Here is a list of my papers and preprints:
Weak turbulence
in Schrödinger type equations
Lower bounds results:
"Growth of Sobolev norms for completely resonant quantum harmonic oscillators on R^2", by Beatrice Langella, Alberto Maspero, and Maria Teresa Rotolo. J. Differ. Equ., 433: 113221, 2025
Upper bounds results:
"Growth of Sobolev norms in quasi integrable quantum systems", by Dario Bambusi and Beatrice Langella. Ann. Scient. Éc. Norm. Sup. 4e série, vol. 58, p. 997 -- 1035, 2025
"Almost global existence for some Hamiltonian PDEs on manifolds with globally integrable geodesic flow", by Dario Bambusi, Roberto Feola, Beatrice Langella, and Francesco Monzani. Nonlinearity, 38(5):055013, 2025
"Globally integrable quantum systems and their perturbations", by Dario Bambusi and Beatrice Langella. Singularities, Asymptotics and Limiting Models. INdAM–Springer Series, Springer International Publishing, pp. 64‐103, 2024
"Growth of Sobolev norms for unbounded perturbations of the Schrödinger equation on flat tori", by Dario Bambusi, Beatrice Langella, and Riccardo Montalto. J. Differ. Equ., 318:344–358, 2022
Long time stability à la Nekhoroshev
in classical and quantum dynamical systems
"Polynomial prethermal lifetimes in non smoothly driven quantum systems", by Matteo Gallone and Beatrice Langella. Preprint on arXiv:2510.04137, 2025
"Prethermalization and conservation laws in quasi‐periodically driven quantum systems", by Matteo Gallone and Beatrice Langella. Journal of Statistical Physics, 191:100, 2024
"A C^\infty Nekhoroshev theorem", by Dario Bambusi and Beatrice Langella. Mathematics in Engineering, 3(2):117, 2021
Existence of time periodic solutions
in a completely resonant wave equation
"Time periodic solutions of completely resonant Klein‐Gordon equations on S^3", by Massimiliano Berti, Beatrice Langella, and Diego Silimbani. Ann. Inst. H. Poincaré C Anal. Non Linéaire. Ann. Inst. H. Poincaré C Anal. Non Linéaire (Online first) DOI 10.4171/AIHPC/125
Infinite dimensional reducibility results
"Reducibility of non‐resonant transport equation on T^d with unbounded perturbations", by Dario Bambusi, Beatrice Langella, and Riccardo Montalto. Ann. Henri Poincaré, 20(6):1893– 1929, 2019
"Reducibility and nonlinear stability for a quasi‐periodically forced NLS", by Emanuele Haus, Beatrice Langella, Alberto Maspero, and Michela Procesi. Pure and Applied Mathematics Quarterly, 20(3):1313–1370, 2024
Spectral (in)stability in Schrödinger type operators
"On the stable eigenvalues of perturbed anharmonic oscillators in dimension two" , by Dario Bambusi, Beatrice Langella, and Marc Rouveyrol. Comm. Math. Phys., 390(1):309–348, 2022
"Spectral asymptotics of all the eigenvalues of Schrödinger operators on flat tori" by Dario Bambusi, Beatrice Langella and Riccardo Montalto. Nonlinear Analysis, 216:112679, 2022
"On the spectrum of the Schrödinger operator on T^d : a normal form approach", by Dario Bambusi, Beatrice Langella, and Riccardo Montalto. Communications in Partial Differential Equations, 45:1–18, 2020
"Absolute continuity of the spectrum of coupled identical systems on 1D lattices" , by Beatrice Langella and Dario Bambusi. Math. Phys. Anal. Geom., 21(4):Paper No. 31, 5, 2018
Title of my PhD thesis:
"Normal form and KAM methods for higher dimensional linear PDEs”