Growth of Sobolev norms for linear Schrödinger operators
Annales Henri Lebesgue, Volume 4 (2021), pp. 1595-1618.

KeywordsLinear Schrödinger equation, time-dependent potential, growth of Sobolev norms, reducibility.

Abstract

We give an example of a linear, time-dependent, Schrödinger operator with optimal growth of Sobolev norms. The construction is explicit, and relies on a comprehensive study of the linear Lowest Landau Level equation with a time-dependent potential.

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