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

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 ;
F. Colombo, E. Pozzi, I. Sabadini, B.D. Wick, "Aharonov-Bohm effect and superoscillations", J. Math. Phys. 66, 073501, 2025;
F. Colombo, I. Sabadini, D.C. Struppa, A. Yger, "Analyticity, superoscillations and supershifts in several variables", Collect. Math. online, 2025;
D. Pierotti, G. Verzini, J. Yu, "Normalized solutions for Sobolev critical Schrödinger equations on bounded domains", SIAM J. Math. Anal. 57, 262–285, 2025;
P. Hege, M. Moscolari, S. Teufel, "Computing the spectrum and pseudospectrum of infinite-volume operators from local patches", Math. Comp. online, 2025;
M. Correggi, E.L. Giacomelli, A. Kachmar, "On the Ginzburg-Landau Energy of Corners", Nonlinearity 38, 045025, 2025;
Á. Capel, M. Moscolari, S. Teufel, T. Wessel, "From decay of correlations to locality and stability of the Gibbs state", Commun. Math. Phys. 406, 43, 2025;
M. Correggi, D. Fermi, “Schrödinger operators with multiple Aharonov-Bohm fluxes”, Ann. H. Poincaré 26, 123–163, 2025;
V. Felli, B. Noris, R. Ognibene, G. Siclari, “Quantitative spectral stability for Aharonov-Bohm operators with many coalescing poles”, J. Eur. Math. Soc. online, 2025;
M. Falconi, J. Lampart, N. Leopold, D. Mitrouskas, “Renormalized Bogoliubov Theory for the Nelson Model”, Ann. Inst. H. Poincaré C - Anal. Non Linéaire online, 2025;