mathematical features of quantum mechanics

scientific coordinator: Michele Correggi

The image above has been generated using OpenAI Dall-e 2 as an
"abstract visual conceptualization of quantum mechanics"

The modelization of several quantum phenomena, as decoherence, entanglement or dissipation, as well as the emergence of effective (nonlinear) models in suitable regimes and the relation between the quantum and classical worlds, as in the measurement process, are addressed by a combination of analytic, geometric and probabilistic methods.

Publications

2026

V. Jakšić, C.-A. Pillet, A. Szczepanek, "Approach to Equilibrium in Translation-Invariant Quantum Systems: Structural Results II", preprint arXiv:2610.21475 [math-ph], 2026;
V. Jakšić, C.-A. Pillet, A. Szczepanek, "Dynamical Conservation Laws in Quantum Spin Systems", preprint arXiv:2610.21489 [math-ph], 2026;
Á. Capel, M. Castrillón-López, S. Iblisdir, A. Lucia, P. Páez-Velasco, D. Pérez-García, "Rapid mixing for Gibbs measures in Riemannian manifolds", preprint arXiv:2606.13453 [math-ph], 2026;
S. Stengele, Á. Capel, L. Gao, A. Lucia, D. Pérez-García, A. Pérez-Hernández, C. Rouzé, S. Warzel, "Modified logarithmic Sobolev inequalities for Abelian quantum double models", preprint arXiv:2605.19640 [quant-ph], 2026;
S. Stengele, Á. Capel, L. Gao, A. Lucia, D. Pérez-García, A. Pérez-Hernández, C. Rouzé, S. Warzel, "Modified logarithmic Sobolev inequalities for CSS codes", Commun. Math. Phys. 407, 195, 2026;
G. Basti, M. Brooks, S. Cenatiempo, A. Olgiati, B. Schlein, "The Lee-Huang-Yang energy for a dilute gas of hard spheres: an upper bound", preprint arXiv:2603.13084 [math-ph], 2026.
G. Basti, M. Brooks, S. Cenatiempo, A. Olgiati, B. Schlein, "Lee-Huang-Yang Energy for Dilute Bose Gases: an Upper Bound for General Potentials", preprint arXiv:2609.25314 [math-ph], 2026.
M. Falconi, B. Hinrichs, J.V. Martín, "Wave Function Renormalization for Particle-Field Interactions", preprint arXiv:2603.07045 [math-ph], 2026;
M. Falconi, C. Fermanian Kammerer, R. Gautier, "Measuring a Quantum System Thanks to the Correspondence Principle", preprint arXiv:2606.21211 [math-ph], 2026;
F. Colombo, E. Pozzi, I. Sabadini, B.D. Wick, "Some infinite order differential operators associated with superoscillations in several variables", Complex Anal. Oper. Theory 20, 69, 2026;
F. Colombo, F. Mantovani, P. Schlosser, "Quadratic estimates for the H∞-functional calculus of bisectorial Clifford operators", J. Geom. Anal. 36, 46, 2026;
I. Beschastnyi, F. Colombo, S. Andrade Lucas, I. Sabadini, "The S-resolvent estimates for the Dirac operator on hyperbolic and spherical spaces", J. Geom. Anal. 36, 177, 2026;
V. Jakšić, C.-A. Pillet, A. Szczepanek, "Entropy Maximization and Weak Gibbsianity of Quasi-Free Fermionic States", Lett. Math. Phys. 116, 103, 2026;
W. Borrelli, P. Carimati, D. Fermi, "On two-dimensional Dirac operators with critical delta-shell interactions", J. Math. Anal. Appl. 564, 130880, 2026;
J. Derezinski, V. Jakšić, C.-A. Pillet, "Miniatures on Open Quantum Systems", arXiv:2601.20373 [math-ph], 2026;
D. Cafiero, M. Correggi, D. Fermi, "Homogenization of point interactions", arXiv:2603.21400 [math-ph], 2026;
T. Benoist, L. Bruneau, V. Jakšić, A. Panati, C.-A. Pillet, "Entropic Fluctuation Theorems for the Spin–Fermion Model", J. Math. Phys. 67, 022101, 2026;
N. Cuneo, V. Jakšić, C.-A. Pillet, A. Shirikyan, What is a Fluctuation Theorem?, SpringerBriefs Math. Phys. 54, Springer, 2026;
M. Correggi, A. Kachmar, "Existence of Bulk Vortices in Superconductors with Strong Magnetic Fields", Ann. Inst. H. Poincaré C - Anal. Non Linéaire online first, 2026;

2025

M. Falconi, A. Olgiati, N. Rougerie, "Convergence of states for polaron models in the classical limit", Ann H. Lebesgue 8, 661-697, 2025.