators.
    Viet. Jour. Math. Vol. 26 [3] (1998).
    
55. Band edge behaviour for the integrated density of states of random Jacobi matrices in dimension 1.
    Jour. Stat. Phys., vol. 90 [3-4], pp. 927-947 (1998).
    
56. Etude semi-classique d'une perturbation d'un opérateur de Schrödinger périodique : cas d'un nombre fini de perturbations.
    Asymp. Anal., vol. 15, pp 55-102 (1997).
    
57. On the spectrum of odd order self-adjoint ordinary differential operators on the real line with quasi-periodic coefficients.
    En collaboration avec B. Grébert et J.-C. Guillot.
    Jour. Diff. Equ., vol. 135, pp. 41-65 (1997).
    
58. Generic simplicity for resonances.
    En collaboration avec M. Zworski.
    Helv. Phys. Act., vol 68, pp. 531-538 (1995).
    
59. Développement asymptotique pour lqa densité d'états d'un opérateur de Schrödinger aléatoire.
    Exposé IV. Proceedings of the Séminaire "Équations aux Dérivées Partielles", École Polytechnique (1995-1996).
    
60. An asymptotic expansion for the density of states of a random Schrödinger operator with Poisson disorder.
    Jour. Funct. Anal., vol 145, pp. 267-295 (1997).
    
61. Valeurs propres et résonances au voisinage d'un seuil.
    En collaboration avec A. Grigis.
    Bull. S.M.F. , vol 124, pp 477-501 (1996).
    
62. The density of states for multidimensional continuous random Schrödinger operators with singular randomness.
    Actes de la conférence ``Spectral Theory of Schrödinger operators'', Madras (Inde) Décembre 1995. The paper is here.
    
63. A low concentration asymptotic expansion for the density of states of a random Schrödinger operator with Bernoulli disorder.
    Rand. Op. Stoch. Eq., vol 3, pp. 315-332 (1995).
    
64. Resonances for perturbations of a semi-classical periodic Schrödinger operator.
    Ark. Mat., vol. 32, pp 323-371 (1994).
    
65. Localization for some continuous random Schrödinger operators.
    Comm. Math. Phys., vol. 167, pp. 553-571 (1995).
    
66. Localization for continuous random Schrödinger operators in the semiclassical limit.
    Proceedings of the conference ``Asymptotic Methods in Spectral Theory'', Institut Euler (Saint Pétersbourg), September 1993,
    St Petersburg Math. Journal, vol. 8, pages 105--110 (1997)
    
67. Localization for semi-classical continuous random Schrödinger operators II: the random displacement model.
    Helv. Phys. Act., vol. 66, pp. 810-841 (1993).
    
68. Localisation pour des opérateurs de Schrödinger aléatoires dans $L^2(R^d)$ : un modèle semi-classique.
    Ann. Institut Fourier., vol 45, pp. 265-316 (1995).
    
69. Etude semi-classique d'une perturbation d'un opérateur de Schrödinger périodique.
    Ann. Inst. Henri Poincaré, sér. Phys. Théor., Vol 55, pages 459--509 (1991).
    
70. Impuretés dans une structure périodique.
    Exposé no 20, Actes des Journées E.D.P, St Jean-de-Monts, 1990.
    

Unpublished:

• The integrated density of states for an interacting multielectron homogeneous model
  In collaboration with H. Zenk.
  
• Anderson transitions for quasi-periodic Schrödinger operators in dimension 1
  In collaboration with A. Fedotov.
  Université Paris-Nord preprint no 98-29 (1998).
  Here is the (commented) Maple worksheet used to perform the numerics of the paper.
  
• The monodromy matrix for a family of almost periodic Schrödinger equations in the adiabatic case.
  In collaboration with A. Fedotov.
  Preprint of the Fields (Toronto) FI-ML 1997-003 (1997).