Jean-Claude Zambrini

Professor Associado com Agregação aposentado.

Antigo presidente do Grupo de Física Matemática, de 2002 até janeiro de 2024.

Investigador responsável do projecto “Schroedinger’s problem and Optimal Transport: a multidisciplinary perspective” (PTDC/MAT-STA/28812/2017), financiado pela FCT.

Interesses científicos

• Métodos probabilísticos em física matemática.
• Método dos integrais de caminho em teoria quântica (e teoria quântica de campo).
• Sistemas dinâmicos clássicos e quânticos (métodos geométricos e algébricos). Deformação estocástica.
• Aplicações da análise estocástica.

Algumas publicações recentes

• Com Q. Huang:
  From second order differential geometry to stochastic geometric mechanics, J. Nonlinear Sci. 33 (2023), 6, 127 pp.

• Com Q. Huang:
  “Stochastic geometric mechanics in nonequilibrium thermodynamics: Schrödinger meets Onsager”, J. Phys A 56 (2023), 134003, 24 pp.

• Com A.B. Cruzeiro e C. Oliveira:
  “Time-symmetric optimal stochastic control problems in space-time domains”, Optimization 71 (2022), 3241-3275.

• Com M. Arnaudon, A. B. Cruzeiro e C. Léonard:
  “An entropic interpolation problem for incompressible viscous fluids”, Annales de l’Institut Henri Poincaré – Probabilités et Statistiques 56, 3 (2020), 2211-2235. URL: http://gfm.cii.fc.ul.pt/people/jczambrini/AIHP1036.pdf
• Com M. Arnaudon:
  “A Stochastic Look at Geodesics on the Sphere” in Geometric Science of
  Information”, Springer International Publishing (2017).
• Com R. Lassalle:
  “A weak approach to the stochastic deformation of classical mechanics”, J. Geom. Mech. 8, 2 (2016), 221-233.
• Com P. Vuillermot:
  “On some Gaussian Bernstein processes in R^N and the periodic Ornstein–Uhlenbeck process”, Stoch. Anal. Appl. 34, 4 (2016), 573-597.
• Com N. Privault e X. Yang:
  “Large deviations for Bernstein bridges”, Stoch. Process. Appl.
  126, 5 (2016), 1285-1305.
• Com C. Léonard e S. Roelly:
  “Reciprocal processes. A measure-theoretical point of view”, Probab.
  Surv. 11 (2014), 237-269.
• “Stochastic Deformation of Classical Mechanics”, Discrete and Continuous Dynamical Systems, 2013 supplement (2013), 807-813.
• “The research program of Stochastic Deformation (with a view toward Geometric Mechanics)”
  Progress in Probability 68, Springer (2015), 359-393.
  URL: http://gfm.cii.fc.ul.pt/people/jczambrini/JCZambrini_EPFL.pdf
• Com Pierre A. Vuillermot:
  “Bernstein Diffusions for a Class of Linear Parabolic Partial
  Differential Equations”, Journal of Theoretical Probability (May 2012).
  URL: http://gfm.cii.fc.ul.pt/people/jczambrini/vuizambrini1.pdf
• Com N. Privault:
  “Stochastic deformation of integrable dynamical systems and random time
  symmetry”,
  URL: http://www.ntu.edu.sg/home/nprivault/papers/deformation.pdf
• “On the geometry of the Hamilton-Jacobi-Bellman equation”, Journal of Geometric Mechanics 1, 3 (Sep 2009).
  URL: http://gfm.cii.fc.ul.pt/people/jczambrini/geometry-hamilton-jacobi-bellman.pdf
• Com Wu Liming e A. B. Cruzeiro:
  “Bernstein processes associated with a Markov process”, in Stochastic Analysis and Mathematical Physics, ANESTOC’98, Proceedings of the Third
  International Workshop, Ed. R. Rebolledo, Trends in Mathematics Series, Birkhäuser, Boston (2000).
  URL: http://www.birkhauser.ch/books/math/4185.htm
• Com Kai Lai Chung:
  Introduction to Random Time and Quantum Randomness, New Edition, Monographs of the Portuguese Mathematical Society vol. 1, World Scientific (2003).
  URL: http://www.worldscibooks.com/physics/5288.html
• Com N. Privault:
  “Markovian bridges and reversible diffusion processes with jumps”, Annales de l’Institut Henri Poincaré (Probabilités & Statistiques) 40 (2004), 599-633.
  URL: http://www.ntu.edu.sg/home/nprivault/papers/bridges.pdf
• Com P. Lescot:
  “Probabilistic deformation of contact geometry, diffusion processes and their quadratures”, Progress in Probability 59, Birkhauser Verlag Basel (2007), 203-226.
  URL:
  http://gfm.cii.fc.ul.pt/people/jczambrini/lescot-zambrini-ascona.pdf
• Com N. Privault:
  “Euclidean quantum mechanics in the momentum representation”,
  Journal of Mathematical Physics 46 (2005).
  URL: http://www.ntu.edu.sg/home/nprivault/papers/euclidean.pdf
• Editor, com Rolando Rebolledo e Jorge Rezende:
  Stochastic Analysis and Mathematical Physics (SAMP/ANESTOC 2002), Proceedings of the Mathematical Legacy of R P Feynman (Lisbon, Portugal, 3-7 June 2002), Proceedings of the Open Systems and Quantum Statistical Mechanics (Santiago, Chile, 7-11 January 2002), World Scientific (2004).
  URL: http://www.worldscibooks.com/physics/5676.html
• Editor:
  XIVth International Congress on Mathematical Physics (Lisbon, Portugal 28 July – 2 August 2003), World Scientific (2006).
  URL: http://www.worldscibooks.com/physics/5778.html
• Editor, com J. C. Mourão, J. P. Nunes, R. Picken:
  Prospects in Mathematical Physics (YRS of 14th ICMP 2003), Contemporary Mathematics no 437, American Mathematical Society (2007).
  URL: http://www.ams.org/bookstore?fn=20&item=CONM-437
• Com S. Albeverio e J. Rezende:
  “Probability and quantum symmetries II.The theorem of Noether in
  quantum mechanics”, Journal of Mathematical Physics 47 (2006).
  URL: http://gfm.cii.fc.ul.pt/people/jczambrini/JMathPhys-47-062107.pdf
• Editor, com Gerard Ben Arous, Ana Bela Cruzeiro, Yves Le Jan:
  Stochastic Analysis in Mathematical Physics, Proceedings of a Satellite Conference of ICM 2006 (Lisbon, Portugal 4-8 September 2006), World
  Scientific (2008).
  URL http://www.worldscibooks.com/mathematics/6734.html