Retired associate professor.
Former director of the Grupo de Física Matemática, from 2002 to January 2024.
Principal investigator in the project “Schroedinger’s problem and Optimal Transport: a multidisciplinary perspective” (PTDC/MAT-STA/28812/2017), financed by the FCT.
Research interests
- Probabilistic methods in mathematical physics.
- Path integral methods in quantum theory (and quantum field theory).
- Classical and quantum dynamical systems (geometric and algebraic methods). Stochastic deformation.
- Applications of stochastic analysis.
Selected publications
-
With Q. Huang:
From second order differential geometry to stochastic geometric mechanics, J. Nonlinear Sci. 33 (2023), 6, 127 pp. -
With Q. Huang:
“Stochastic geometric mechanics in nonequilibrium thermodynamics: Schrödinger meets Onsager”, J. Phys A 56 (2023), 134003, 24 pp. -
With A.B. Cruzeiro and C. Oliveira:
“Time-symmetric optimal stochastic control problems in space-time domains”, Optimization 71 (2022), 3241-3275. - With M. Arnaudon, A. B. Cruzeiro and 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 - With M. Arnaudon:
“A Stochastic Look at Geodesics on the Sphere” in Geometric Science of
Information”, Springer International Publishing (2017). - With R. Lassalle:
“A weak approach to the stochastic deformation of classical mechanics”, J. Geom. Mech. 8, 2 (2016), 221-233. - With P. Vuillermot:
“On some Gaussian Bernstein processes in R^N and the periodic Ornstein–Uhlenbeck process”, Stoch. Anal. Appl. 34, 4 (2016), 573-597. - With N. Privault and X. Yang:
“Large deviations for Bernstein bridges”, Stoch. Process. Appl.
126, 5 (2016), 1285-1305. - With C. Léonard and 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 - With 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 - With 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 - With Wu Liming and 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 - With 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 - With 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 - With 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 - With 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, with Rolando Rebolledo and 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, with 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 - With S. Albeverio and 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, with 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