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
- F. Colombo, E. Pozzi, I. Sabadini, B.D. Wick, “Evolution of Superoscillations for Spinning Particles”, Proc. Am. Math. Soc. Series B 10, 129–143, 2023;
- M. Falconi, J. Lampart, N. Leopold, D. Mitrouskas, “Renormalized Bogoliubov Theory for the Nelson Model”, preprint arXiv:2305.06722 [math-ph];
- V. Felli, B. Noris, R. Ognibene, G. Siclari, “Quantitative spectral stability for Aharonov-Bohm operators with many coalescing poles”, preprint arXiv:2306.05008 [math.AP];
- M. Correggi, D. Fermi, “Schrödinger operators with multiple Aharonov-Bohm fluxes”, Ann. H. Poincaré published online, 2024;
- J. Behrndt, F. Colombo, P. Schlosser, D.C. Struppa, "Integral representation of superoscillations via Borel measures and their convergence", Trans. Am. Math. Soc. 376, 6315–6340, 2023;
- D. Alpay, F. Colombo, K. Diki, I. Sabadini, D.C. Struppa, "Superoscillations and Fock spaces", J. Math. Phys. 64, 093505, 2023;
- Á. Capel, M. Moscolari, S. Teufel, T. Wessel, "From decay of correlations to locality and stability of the Gibbs state", preprint arXiv:2310.09182 [math-ph];
- D. Fermi, D. Ferretti, A. Teta, "Rigorous derivation of the Efimov effect in a simple model", Lett. Math. Phys. 113, 113, 2023;
- M. Correggi, D. Fermi, "Deficiency indices for singular magnetic Schrödinger operators", Milan J. Math. 92, 25–39, 2024;
- W. Borrelli, M. Correggi, D. Fermi, "Pauli Hamiltonians with an Aharonov-Bohm Flux", J. Spectr. Theor. 14, 1147–1193, 2024;
- L. Abatangelo, R. Ognibene, "Sharp behavior of Dirichlet–Laplacian eigenvalues for a class of singularly perturbed problems", SIAM J. Math. Anal. 56, 474–500, 2024;
- F. Colombo, I. Sabadini, D. C. Struppa, A. Yger, "Analyticity and supershift with regular sampling", Complex Anal. Synerg. 10, n. 10, 2024;
- M. Correggi, E.L. Giacomelli, A. Kachmar, "On the Ginzburg-Landau Energy of Corners", preprint arXiv:2403.11286 [math-ph];
- P. Hege, M. Moscolari, S. Teufel, "Computing the spectrum and pseudospectrum of infinite-volume operators from local patches", preprint arXiv:2403.19055 [math.SP];
- J. Lampart, M. Moscolari, S. Teufel, T. Wessel, "Equality of magnetization and edge current for interacting lattice fermions at positive temperature", preprint arXiv:2403.17566 [math-ph];
- B. Pellacci, A. Pistoia, G. Vaira, G. Verzini, "Partially concentrating standing waves for weakly coupled Schrödinger systems", Math. Ann. 390, 3691–3722, 2024;
- D. Pierotti, G. Verzini, J. Yu, "Normalized solutions for Sobolev critical Schrödinger equations on bounded domains", preprint arXiv:2404.04594 [math.AP];
- F. Colombo, I. Sabadini, D.C. Struppa, A. Yger, "Analyticity, superoscillations and supershifts in several variables", preprint arXiv:2403.06169 [math.CV];
- F. Colombo, E. Pozzi, I. Sabadini, B.D. Wick, "Aharonov-Bohm effect and superoscillations", preprint arXiv:2404.17828 [math-ph];
- F. Fagnola, D. Poletti, "A Note on Invariant States of Gaussian Quantum Markov Semigroups", Infin. Dimens. Anal. Quantum Probab. Relat. Top. online, 2024;
- F. Fagnola, D. Poletti, E. Sasso, V. Umanità, "The Spectral Gap of a Gaussian Quantum Markovian Generator", preprint arXiv:2405.04947 [math.FA];
- F. Girotti, A. Godley, M. Guta, "Optimal estimation of pure states with displaced-null measurements", J. Phys. A. 57, 245304, 2024;
- D. Alpay, A. De Martino, K. Diki, D.C. Struppa, "Short-time Fourier transform and superoscillations", Appl. Comput. Harmon. Anal. 73, 101689, 2024;
- S. Breteaux, M. Correggi, M. Falconi, J. Faupin, "Quantum Point Charges Interacting with Quasi-classical Electromagnetic Fields", preprint arXiv:2407.18600 [math-ph];
- M. Correggi, M.. Falconi, M. Fantechi, M. Merkli, "Quasi-classical Limit of a Spin Coupled to a Reservoir", preprint arXiv:2408.02515 [quant-ph];
- M. Fantechi, M. Merkli, “Quantum systems coupled to environments via mean field interactions”, preprint arXiv:2409.15850 [quant-ph];
- L. Accardi, A. Dhahri, "Quasi-invariant states", Infin. Dimens. Anal. Quantum Probab. Relat. Top. online, 2024.