Dispersion for Schr\"odinger Operators with One-gap Periodic Potentials on R^1

We prove $t^{- \frac 14}-$decay for the solutions of the 1-dim Schrodinger equation with a one-gap periodic potential as $t \to +\infty $. Generically, one has $t^{- \frac 13}$-decay and this decay is optimal. Our approach is to analyze the stationary phase in the Schr\"odinger evolution as an...

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Bibliographic Details
Main Author Cai, Kaihua
Format Journal Article
LanguageEnglish
Published 31.10.2004
Subjects
Mathematics - Mathematical Physics
Physics - Mathematical Physics
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Summary:We prove $t^{- \frac 14}-$decay for the solutions of the 1-dim Schrodinger equation with a one-gap periodic potential as $t \to +\infty $. Generically, one has $t^{- \frac 13}$-decay and this decay is optimal. Our approach is to analyze the stationary phase in the Schr\"odinger evolution as an integral operator.
DOI:10.48550/arxiv.math-ph/0411002