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Level Repulsion for Arithmetic Toral Point Scatterers in Dimension 3 by Pär Kurlberg is a Physics and Astronomy article available to read on EtoBox.
What is Level Repulsion for Arithmetic Toral Point Scatterers in Dimension 3 about?
## Abstract We show that arithmetic toral point scatterers in dimension three (“Šeba billiards on $${\mathbb R}^3/{\mathbb Z}^3$$ R 3 / Z 3 ”) exhibit strong level repulsion between the set of “new” eigenvalues. More precisely, let $$\Lambda := \{ \lambda \_{1}< \lambda \_{2} < \ldots \}$$ Λ : = { λ 1 < λ 2 0$$ γ > 0 , $$\begin{aligned} \frac{|\{ i \le N : \lambda \_{i+1}-\lambda \_{i} \le \epsilon \}|}{N} = O\_{\gamma }(\epsilon ^{4-\gamma }) \end{aligned}$$ | { i ≤ N : λ i + 1 - λ i ≤ ε } | N = O γ ( ε 4 - γ ) as $$N \rightarrow \infty $$ N → ∞ (and $$\epsilon >0$$ ε > 0 small.) To the best of our knowledge, this is the first mathematically rigorous demonstration of a level repulsion phenomena for the quantization of a deterministic system.
Who reads Level Repulsion for Arithmetic Toral Point Scatterers in Dimension 3?
It is typically read by researchers, students, and practitioners in Physics and Astronomy.
- Author
- Pär Kurlberg
- Publisher
- Springer Science and Business Media LLC
- Published
- 2022
- Language
- EN
- Field
- Physics and Astronomy (Physical Sciences)