Prépublications. Preprints.

D. Le Peutrec, F. Nier, C. Viterbo. Bar codes of persistent cohomology and Arrhenius law for p-forms. HAL   ArXiiv

Publications dans des revues avec comité de lecture. Published articles.

M. Ben Said, F. Nier, J. Viola. Quaternionic structure and analysis of some Kramers-Fokker-Planck operators. Asymptotic Analysis Vol 119 no 1-2 pp 87-116DOI: 10.3233/ASY-191569

Z. Ammari, F.  Nier, S. Breteaux. Quantum mean field asymptotics and multiscale analysis. Tunisian Journal of Mathematics, Vol 1, No 3 (2019). DOI: 10.2140/tunis.2019.1.221

F. Nier.
Boundary conditions and subelliptic estimates for geometric Kramers-Fokker-Planck operators on manifolds with boundaries.Memoirs AMS Vol 242, No 1200 (2018) . DOI:

T. Lelièvre, F. Nier. Low temperature asymptotics for Quasi-Stationary Distributions in a bounded domain. Analysis & PDE, Vol 8, No 3 (2015) DOI 10.2140/apde.2015.8.561

Z. Ammari,  F. Nier.  Mean field propagation of infinite dimensional Wigner measures with a singular two-body interaction potential. Annali della Scuola Normale Superiore di Pisa, Classe di Sienze, Serie V, Vol XIV, Fasc 1 (2015) DOI 10.2422/2036-2145.201112_004

T. Lelièvre, F. Nier, G. Pavliotis. Optimal Non-reversible Linear Drift for the Convergence of Equilibrium of a Diffusion. Journal of Statistical Physics, Volume 232, No 2, pp 237-274 (2013), DOI:

A. Aftalion,  F. Nier. Adiabatic approximation for a two-level atom in a light beam. Annales de la Faculté des Sciences de Toulouse, Sér. 6, Vol. 22, No 1, pp 43-131 (2013) DOI: 10.5802/afst.1367

D. Le Peutrec, F. Nier, C. Viterbo. Precise Arrhenius law for p-forms: The Witten Laplacian and Morse-Barannikov complex. Annales Henri Poincaré, Vol. 14, No 3, pp 567-610 (2013), DOI:

A. Faraj, A. Mantile, F. Nier. An explicit model for the adiabatic evolution of quantum observables driven by 1D shape resonances, J. Phys. A 43 (2010), no. 47 . DOI:

 Z. Ammari, F. Nier.  Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states, Journal de Mathématiques Pures et Appliquées, Vol. 95, No 6, (2011) pp 585-626. DOI:

A. Faraj, A. Mantile, F. Nier. Adiabatic evolution of 1D shape resonances: an artificial interface conditions approach, M3AS Vol. 21, No. 3 (2011), 541-618. DOI:

T. Hmidi, A. Mantile, F. Nier.  Time-dependent delta-interactions for 1D Schrödinger Hamiltonians,  Mathematical Physics Analysis and Geometry,Volume 13, Number 1(2010). DOI:

V.  Bonnaillie-Noël, A. Faraj, F. Nier. Simulation of resonant tunneling heterostructures: numerical comparison of a complete Schr{\"o}dinger-Poisson system and a reduced nonlinear model.   Journal Comput. Electronics, Volume 8, Number 1 (2009). DOI:

 Z. Ammari, F. Nier. Mean field limit for bosons and propagation of Wigner measures. J. Math. Phys. 50 (4) (2009). DOI:
I. Gallagher, T. Gallay, F. Nier.  Spectral asymptotics for large skew-symmetric perturbations of the harmonic oscillator. Int. Math. Res. Not. IMRN 2009, no. 12, 2147--2199.

A. Faraj, A. Mantile, F. Nier.  Double scale analysis of a Schrödinger-Poisson system with quantum wells and macroscopic nonlinearities in dimensions 2 and 3.  Asymptotic Analysis 62 (3-4) (2009). DOI:10.3233/ASY-2009-0919

C. Chniti, F. Nataf, F. Nier. Improved interface condition for 2D domain decomposition with corner : numerical applications. Journal of Scientific Computing 38(2) (2009). DOI:

V. Bonaillie, F. Nier, Y. Patel.  Far from equlibrium steady states of 1D-Schrödinger-Poisson systems with quantum wells II.  Jourrnal of the Mathematical Society of Japan, 61(1) (2009). DOI:10.2969/jmsj/06110065
V. Bonnaillie, F. Nier, Y. Patel. Far from equlibrium steady states of 1D-Schrödinger-Poisson systems with quantum wells I.  Ann. Inst. H. Poincaré Anal. Non Linéaire 25(5) (2008). DOI:

