Vie estudiantine

École doctorale



General informations
Name & Surname : NAJAR Hatem
Email :

Research interest:

  • Spectral Theory.

  • Random Shrödinger operators.

  • Partial Differential Equations.

  • Quantum waveguides.

  • Graph theory.


Schooling & Qualifications


1992–1994 Under Graduate Diploma in Mathematical Physics, Faculty of Sciences in Tunis, very good scores upon graduation,

1994–196 Graduate Diploma in Mathematical Sciences, Faculty of Sciences in Tunis, , good scores upon graduation

          1996–1997 Master Degree in Mathematical Sciences, University of Paris                 13, Paris, good scores upon graduation

Ph. D thesis: 1997-2000, University of Paris 13, France.

Title: Lifshitz asymptotic for random acoustic operators

supervisor: F. klopp

Jury : B. Helfer ( University Paris 11 (France)), A. Grigis (University Paris 13 (France)), W-M Wang (Ecole polytechnique (France) ), J-C Guillot (University of Paris 13 (France)), L. Pastur ( referee, University Paris 7 (France) ), P. Stollmann (referee, Chemnitz university (Germany))

Habilitation: 2007, University of Safax, Tunisia


Title Some results on the spectral theory of partial differential operators with random coefficient
Jury  W. Kirsch (referee) M. Selmi (referee), A. Baklouti, M. Ben Ammar, M. Ben Ayed, M. Menif, F. Ammar.



Teaching courses:

  • Undergraduate courses: Probability, Algebra , Linear Algebra, Calculus I,II,III, Discrete Mathematics.

  • Graduate courses: Mathematics for Engineering, Topologies, Probability theory, Analysis II.

  • Master courses: Hilbert and spectral analysis, Spectral theory of bounded and unbounded operators, convex functions and optimization, Functional Analysis, Soboblev Spaces.


Publications in Refereed Journals:


  1. H. Najar:Asymptotique de la densité d’états intégrée des opérateurs acoustiques  aléatoires.  C.  R. Acad. Sci. Paris, 333 I, p 191-194 (2001)

  2. H. Najar: Lifshitz tails for random acoustic operators. Jour. Math. Phys. 44 N 4 (2003) p 1842-1867.

  3. H. Najar: Asymptotic behavior of the integrated density of states of acoustic operators with random  long range perturbations. Jour. Stat. Phys. 115, no. 3-4, p 977-996 (2004).

  4. H. Najar: The spectrum minimum for random Schrödinger operators with indefinite sign potentials.

Jour. Math. Phys. 47 (2006), no. 1

  1. H. Najar: 2-Dimensional localization of acoustic waves in random perturbation of periodic media.

Jour. Math. Anal. Appl. 322 (2006), no. 1, p 1-17.

  1. H. Najar: Internal Lifshitz tails for discrete Schrödinger operators. Inter. Jour. Math. Math. Sci (2006).

  2. H. Najar: Results dealing with the behavior of the integrated density of states of random divergence operators . C. R. Acad. Sci. Ser I (344) p 367-372; (2007).

  3. H. Najar: Lifshitz tails for acoustic waves in random quantum waveguide . Jour. Stat. Phy. Vol

128 No 4, p 1093-1112 (2007).

  1. H. Najar: Non-Lifshitz tails at the spectrum bottom of some random operators. Jour. Stat. Phy. (2008).

  2. H. Najar, S. Ben Hariz, M. Ben Salah On the Discrete Spectrum of a Spatial Quantum Waveguide with a Disc Window Mathematical Physics, Analysis and Geometry (2009)

  3. M. Marx, H. Najar: On the singular spectrum for adiabatic quasi-periodic Schrödinger Operators Ad-

vances in Mathematical Physics Vol. 2010, Article ID 145436, 30 pages (2010). doi:10.1155/2010/145436

  1. H. Najar, O. Olendski: Localization properties of Dirichlet spatial quantum waveguide with

two concentric Neumann disc windows J. Phys. A: Math. Theor. 44 (2011) 305304 doi:10.1088/1751- 8113/44/30/305304

  1. W. Kirsch, H. Najar: Lifshitz tails for continuous Laplacian in the site percolation case Random Operators and Stochastic Equations. Volume 22, Issue 2, Pages 109–117 (2014).

  2. H. Najar, M. Raissi: A quantum waveguide with Aharonov-Bohm field. Math. Meth. App. Sciences (2015).

  3. H. Boumaza, H. Najar: Lifshitz Tails For Continuous Matrix-valued Anderson Models J. Stat. Phys. 160(2), p 371-396. (2015).

  4. H. Najar and M. Raissi: Eigenvalues asymptotics for Stark operators e-Journal of Analysis and Applied Mathematics 2019(1) (2019), p. 1 – 14.

  5. H. Najar: Lifshitz Tails for Quantum Waveguides with Random Boundary Conditions. Math Phys Anal Geom 22, 17 (2019) doi:10.1007/s11040-019-9314-8.

  6. H. Najar and M. Zahri: Stark operators on finite intervals: Self-adjointness and spectrum submitted.

  7. R. Gargouri, H. Najar: A remark on the characterization of triangulated graphs. Subbmited.

  8. H. Najar, I. Y. Popov, A. S. Bagmutov, I. F. Melikhov: On the discrete spectrum of quantum layers with Neumann windows in the presence of external electric field. Work in progress.

Communication in internationals conferences

  • First Franco-Tunisian days in PDE, Marsa, Tunisia 2001.

  • Mediterranean Days in Mathematics and applications, Mars 2005, Tozeur; Tunisia.

