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

  • 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. published online, 2024;
  • W. Borrelli, M. Correggi, D. Fermi, "Pauli Hamiltonians with an Aharonov-Bohm Flux", preprint arXiv:2312.11971 [math-ph];
  • 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", preprint arXiv:2310.11528 [math.CV];
  • 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., 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 and supershift with irregular sampling", Complex Anal. Synerg. 10, n. 10, 2024;
  • 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].