Exponential Lower Bounds for Quasimodes of Semiclassical Schrödinger Operators

Details Exponential Lower Bounds for Quasimodes of Semiclassical Schrödinger Operators Exponential Lower Bounds for Quasimodes of Semiclassical Schrödinger Operators

2008-08-22

arxiv.org/abs/0808.3035v3

Math. Res. Lett. 16 (2009), no. 4, 721--734

Mathematics

Analysis of PDEs

14 pages, no figures; cosmetic changes. Final version, to appear in Mathematical Research Letters

Scientific paper

We prove quantitative unique continuation results for the semiclassical
Schrodinger operator on smooth, compact domains. These take the form of
exponentially decreasing (in h) local L^{2} lower bounds for exponentially
precise quasimodes. We also show that these lower bounds are sharp in h, and
that, moreover, the hypothesized quasimode accuracy is also sharp.

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