2006. "Prequantum chaos: Resonances of the prequantum cat map", F. Faure, Journal of Modern Dynamics, Vol.1 No.2, 255-285, (2007), Paper, preprint 2006.
2006. "Ruelle-Pollicott resonances for real analytic hyperbolic map", F. Faure and N. Roy, Nonlinearity Vol. 19, 1233-1252, (2006), Paper, or preprint 2006
2008. "Semi-classical approach for Anosov diffeomorphisms and Ruelle resonances" F. Faure, N. Roy and J. Sjöstrand, Open Math. Journal, vol. 1, 35--81, (2008). Paper, or preprint 2008
2009. "Semiclassical origin of the spectral gap for transfer operators of partially expanding map" F. Faure. Nonlinearity Vol. 24, 1473-1498, (2011), Paper, or preprint 2009. Movies related to this paper.
2010. "Upper bound on the density of Ruelle resonances for Anosov flows" F. Faure and J. Sjöstrand, Comm. in Math. Physics, vol. 308, 325-364, (2011) Paper. or preprint 2010
2012. "Prequantum transfer operator for Anosov diffeomorphism" F. Faure and M. Tsujii. Astérisque 375 (2015). preprint 2012. article.
2013. "Band structure of the Ruelle spectrum of contact Anosov flows" F. Faure and M. Tsujii. Comptes rendus - Mathématique 351 , 385-391, (2013). paper, preprint 2013.
2013. "Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps", J.F. Arnoldi, F.Faure, T. Weich. Ergodic Theory of Dynamical Systems (2015). preprint 2013
2013. "The semiclassical zeta function for geodesic flows on negatively curved manifolds", F. Faure and M. Tsujii, Invent. math. (2017) 208: 851. paper. preprint 2013
2014. "Power spectrum of the geodesic flow on hyperbolic manifolds", S. Dyatlov, F. Faure, C. Guillarmou, Analysis & PDE 8 (2015), 923–1000. paper, preprint 2014
2014. "Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum" S. Barkhofen, F. Faure, T. Weich, Nonlinearity Vol. 27, 1829, (2014), preprint 2014
2015. "Asymptotic spectral gap for open partially expanding maps" F.Faure, T. Weich. Communications in Mathematical Physics 2017, 356(3), 755-822. Paper. preprint 2015
2017. "Horocyclic invariance of Ruelle resonant states for contact Anosov flows in dimension 3" C. Guillarmou, F.Faure Math. Res. Lett., Volume 25, Number 5, 1405–1427, 2018, paper,preprint 2017.
2017. "Fractal Weyl law for the Ruelle spectrum of Anosov flows", F. Faure and M. Tsujii. preprint 2017. Slides. Video talk.
2013. "Semiclassical approach for the Ruelle-Pollicott spectrum of hyperbolic dynamics". May 2013. Lectures notes for summer school 13-17 May 2013 at ROMA.
2013. "Mathematical relations between Deterministic classical Chaos and Quantum Chaos via Ruelle resonances". Slides, for S.F.P. meeting, Marseille, july 2013. Movies related to this talk.
2018.“Spectrum, traces and zeta functions in hyperbolic dynamics”. Lectures notes for the school 23-27 April 2018 at the University Cheikh Anta Diop in Dakar, Sénégal. Movies related to the notes.
2019.“From classical chaos to quantum chaos”. Lectures notes for the school 22-26 April 2019 at CIRM.
2019.Slides and Video on Youtube “Emergence of quantum dynamics in hyperbolic dynamics”. may 2019.
2019.“Micro-local analysis of hyperbolic dynamics”. Slides for the school 1-5 july 2019 at CIRM.
3
Quantum chaos
3.1 Publications
2002. "Propagating modes in a periodic wave guide in the semi-classical limit", F.Faure, J. Phys. A: Math. Gen. 35, 1339-1356, (2002). Paper
2003. "Scarred eigenstates for quantum cat maps of minimal periods", F. Faure, S. Nonnenmacher and S. De Bièvre, Communications in Mathematical Physics ,Vol. 239, 449-492, (2003). Paper, or preprint 2002
2003. "On the maximal scarring for quantum cat map eigenstates", F. Faure, S. Nonnenmacher , Communications in Mathematical Physics, Vol 245, 201 - 214, (2004). Paper, or preprint 2003
2006. "Semi-classical formula beyond the Ehrenfest time in quantum chaos. (I) Trace formula", F. Faure, Annales de l'Institut Fourier, Vol. 57 No.7, p. 2525-2599 (2007)., Paper, or preprint 2006 ., Movies related to this paper.
3.2 Lecture notes
2012. "Ergodicity of quantum maps". Manuscript lectures notes given in Marburg, september 2012. pdf file.
