Lorenzo Zanelli Home Page

Lorenzo Zanelli (Associate Professor in Mathematical Physics)

Office 6DA2

Email lzanelliATmath.unipd.it

Research Interests

Many body operators on Fock-Bargmann space
Mean Field asymptotics for many body problems and Hartree dynamics.
Phase space Analysis of Wick operators.
Semi-classical and effective theories of gravity.
Periodic Schrödinger operators
The semiclassical study of quasimodes and eigenfunctions for periodic Schrödinger operators.
Wigner measures related to solutions of Schrödinger equations on the flat torus.
Schrödinger spectrum and homogenization theory.
Global Fourier Integral Operators
The global FIO structure of the Schrödinger evolution operator.

Member of the group Math4Quantum

Preprints and Publications

(26) A. Maiocchi, A. Ponno, L. Zanelli: Statistical dynamics of cold atoms in finite optical lattices. work in progress (2026)
(25) G. Marangon, A. Ponno, L. Zanelli: From Klein-Gordon-Wave to Schroedinger-Wave: a Normal Form Approach.
(2026) J. Phys. A: Math. Theor. 59 015202
(24) G. Marangon, A. Ponno, L. Zanelli: On the scaling properties of excited stationary states of the Schroedinger-Poisson model.
Commun. Nonlinear Sci. Numer. Simulat. 152 (2026) 109486
(23) G. Marangon, A. Ponno, L. Zanelli: Scaling of highly excited Schroedinger - Poisson eigenstates.
Physics Letters A, online june 2025, https://doi.org/10.1016/j.physleta.2025.130761
(22) A. Ponno, H. P. Singh, L. Zanelli: Gibbs estimates for the convergence to Hartree dynamics in the Hardy class of potentials. Preprint (2025)
(21) L. Zanelli: Mean field asymptotics and invariant measures for the flow of dNLS. To appear on Asymptotic Analysis. Preprint (2026)
(20) E. Picari, A. Ponno, L. Zanelli: Mean Field derivation of DNLS from the Bose-Hubbard model.
Ann. Henri Poincare 23 (2022), 1525--1553
(19) L. Zanelli: Schroedinger dynamics and optimal transport of measures.
Infinite Dimensional Analysis, Quantum Probability and Related Topics, Online first (2021), DOI 10.1142/S0219025721500168
(18) L. Zanelli: Hamilton-Jacobi homogenization and the isospectral problem.
Symmetry (2021), 13, 1196.
(17) L. Zanelli, F. Mandreoli, F. Cardin: A weak KAM approach to the periodic stationary Hartree equation.
Nonlinear Differential Equations and Appl. (2021) 28:56
(16) L. Zanelli: Periodic coherent states decomposition and quantum dynamics on the flat torus.
In: Bastos M.A., Castro L., Karlovich A.Y. (eds) Operator Theory, Functional Analysis and Applications. Operator Theory: Advances and Applications, vol 282. Birkhauser (2021)
(15) A. Parmeggiani, L. Zanelli: An exact version of the Egorov Theorem for one dimensional periodic Schroedinger operators.
Journal of Fourier Analysis and Applications, (2019) 25:1759--1781.
(14) F. Cardin, L. Zanelli: The semiclassical Wave Front Set for Schroedinger eigenfunctions on the torus.
Mathematical Physics, Analysis and Geometry, online first 11 march 2017, June 2017, 20:10.
(13)L. Zanelli, S. Todros, E.L. Carniel, P.G. Pavan, A.N. Natali: Mechanical properties variation and constitutive modelling of biomedical polymers.
Acta of Bioengineering and Biomechanics, Vol. 19, N. 3, 2017.
(12) L. Zanelli, A. Montanaro, E.L. Carniel, P.G. Pavan, A.N. Natali: The study of equivalent material parameters in a hyperelastic model.
International Journal of Non-Linear Mechanics, Volume 89, March 2017, pp 142--150.
(11) L. Zanelli: Schroedinger spectra and the effective Hamiltonian of the weak KAM theory on the flat torus.
Journal of Mathematical Physics, 57 (2016), no. 8, 081507, 12 pp.
(10) L. Zanelli: On the optimal transport of semiclassical measures.
Applied Mathematics and Optimization, Volume 74 Issue 2, October 2016, pp 325--342
(9) T. Paul, L. Zanelli: On the dynamics of WKB wave functions whose phase are weak KAM solutions of H-J equation.
Journal of Fourier Analysis and Applications. Vol 20 Issue 6 pp 1291-1327 (2014)
(8) A. Parmeggiani, L. Zanelli: Wigner measures supported on weak KAM tori.
Journal D'Analyse Mathematique. July 2014, Vol. 123, Issue 1, pp 107-137.
(7) L. Zanelli: Mather measures in semiclassical Analysis.
Proceedings of the 14 th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 24 - 29 june 2012. AIMS on Applied Mathematics Vol. 8.
(6) O. Bernardi, A. Parmeggiani, L. Zanelli. Mather measures associated with a class of Bloch wave functions.
Annales Henri Poincarè. Volume 13, Issue 8 (2012), Page 1807-1839.
(5) S. Graffi, L. Zanelli. The geometric approach to the Hamilton-Jacobi equation and global parametrices for the Schrödinger propagator.
Reviews in Mathematical Physics, vol 23, issue 9, 2011.
(4) S. Graffi, L. Zanelli. Global parametrices for the Schrödinger propagator and geometric approach to the Hamilton-Jacobi equation.
Rendiconti Lincei - Matematica e Applicazioni, vol. 22, issue 1, 2011.
(3) P. Guiotto, L. Zanelli. The Geometry of Generating Functions for a class of Hamiltonian flows in the non compact case.
Journal of Geometry and Physics, vol. 60, pp 1381-1401, 2010.
(2) O. Bernardi, F. Cardin, M. Guzzo, L. Zanelli. A PDE approach to finite time indicators in ergodic theory.
Journal of Nonlinear Mathematical Physics, vol. 16, issue 2, 2009.
(1) F. Cardin, P. Guiotto, L. Zanelli. Integral representations of the Schrödinger propagator.
Reports on Mathematical Physics, vol. 62, issue 1, 2008.

