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

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;
J. Lampart, M. Moscolari, S. Teufel, T. Wessel, "Equality of magnetization and edge current for interacting lattice fermions at positive temperature", Math. Phys. Anal. Geom. 27, n. 24, 2024;
F. Colombo, I. Sabadini, D. C. Struppa, A. Yger, "Analyticity and supershift with irregular sampling", Complex Anal. Synerg. 10, n. 10, 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;
W. Borrelli, M. Correggi, D. Fermi, "Pauli Hamiltonians with an Aharonov-Bohm Flux", J. Spectr. Theor. 14, 1147–1193, 2024;
M. Correggi, D. Fermi, "Deficiency indices for singular magnetic Schrödinger operators", Milan J. Math. 92, 25–39, 2024;

2023

D. Fermi, D. Ferretti, A. Teta, "Rigorous derivation of the Efimov effect in a simple model", Lett. Math. Phys. 113, 113, 2023.
D. Alpay, F. Colombo, K. Diki, I. Sabadini, D.C. Struppa, "Superoscillations and Fock spaces", J. Math. Phys. 64, 093505, 2023;
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;
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;