2005. "Long time semiclassical evolution of wave packets in quantum chaos. Example of non quantum unique ergodicity with hyperbolic maps" Lecture notes for I.H.P. School, june 2005. format ps.gz ou pdf
2014. “Introduction au chaos classique et chaos”(Notes d'exposé pour les journées mathématiques (journées X-UPS) à l'intention des professeurs de math de classes préparatoires, lundi 28 et mardi 29 avril 2014.)
4
General Quantum physics
4.1 Publications
2005. "Loss of quantum coherence in a system coupled to a zero-temperature environment", A. Ratchov, F. Faure, F. W. J. Hekking , Eur. Phys. J. B. Vol 46, 519-528, (2005). Paper, or preprint
4.2 Lecture notes
1993. "Approche géométrique de la limite semi-classique par les états cohérents", Exposé à grenoble 1993.
1997. "La quantification du champ électromagnétique" Exposé le juin 1997 à l'institut Fourier. (fichier ps).
2000. "La quantification géométrique" Exposé le 27 avril 2000 à l'institut Fourier.
2003. "Introduction à la mécanique quantique et au paradoxe E.P.R" (exposé au magistère de mathématiques, UJF, janvier 2003).
2017. "Exposé sur le théorème adiabatique en mécanique quantique. Description par l'analyse semiclassique". Exposé le 5 mai 2017 à l'institut Fourier.
5
Topological phenomena for slow-fast dynamical systems and molecular physics
5.1 Publications
2000. "Topological Chern indices in molecular spectra" F. Faure, B. Zhilinskii, Physical Review Letters , 85, 960-963 , (2000). Paper, or preprint.
2001. "Topological properties of the Born-Oppenheimer approximation and implications for the exact spectrum" F. Faure, B. Zhilinskii, Letters in Math. Physics vol 55, 219-238, (2001). Paper or preprint.
2002. "Qualitative features of intra-molecular dynamics. What can be learned from symmetry and topology" F. Faure and B. Zhilinskií, Acta Appl. Math. 70, 265-282 (2002). Paper in ps.gz .
2002. "Topologically coupled energy bands in molecules" F. Faure and B. Zhilinskií, Phys. Letters A, 302, p.242-252, 2002. Paper, or preprint.
2007. "Adiabatically coupled systems and fractional monodromy" M. Hansen, F. Faure, B. Zhilinskii, J. Phys. A: Math. Theor. 40 (2007) 13075-13089. Paper of preprint
2019. "Manifestation of the topological index formula in quantum waves and geophysical waves" F. Faure, preprint.
6
Semi-classical and topological analysis of the quantum Hall effect
6.1 Publications
1993. "Mécanique quantique sur le tore et dégénérescences dans le spectre". F. Faure, Séminaires d'analyse spectrale de l'Institut Fourier, Vol n°11, 1993. Paper.
1994. "Generic description of the degeneracies in Harper like models." F. Faure, Journal of Physics A: Math. and gen. 27, (1994), 7519-7532. Paper.
2000. "Semi-classical Quantum Hall conductivity" F. Faure, B.Parisse, Journal of Mathematical physics, 41, 62-75, (2000). Paper or preprint
2000. "Topological properties of quantum periodic Hamiltonians" F. Faure, Journal of physics A: math and general, 33 , 531-555 (2000). Paper or preprint.
6.2 Lecture notes
1992. "Structure of wave functions on the torus characterized by a topological Chern index" in Proceedings to workshop in Trieste 1992. Paper.
2000. "Rôle des indices topologiques de Chern en physique du solide et physique moléculaire. Calculs dans des modèles simples." Notes de cours à l'école d'été interdisciplinaire MÉTHODES TOPOLOGIQUES ET GÉOMÉTRIQUES: APPLICATION AUX SYSTÈMES DYNAMIQUES PHYSIQUE, CHIMIE, BIOLOGIE. Dijon, 26-30 juin 2000. (fichier ps).
2002. "Geometric and topological aspects of slow and fast coupled dynamical systems in quantum and classical dynamics". Lectures notes for lectures given in:Saclay. Spth., march-april 2002, and M.A.S.I.E. Spring School, Warwick, march 2002. Lecture notes: format ps.gz ou pdf (or 2 pages / page: format ps.gz ou pdf) or html.
2003. "Topological indices in molecular spectra". Exposé en avril 2003 au Mathematical Science Research Institute (MSRI) Berkeley Vidéo et PDF.
7
Mathematics and music
7.1 Publications
2015. "Analyse et jeu musical en tempérament juste adaptatif " F.Faure M. Mezzadri, A. Ratchov, preprint. février 2015.
1993. "Approche géométrique de la limite semi-classique par les états cohérents et mécanique quantique sur le tore" Thèse de doctorat (2 novembre 1993). pdf
2006. "Aspects topologiques et chaotiques en mécanique quantique" Thèse d'habilitation (17 octobre 2006). pdf