Teaching Activity

Analisi 1, master degree course, a.a. 2024/25, Department of Industrial Engineering, University of Padova.
Analisi 1, master degree course, a.a. 2023/24, Department of Industrial Engineering, University of Padova.
Fisica Matematica, master degree course, a.a. 2022/23, Department of Mathematics, University of Padova.
Analisi 1, master degree course, a.a. 2022/23, Department of Industrial Engineering, University of Padova.
PhD course, a.a. 2021/22, Mathematical methods of Quantum Mechanics, Department of Mathematics, University of Padova.

Program

Analisi 1, master degree course, a.a. 2020/21, Department of Industrial Engineering, University of Padova.
Meccanica Razionale, master degree course, a.a. 2020/21, Department of Industrial Engineering, University of Padova.
Analisi 1, master degree course, a.a. 2019/20, Department of Industrial Engineering, University of Padova.
Analisi 1, master degree course, a.a. 2018/19, Department of Industrial Engineering, University of Padova.
Meccanica Razionale, master degree course, a.a. 2018/19, Department of Industrial Engineering, University of Padova.
Meccanica Razionale, master degree course, a.a. 2017/18, Department of Industrial Engineering, University of Padova.
Meccanica Razionale, master degree course, a.a. 2016/17, Department of Industrial Engineering, University of Padova.
Fisica Matematica, master degree course, a.a. 2015/16, Department of Mathematics, University of Padova.
Meccanica Razionale, master degree course, a.a. 2015/16, Department of Industrial Engineering, University of Padova.
Analisi Matematica, summer course 2014 in Bressanone (I - week) organized by University of Padova.
Fisica Matematica, master degree course, a.a. 2010/11, Department of Mathematics, University of Bologna.
Matematica 1, master degree course, a.a. 2009/10, Department of Chemistry, University of Bologna.
Matematica 1, master degree course, a.a. 2007/08, Department of Biotechnology, University of Padova.
Istituzioni di Analisi Matematica 2, master degree course, a.a. 2006/07, Department of Statistics, University of Padova.
Matematica 1, master degree course, a.a. 2005/06, Department of Physics, University of Padova.
Fisica Matematica, master degree course, a.a. 2005/06, Department of Mathematics, University of Padova.

