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

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. Jaksic, C.-A. Pillet, A. Szczepanek, "Entropy Maximization and Weak Gibbsianity of Quasi-Free Fermionic States", arXiv:2603.14020 [math-ph], 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. Jaksic, 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. Jaksic, A. Panati, C.-A. Pillet, "Entropic Fluctuation Theorems for the Spin–Fermion Model", J. Math. Phys. 67, 022101, 2026;
N. Cuneo, V. Jaksic, 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.
C. Caraci, A. Olgiati, D. Saint Aubin, B. Schlein, "Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime", Commun. Math. Phys. 406, 153, 2025;
T. Benoist, N. Cuneo, V. Jaksic, C.-A. Pillet, "On entropy production of repeated quantum measurements III. Quantum detailed balance", arXiv:2511.00910 [quant-ph], 2025;
Z. Ammari, M. Correggi, M. Falconi, R. Gautier, "Semiclassical limit of entropies and free energies", arXiv:2510.15777 [math-ph], 2025;
T. Benoist, L. Bruneau, V. Jaksic, A. Panati, C.-A. Pillet, "Entropic Fluctuations in Statistical Mechanics II. Quantum Dynamical Systems", Commun. Math. Phys. 406, 201, 2025;
M. Falconi, B. Hinrichs, J.V. Martín, "Non-trivial Renormalization of Spin-Boson Models with Supercritical Form Factors", arXiv:2508.00805 [math-ph], 2025;
M. Falconi, B. Hinrichs, "Ultraviolet Renormalization of the van Hove-Miyatake Model: an Algebraic and Hamiltonian Approach", arXiv:2505.19977 [math-ph], 2025;
A. Dhahri, E. Ricard, "Quasi-invariant States with Uniformly Bounded Cocycles", Commun. Math. Phys. 406, 133, 2025;
G. Verzini, J. Yu, “Normalized solutions for the nonlinear Schrödinger equation with potential: the purely Sobolev critical case”, arXiv:2505.05357 [math.AP], 2025;
H.D. Cornean, M. Moscolari, "On the magnetic perturbation theory for Chern insulators", in: D. Alpay, I. Sabadini, F. Colombo (eds), Operator Theory, Springer, Basel, 2025;