Z. Ammari, F. Nier.  Mean field limit for bosons and infinite dimensional phase-space analysis.  Annales Henri Poincaré, 9(8) (2008). DOI: https//

F. Nier. Accurate WKB approximation for a 1D problem with low regularity. Serdica Math. J. 34(1) (2008), pp 113-126.

C. Chniti, F. Nataf, F. Nier. Improved interface condition for 2D domain decomposition with corner : a theoretical determination. Calcolo 45(2) (2008) pp 111-147. DOI:

F. Nier. Bose-Einstein condensates in the Lowest Landau Level : Hamiltonian dynamics.  Reviews in Mathematical Physics, 19(1) (2007) pp 101-130. DOI:

A. Aftalion, X. Blanc, F. Nier.  Lowest Landau Level functional and Bargmann spaces for Bose Einstein Condensates. Journal Functional Analysis 241(2) (2006) 661-702. DOI:

V. Bonaillie, F. Nier, Y. Patel. Computing the steady states for an asymptotic model of quantum transport in resonant heterostructures. Journal of Computational Physics, 219(2)  (2006) DOI:

B. Helffer, F. Nier. Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach: the case with boundary. Mémoires de la SMF vol. 105, (2006). DOI:10.24033/msmf.417

C. Chniti, F. Nataf, F. Nier. Improved Interface Conditions for the Domain Decomposition of a Non-Convex Polygonal Domain. CRAS 342(11) (2006), pp 883-886. DOI: 10.1016/j.crma.2006.03.024

A. Aftalion, X. Blanc, F. Nier. Vortex Distribution in the Lowest Landau Level.  Phys. Rev. A 73 (1), 2006. DOI:

B. Helffer, F. Nier.  Hypoellliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians, Lecture Notes in Mathematics, Vol 1862, Springer (2005). DOI:

B. Helffer, M. Klein, F. Nier. Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach. Matematica Contemporanea (Brasilian Mathematical Society), Vol. 26, p. 41-86 (2004).

F.  Hérau,  F. Nier. Isotropic hypoellipticity and trend to the equilibrium for the Fokker-Planck equation with high degree potential.  Arch. Rational Mech. Anal. Vol 171, No 2, (2004). DOI:

B. Helffer, F. Nier. Criteria to the Poincaré inequality associated with Dirichlet forms in R^d, d >=2. IMRN, 22 (2003) . DOI:

F. Nier, A. Soffer. Dispersion and Strichartz estimates for some finite rank perturbations of the Laplace operator. J. of Funct. Analysis, 198 (2003), 511-535. DOI:

C. Gérard, F. Nier. Scattering theory for the perturbations of periodic Schrödinger operators. J. Math. Kyoto Univ., 38(4):595--634, 1998. DOI:10.1215/kjm/1250518000
F. Nier. The Dynamics of some Quantum Open Systems with Short-Range Nonlinearities. Nonlinearity, 11:1127--1172, 1998. DOI:

F. Nataf, F. Nier. Convergence of domain decomposition methods via semi-classical calculus. Comm. Partial Differential Equations, 23(5--6):1007--1059, 1998. DOI:

C. Gérard, F. Nier. The Mourre Theory for Analytically Fibered Operators. J. Funct. Analysis, 152(1):202--219, 1998.

F. Nataf, F. Nier. Convergence rate of some domain decomposition methods for overlapping and nonoverlapping subdomains. Numerische Mathematik, 75(3):357--377, 1997. DOI:

F. Nier. A Semi-Classical Picture of Quantum Scattering. Ann. scient. Ec. Norm. Sup. 4esérie, 29:149--183, 1996. DOI : 10.24033/asens.1738

F. Nier. Asymptotic Analysis of a Scaled Wigner Equation. Transp. Theory Stat. Phys., 24(4-5):591--628, 1995. DOI:

F. Nier. Schrödinger-Poisson Systems in Dimension d>= 3: The Whole-Space Case.
Proc. Roy. Soc. Edinburgh, 123A:1179--1201, 1993. DOI:

F. Nier. A Variational Formulation of Schrödinger Poisson Systems in Dimension >= 3. CPDE, 18(7--8):1125--1147, 1993.DOI:

A. Arnold, F. Nier. Numerical Analysis of the Deterministic Particle Method Applied to the Wigner Equation. Math. of Comp., 58(198):645--669, 1992. DOI:

 A. Arnold, F. Nier. The Two-dimensional Wigner-Poisson Problem for an Electron Gaz in the Charge Neutral Case. Math. Meth. in Appl. Sci., 14:595--613, 1991. DOI:

F. Nier. A Stationary Schrödinger-Poisson System Arising from the Modelling of Electronic Devices. Forum Math., 2:489--510, 1990. DOI:

F. Nier. Solutions stationnaires de l'équation de Wigner. cas de la symétrie sphérique.
C.R. Acad. Sci. Paris, Série 1, 310:537--540, 1990.

