Growth of Sobolev norms for abstract linear Schr\"odinger Equations

Dario Bambusi, Benoît Grébert, Alberto Maspero, Didier Robert

Type: Preprint

Publication Date: 2017-06-29

Citations: 25

Locations

arXiv (Cornell University) - View

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+	Reducibility of quantum harmonic oscillator on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:math> with differential and quasi-periodic in time potential	2019	Zhenguo Liang Zhiguo Wang
+ PDF Chat	Growth of Sobolev Norms in 1-d Quantum Harmonic Oscillator with Polynomial Time Quasi-periodic Perturbation	2022	Jiawen Luo Zhenguo Liang Zhiyan Zhao
+	Linear Schr\"odinger equation with an almost periodic potential	2019	Riccardo Montalto Michela Procesi
+	Long time stability of small finite gap solutions of the cubic nonlinear Schrödinger equation on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">T</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>	2018	Alberto Maspero Michela Procesi
+	Reducibility of 1D quantum harmonic oscillator with decaying conditions on the derivative of perturbation potentials	2022	Zhenguo Liang Zhiqiang Wang
+	Reducibility of 1-d quantum harmonic oscillator equation with unbounded oscillation perturbations	2020	Zonghui Liang Jiawen Luo
+	1-d Quantum Harmonic Oscillator with Time Quasi-periodic Quadratic Perturbation: Reducibility and Growth of Sobolev Norms	2020	Zhenguo Liang Zhiyan Zhao Qi Zhou
+ PDF Chat	Tame majorant analyticity for the Birkhoff map of the defocusing nonlinear Schrödinger equation on the circle	2018	Alberto Maspero
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Works Cited by This (14)

Action	Title	Year	Authors
+	Scattering Theory of Classical and Quantum N-Particle Systems	1997	Jan Dereziński Christian Gérard
+	The analysis of linear partial differential operators	1990	Lars Hörmander
+ PDF Chat	Lectures on the geometry of numbers	1990	K. Chandrasekharan
+	Expectation Values of Observables in Time-Dependent Quantum Mechanics	1998	Jean-Marie Barbaroux Alain Joye
+	Asymptotique des niveaux d’énergie pour des hamiltoniens a un degre de liberté	1982	Bernard Helffer D. Robert
+ PDF Chat	On the Energy Growth of Some Periodically Driven Quantum Systems with Shrinking Gaps in the Spectrum	2007	Pierre Duclos Ondra Lev P. Šťovı́ček
+	On reducibility of Quantum Harmonic Oscillator on $\mathbb{R}^d$ with quasiperiodic in time potential	2016	Éric Paturel Benoît Grébert
+	Floquet operators with singular spectrum. II	1989	James S. Howland
+	Adiabatic theory : stability of systems with increasing gaps	1997	G. Nenciu
+	On the growth of Sobolev norms for a class of linear Schr\"odinger equations on the torus with superlinear dispersion	2017	Riccardo Montalto