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

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;
F. Colombo, I. Sabadini, D. C. Struppa, A. Yger, "Supershift properties for nonanalytic signals", Nanophotonics, 2025;
F. Colombo, I. Sabadini, D. C. Struppa, A. Yger, "Analyticity and supershift with regular sampling", Complex Anal. Synerg. 11, n. 6, 2025;
L. Abatangelo, V. Felli, "Bifurcation of double eigenvalues for Aharonov-Bohm operators with a moving pole", Nonlinear Anal. 256, 113798, 2025;
F. Colombo, P. Schlosser, "Interpolation between domains of powers of operators in quaternionic Banach spaces", Proc. Amer. Math. Soc. 153, 625–639, 2025;
V. Felli, B. Noris, G. Siclari, "On Aharonov-Bohm operators with multiple colliding poles of any circulation", Nonlinear Anal. 258, 113813, 2025;
W. Borrelli, U. Morellini, "Global well-posedness in a Hartree-Fock model for graphene", J. Phys A 58, 215202, 2025;
A. Dhahri, F. Fagnola, D. Poletti, H.J. Yoo, "Environment induced entanglement in Gaussian open quantum systems", Quantum Inf. Process. 24, 4, 2025;
D. Fermi, "The Aharonov-Bohm Hamiltonian: self-adjointness, spectral and scattering properties", in D. Alpay, I. Sabadini, F. Colombo (Eds.), Operator Theory, Springer, Basel (2025);
M. Fantechi, M. Merkli, “Quantum systems coupled to environments via mean field interactions”, Ann. Phys. 476, 169981, 2025;
S. Breteaux, M. Correggi, M. Falconi, J. Faupin, "Quantum Point Charges Interacting with Quasi-classical Electromagnetic Fields", Pure Appl. Anal. 7, 219–241, 2025;
F. Fagnola, D. Poletti, E. Sasso, V. Umanità, "The Spectral Gap of a Gaussian Quantum Markovian Generator", J. Funct. Anal. 289, 111119, 2025 ;