Publications / Research
Maitre de conférence en physique, Université Grenoble Alpes.
2
Hyperbolic dynamical systems, Classical chaos
2.1 Publications
- 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.
- 2018. "Ruelle spectrum of linear pseudo-Anosov maps”, F. Faure, S. Gouëzel, E. Lanneau preprint 2018. talk on Youtube by Sebastien Gouezel at I.C.M. 2018.
2.2
Lecture notes and slides
- 2009. "Origine de l'irréversibilité en mécanique. Les résonances de Ruelle."(juin 2009)
- 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.
- 2014. "Resonances for geodesic flows on negatively curved manifolds", talk on Youtube by Masato Tsujii at I.C.M. 2014.
- 2015. "Spectre du flot géodésique en courbure négative [d'après F. Faure et M. Tsuji]" exposé de Sébastien Gouezel au séminaire Bourbaki du 21/3/2015.
- 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.
- 2019. “Micro-local analysis of hyperbolic dynamics”. Video and slides, october 18th, 2019 at MSRI.
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
- 2007. "Introduction au chaos quantique"(Cours à l'école d'été de Peyresq 2007).
- 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
7.2 Lecture notes and slides
7.3 Softwares
7.3.1 Music with just intonation and Analysis of sounds
7.4 External links
8
Thèses (Thesis)
- 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
9
Liens, External links
9.1 In Grenoble
9.2 In General