  • Stochastic Process in Mathematical Physics" New York University , Juin 2006.

  • First and second spectral theory days in Sfax, Tunisia (2006-07, Sfax)

  • Disordered Systems: Random Schrödinger Operators and Random Matrices, Mars 2008 Oberwolfach, Germany.

  • Mathematics and Physics of Anderson Localization, July 2008, Cambridge university, United Kingdom.

  • Quantum mathematics for disordered system. Universitis Paris 6-Paris 13, 28-30 May 2012.

  • Mathematical Physics of Disordered Systems 13-17 May, 2013 Fer. Uni. Hagen, Germany.

  • Spectra and Graphs, Jun 2013 Bizerte, Tunisia.

  • Spectra of Random Operators and Related Topics Research Institute In Mathematical Sciences Kyoto University, Japan. 5-7 December 2013.

  • Spectral and Scattering Theory and Related Topics: Research Institute In Mathematical Sciences Kyoto University, Japan. 11-13 December 2013.

  • International conference on Advances in Applied Mathematics, Hammamet, Tunisia, 18-22 December 2013.

  • Spectra and Graphs, Jun 2014 Bizerte, Tunisia.

  • International Mathematical Center of Pur and Applied Mathematics (CIMPA) Spectral theory of graphs and manifolds, Kairouan Tunisia, 7-19 November 2016. http://www.math.sciences.univ-

  • Mathematical Challenge of Quantum Transport in Nanosystems “Pierre Duclos Workshop"ITMO University, Saint Petersburg, Russia (September 14-16, 2020)

Conference Proceedings

  • H. Najar: Asymptotique de la densité d’états  intégrée  des  opérateurs  acoustiques  aléatoires.  p 102-111 First Franco-Tunisien days in PDE, By B. Dahmen C. Zouili, J. Lebau (2001).

  • H. Najar Spectral properties of a quantum waveguide with Neumann Window Spectral and Scattering Theory abd Related Topics : Edited by Takuya Mine, p 82-102, ISSN 1880-2818 N 6 (2014).

  • H. Najar Spectral results on Quantum waveguide Advances in Applied Mathematics: International Conference on Advances in Applied Mathematics (ICAAM) 2013 Edited by A. Jeribi. Springer (2015).

  • H. najar Introduction to Spectral Theory of Unbounded Operators, by H. Najar p1-34. Spectral Theory on Graphs and Manifolds, the CIMPA Research SMF; Seminaires et Congres Volume: 32; 2018 Edited by C. Anné: Laboratoire de Mathématiques Jean Leray, Nantes, France, N. Torki-Hamza.

  • Igor Y. Popov, Alexander S. Bagmutov, Ivan F. Melikhov, and Hatem Najar Numerical analysis of multi-particle states in coupled nano-layers in electric field AIP Conference Proceedings 2293, 360006 (2020);

  • Master thesis: Mr Dhafer Hadj Dahmen Title: Spectral theorem for Self-adjoint operators and applications Jury: E. Bouassida (F.S. Sfax), H. Najar (I.P.E.I. Monastir), M. Ben Ammar (F.S. Sfax), M. Damak (F.S. Sfax), M. Menif (F.S. Sfax) (2007).

  • Master thesis: Mr Mohsen Miraoui. Title: Spectral properties of quantum waveguide. Jury: A. Jeribi (F.S. Sfax) M. Ben Ammar (F.S. Sfax) M. Menif (F.S.Sfax). (2009)

  • Matser thesis: Mlle Monia Raissi. Title: Spectral studies for a quantum wavguide in the presence of external electric field. Jury members: M. Damak (F.S. Sfax) M. Menif (F.S. Sfax) H. Jerbi (F.S. Sfax) (2011)

  • Master thesis: Mlle Hiba Hammadi. Title: "Spectral properties of twisted quantum waveguides". Jury members: M. Damak (F.S. Sfax) M. Menif (F.S. Sfax) H. Jerbi (F.S. Sfax) (2011)

  • Supervising Master thesis : Khemily yousef. Title: Spectral theory for Quantum Graphs. Jury members: K. Ammari (F.S. Monastir), N. Turki (ISIG Kairouan). (2014)

  • Supervising Ph. D.: Monia raissi. Title: Spectrum of a Quantum waveguide with Magnetic field . Defended on 11 th November 2016.


Professional experience
Member associations

2008-Present Reviewer, Math reviews

2010-Present Member, Editor board, American Journal of Mathematics and Sciences

2008-Present Member, IAMP, International Association of Mathematical Physics,

2002-Present Member, SMT, Mathematical Tunisian Society ,

2007-Present Member, AMA,Association of Mathematics and Application, Tunisia ,


  • Research Projects:

    • 2005-2008: Grants for DGRSRT-CNRS Project between Tunisia and France N 06/R 15-04. Subject: Spectral Theory for Random Operators.

    • 2008-2011: Grants for Tunisian-French Conjoint Project CMCU N 09/G1504. Subject : Spectral Theory for Partial Differential Equations.

    • 2011-2014: Grants for DGRSRT-CNRS Project between Tunisia and France N 12/R 15-01. Subject: Transport and spectral theory in quantum waveguides.

  • Administrative and European projects:

    • TEMPUS Project: TIES: Towards an internationalization of Higher Education Network for MEDA region .

    • TEMPUS Project: QUALYCERT: Quality Assurance and Certification at University.

    • TEMPUS Projet: EOLES: Electronic and Optic E-learning for Embedded Systems.

    • TEMPUS Project: OSMOSE: Ouverture Structurée Université Monde Socio-Economique.