mathematical features of quantum mechanics
scientific coordinator: Michele Correggi
"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, 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;
2024
- F. Colombo, F. Mantovani, P. Schlosser, "Spectral properties of the gradient operator with nonconstant coefficients", Anal. Math. Phys. 14, 108, 2024.
- S. Pinton, P. Schlosser, "Characterization of continuous homomorphisms on entire slice monogenic functions", Proc. R. Soc. Edinb. A: Math. 67, 892–920, 2024;
- F. Colombo, F. Mantovani, S. Pinton, P. Schlosser, "Superoscillations in the hypercomplex setting", J. Geom. Anal. 35, 164, 2024;
- M. Falconi, L. Fratini, "Abstract semiclassical analysis of the van Hove model", preprint arXiv:2407.20603 [math-ph], 2024;
- L. Abatangelo, C. Léna, P. Musolino, "Asymptotic behavior of generalized capacities with applications to eigenvalue perturbations: The higher dimensional case", Nonlinear Anal. 238, 113391, 2024;
- L. Accardi, A. Dhahri, "Quasi-invariant states", Infin. Dimens. Anal. Quantum Probab. Relat. Top. online, 2024;
- M. Correggi, M.. Falconi, M. Fantechi, M. Merkli, "Quasi-classical Limit of a Spin Coupled to a Reservoir", Quantum 8, 1561, 2024;
- D. Alpay, A. De Martino, K. Diki, D.C. Struppa, "Short-time Fourier transform and superoscillations", Appl. Comput. Harmon. Anal. 73, 101689, 2024;
- F. Girotti, A. Godley, M. Guta, "Optimal estimation of pure states with displaced-null measurements", J. Phys. A. 57, 245304, 2024;
- F. Fagnola, D. Poletti, "A Note on Invariant States of Gaussian Quantum Markov Semigroups", Infin. Dimens. Anal. Quantum Probab. Relat. Top. 27, 2440004, 2024;
- B. Pellacci, A. Pistoia, G. Vaira, G. Verzini, "Partially concentrating standing waves for weakly coupled Schrödinger systems", Math. Ann. 390, 3691–3722, 2024;