Professional Activity

01/02/2023 - present: Researcher RTDB in Mathematical Physics.
07/09/2022 - 21/09/2022: Visiting Professor position. Centre de Physique Theorique (CPT), UMR 7332, University of Toulon.
April 2022 -- July 2022 (4 months): Research contract, Department of Mathematics, University of Padova.
03/11/2021 - 10/11/2021: Visiting Professor position. Centre de Physique Theorique (CPT), UMR 7332, University of Toulon.
Oct 2018 - Sept 2021 : Researcher RTDA, Department of Mathematics, University of Padova.
May 2016 - July 2018 : Postdoctoral position, Department of Mathematics, University of Padova.
May 2015 - April 2016 : Postdoctoral position, Department of Industrial Engineering, University of Padova.
Oct 2013 - Dec 2014 : Postdoctoral position, Department of Mathematics, University of Padova.
May 2013 - Sept 2013 : Chercheur contractuel, Ecole Normale Superieure, Paris.
Nov 2012 - April 2013 : Postdoctoral position, Centre de Mathematiques Laurent Schwartz, Ecole Polytechnique, Palaiseau.
Oct 2012 - Nov 2012 : Chercheur contractuel, Ecole Normale Superieure, Paris.
Feb 2012 - July 2012 : Visiting position, Centre de Mathematiques Laurent Schwartz, Ecole Polytechnique, Palaiseau.
Oct 2008 - Sept 2012 : Postdoctoral position, Department of Mathematics, University of Bologna.
Feb 2008 - June 2008 : Postdoctoral position, Department of Mathematics, University of Padova.
2007: Postdoctoral position, Department of Mathematics, University of Padova

Organization of Conferences and Workshops

School-Workshop ''Recent advances in Hamiltonian dynamics and symplectic topology''

web page

63eme Colloque International de Theories Variationnelles (CITV)

web page

Workshop ''A Thermodynamics Day''

