Growth of Sobolev norms and controllability of Schrödinger equation

Abstract

In this paper we obtain a stabilization result for the Schrödinger equation under generic assumptions on the potential. Then we consider the Schrödinger equation with a potential which has a random time-dependent amplitude. We show that if the distribution of the amplitude is sufficiently non-degenerate, then any trajectory of system is almost surely non-bounded in Sobolev spaces.

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