On a Heavy Quantum Particle

D. Bambusi, “Reducibility of 1D Schrödinger Equation with Time Quasiperiodic Unbounded Perturbations. I.,” Trans. Amer. Math. Soc. 370 (3), 1823–1865 (2018).

D. Bambusi, B. Grebert, A. Maspero, and D. Robert, “Growth of Sobolev Norms for Abstract Linear Schrödinger Equations,” arXiv:1706.09708 [math.AP].

D. Bambusi, B. Grebert, A. Maspero, and D. Robert, “Reducibility of the Quantum Harmonic Oscillator in d–Dimensions with Polynomial Time Dependent Perturbation,” Anal. PDE, 11 (3), 775–799 (2018).

J. Bourgain, “Growth of Sobolev Norms in Linear Schrödinger Equations with Quasi–Periodic Potential,” Comm. Math. Phys. 204 (1), 207–247 (1999).

J. Bourgain, “On Growth of Sobolev Norms in Linear Schrödinger Equations with Smooth Time–Dependent Potentials,” J. Anal. Math. 77 (1), 315–348 (1999).

J. Bourgain, “Estimates on Green’s Functions, Localization and the Quantum Kicked Rotor Model,” Ann. of Math. 156 (249), (2002).

M. Combescure, “The Quantum Stability Problem for Time–Periodic Perturbations of the Harmonic Oscillator,” Ann. Inst. H. Poincaré Phys. Théor. 47 (1), 63–83 (1987).

L. Chierchia and J. You, “KAM–Tiri for 1D Nonlinear Wave Equations with Periodic Boundary Conditions,” Comm. Math. Phys. 211 (2), 497–525 (2000).

D. Fang, Z. Han, and W.–M. Wang, “Bounded Sobolev Norms for Klein–Gordon Equations under Non–Resonant Perturbation,” J. Math. Phys. 55 (12), (2014).

B. Grébert and E. Paturel, “KAM for the Klein–Gordon Equation on Sd,” ArXiv e–prints, arXiv: 1601.00610 (2016).

B. Grébert and E. Paturel, “On Reducibility of Quantum Harmonic Oscillator on ℝd with Quasiperiodic in Time Potential,” ArXiv e–prints, arXiv: 1603.07455 (2016).

B. Grébert and L. Thomann, “KAM for the Quantum Harmonic Oscillator,” Comm. Math. Phys. 307 (2), 383–427 (2011).

F. M. Izrailev and D. L. Shepelyansky, “Quantum Resonans for a Rotator in Nonlinear Periodic Field,” Dokl. Phys. 43 (3), (1980).

S. Kuksin, “Growth and Oscillations of Solutions of Nonlinear Schrödinger Equation,” Comm. Math. Phys. 178 (2), 265–280 (1996).

S. B. Kuksin, “Spectral Properties of Solutions for Nonlinear PDEs in the Turbulent Regime,” GAFA Geom. Funct. Anal. 9, 141–184 (1999).

S. Kuksin and A. Neishtadt, “On Quantum Averaging, Quantum KAM, and Quantum Diffusion,” Russ. Math. Surveys 68 (2), 335–348 (2013).

A. Maspero, “Lower Bounds on the Growth of Sobolev Norms in Some Linear Time Dependent Schrödinger Equations,” arXiv:1801.06813v2 [math.AP].

R. Montalto, “A Reducibility Result for a Class of Linear Wave Equations on Td,” IMRN, rnx167, DOI: 10.1093/imrn/rnx167/ (2017).

M. V. Safonov, “The Abstract Cauchy–Kovalevskaya Theorem in a Weighted Banach Space,” Comm. Pure Appl. Math. 48, 629–643 (1995).

M. E. Taylor, Partial Differential Equations (III Springer, 2012).

W.–M. Wang, “Pure Point Spectrum of the Floquet Hamiltonian for the Quantum Harmonic Oscillator under Time Quasi–Periodic Perturbations,” Comm. Math. Phys. 277 (2), 459–496 (2008).