 P. Degond, F. Delaurens, F.J. Mustieles, F. Nier.
Particle Simulation of Bidimensional Electron Transport Parallel to a Heterojunction Interface. Compel, 9(2):109--116, 1990.

Communications à des colloques, autres travaux. Proceedings and other things.

F. Nier.  Variations sur un théorème de Stone-Von Neumann. Journées XUPS 2018

F. Nier.  Return to the equilibrium and pseudospectral estimates: a toy model, in MRIT 6th Workshop Math-for-Industry Tutorial:Spectral theories of non-Hermitian operators and their application. (2009)

F. Nier.
Hypoellipticity for Fokker-Planck operators and Witten Laplacians, in Lectures on the Analysis of Nonlinear Partial Differential Equations Vol 1, Morningsifde Lectures in Mathematics (2009).

F. Nier.  Mean field limits and semiclassical techniques. Proceedings of the QMath10 conference, Moeciu, Romania, sept. 2007.

F. Nier.  A propos des fonctions Thêta et des réseaux d'Abrikosov.  Séminaire EDP-Ecole Polytechnique. 2006-2007.

F. Nier. Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach.  Proceedings of the conference on partial differential equations, Forges-les-Eaux, France, June 7-11, 2004. Exp. I-XIII. (.pdf)

F. Nier.  Quelques critères  pour l'inégalité de Poincaré dans R^d, d>=2. Séminaire EDP-Ecole Polytechnique. 2002-2003.

F. Nier, Y. Patel.  Nonlinear asymptotics for quantum out of equilibrium 1D systems: Reduced models and algorithms. Conference "Multiscale methods in quantum mechanics, theory and experiments", Accademia dei Lincei Roma dec. 2002. (.ps)

F. Nier. Un cadre fonctionnel pour le transport quantique dans les semi-conducteurs. Mesures de Wigner, théorie cinétique et ondes de Bloch , CIRM Luminy 03/1999.(.ps)(.pdf)

F. Nier. The Dynamics of some Quatum Open Systems with Short-Range Nonlinearities. In J.L. Rouet E.Fijalkow P.G. Leach, S.E. Bouquet, editor, Dynamical Systems, Plasmas and Gravitation, volume 516 of Lecture Notes in Physics. Springer, 1999. Selected papers from a conference held in Orleans, 22-24 june 1997.

F. Nier.
Quelques remarques sur les algorithmes de décomposition de domaines. In Séminaire EDP-Ecole Polytechnique, 1998-99.

F. Nier. Mourre Theory for Analytically Fibered Operators. Colloque Théorie Spectrale et Physique Mathématique, RIMS-Kyoto 2-5 déc. 1997. (.ps)(.pdf)

F. Nier. Quelques problèmes posés ou traités dans un cadre << espace des phases >>. Habilitation à diriger les recherches, Université Paris-Sud 12/11/1997, 1997. (.ps)(.pdf)

F. Nier. Théorie de Mourre pour des opérateurs analytiquement décomposables et application aux opérateurs de schrödinger périodiques. Journées de Scattering, CIRM Luminy 05/1997. (.ps)(.pdf)
F. Nataf, F. Nier. Convergence Rate of Schwarz Type Methods for an Arbitrary Number of Subdomains. In DD9 Proceedings 1996, Editor Petter Bjørstad, Magne Espedal and David Keyes. John Wiley and Sons Ltd.

F. Nier. Théorie de la diffusion pour des opérateurs analytiquement décomposables. In Séminaire EDP-Ecole Polytechnique, 1995-96.

F. Nier. Une description semi-classique de la diffusion quantique. In Séminaire EDP-Ecole Polytechnique, 1994-95.(.ps)

F. Nier. Formulation variationelle d'un système Schrödinger-Poisson.In Journées EDP St-Jean-de-Monts, 1992.

P. Degond, F. Guyot-Delaurens, F. J. Mustieles, F.Nier.
Semiconductor modelling via the Boltzmann equation. In Mathematical aspects of fluid and plasma dynamics, Proc. 3rd Int. Workshop, Salice Terme/Italy 1988, Lect. Notes Math. 1460 (1991) pp 87--106.

F. Nier. Etude mathématique et numérique de modèles cinétiques quantiques issus de la physique des semi-conducteurs, Thèse, Ecole Polytechnique (1991).