web page

Conferences and Seminars

Communication at the GNFM Meeting, Montecatini Terme, 03 - 05 October 2024.
Title: On the phase space Analysis of many body quantum dynamics.
Communication at the International Congress of Mathematical Physics, Strasbourg, 01 - 06 July 2024.
Title: On the phase space Analysis of many body quantum dynamics.
Communication at the Conference Singularities, Asymptotics and Limiting Models University of Bari, 26 - 30 July 2023.
Title: On the convergence to Hartree dynamics by Gaussian thermal estimates.
Seminar at Centre de Physique Theorique, Toulon - 14 September 2022. Seminaire Dynamique Quantique et Classique.
Title: On the convergence to Hartree dynamics by Gaussian thermal estimates.
Seminar at the Department of Mathematics, University of Modena, 16 december 2021. Ciclo di Seminari di Fisica Matematica.
Title: Mean field derivation of discrete nonlinear Schroedinger equations from the Bose-Hubbard model.
Seminar at Centre de Physique Theorique, Toulon - 09 november 2021. Seminaire Dynamique Quantique et Classique.
Title: Bose-Hubbard model and mean field asymptotics.
Seminar at the Department of Mathematics - University of Bologna, 20 october 2021.
Title: Phase space analysis of Wick operators on Bargmann space with applications to dNLS.
Communication at the International Conference Microlocal and Global Analysis, Interactions with Geometry University of Potsdam, February 15 - 19, 2021.
Title: Mean Field asymptotics for Wick operators on Bargmann space.
Communication at the International Conference Microlocal and Global Analysis, Interactions with Geometry, University of Potsdam, February 10-14, 2020.
Title: Semiclassical estimates for eigenfunctions of toroidal Pseudodifferential operators.
Communication at the Workshop Special Functions and Semi-Classical Approximation, 4 - 6 February 2020, CIRM Marseille.
Title: Isospectrality and symplectic homogenization for periodic Schroedinger operators.
Communication at the Workshop Asymptotic Analysis and Spectral Theory, University Paris-Sud, Orsay, september 30--october 4, 2019.
Title: Isospectrality and symplectic homogenization for Schroedinger operators
Communication at the XXVIII International Fall Workshop on Geometry and Physics, Institute for the Mathematical Sciences (ICMAT), Madrid, September 2 - 6, 2019.
Title: The Schroedinger spectral problem and weak KAM theory.
Communication at the 30th International Workshop on Operator Theory and its Applications (July 22-26, 2019 Instituto Superior Tecnico, Lisbon).
Title: Periodic coherent states decomposition and quantum dynamics on the flat torus.
Communication at the Workshop Assemblea Scientifica GNFM 2018, Montecatini Terme, 04 - 06 october 2018.
Title: Inverse spectral problem of periodic Schroedinger operators
Workshop Mathematical Challenges in Quantum Mechanics, University Roma Sapienza, February 19-24, 2018.
Title: An homogenization approach for the inverse spectral problem of periodic Schroedinger operators.
Communication at XVII Italian Meeting on Hyperbolic Equations, University of Pavia, 06 - 08 september 2017.
Title: Schroedinger dynamics and optimal transport problems.
Communication at the Workshop Assemblea Scientifica GNFM 2017, Montecatini Terme, 04 - 06 may 2017.
Title: Schroedinger spectra and the effective Hamiltonian of the weak KAM theory
Communication at the Workshop Assemblea Scientifica GNFM 2015, Montecatini Terme, 22 - 24 october 2015.
Title: Schroedinger dynamics and optimal transport of measures on the torus.
Communication at the Workshop: Problemi attuali in teoria dei sistemi dinamici, Department of Mathematics, Milano-Bicocca University, 22 - 23 may 2014.
Title: On the dynamics of WKB wave functions whose phase are weak KAM solutions of H-J equation.
Communication at Assemblea Scientifica GNFM 2014, Montecatini Terme, 15 - 17 may 2014.
Title: On the localization of the semiclassical Wave Front Set for Schroedinger eigenfunctions on the flat torus.
Seminar at the Institut Henri Poincaré, Paris, 16 november 2012.
Title: Some applications of the Aubry-Mather theory in semiclassical Analysis.
Seminar at Assemblea Scientifica GNFM 2012, Montecatini Terme, 4 - 6 october 2012.
Title: Wigner measures supported on weak KAM tori.
Communication at the Congress: 14 th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, University of Padova, 24 - 29 june 2012.
Title: Mather measures in semiclassical Analysis.
Seminar at the Department of Mathematics University of Padova, 13 december 2011.
Title: The weak KAM theory in semiclassical analysis.
Communication at the Congress: Mathematical Methods in Quantum Mechanics, Bressanone, 14 - 19 february 2011.
Title: Global Fourier Integral Operators and quantum dynamics.
Communication at the Congress: "Classical and weak KAM theorem: the Aubry-Mather sets, a break-trough in the study of dynamical systems" Montegrotto 14-19 february 2010.
Title: The Geometry of Generating Functions for a class of Hamiltonian flows in the non compact case.
Seminar at the Department of Mathematics University of Bologna, 23 november 2009.
Title: Operatori Integrali di Fourier globali e Propagatore di Schrödinger.
Seminar at the Department of Mathematics University of Bologna, 29 september 2008.
Title: Funzioni generatrici quadratiche all'infinito di flussi Hamiltoniani.
Communication at the Congress: Assemblea Scientifica GNFM 2007, Montecatini Terme, 11 - 13 october 2007.
Title: Rappresentazioni Globali del Propagatore di Schrödinger.
Communication at the Congress: Mathematical Modeling, Mechanics and Materials, Bressanone, 19 march 2007.
Title: On the Evolution Operator of the Fokker-Planck equation.
Communication at the Congress: Mathematical Methods in Quantum Mechanics, Bressanone, 26 february - 3 march 2007.
Title: The Schrödinger Propagator.
Communication at the Congress: Problemi Matematici in Meccanica Quantistica, Università di Modena, 05 - 07 october 2006.
Title: Integral representations of the Schrödinger Propagator.
Seminar at the Department of Physics University Roma 3, 24 june 2005.
Title: Rappresentazione Integrale Finita Esatta del Propagatore di Schrödinger.
Seminar at the Summer School of Mathematical Physics, Ravello, september 2005.
Title: Forze di Contatto e di Bulk.
Seminar at the Summer School of Mathematical Physics, Ravello, september 2004.
Title: A lower bound for Von Karman Energy Functional.
Communication at the Congress: Mathematical Problems in Quantum Mechanics, Università di Modena, 19 - 21 december 2003.
Title: Rappresentazione Integrale Finita Esatta del Propagatore di Schrödinger e di Fokker Planck.