arXiv Open Access 2019

Bethe-Sommerfeld conjecture in semiclassical settings

Victor Ivrii
Lihat Sumber

Abstrak

Under certain assumptions (including $d\ge 2)$ we prove that the spectrum of a scalar operator in $\mathscr{L}^2(\mathbb{R}^d)$ \begin{equation*} A_\varepsilon (x,hD)= A^0(hD) + \varepsilon B(x,hD), \end{equation*} covers interval $(τ-ε,τ+ε)$, where $A^0$ is an elliptic operator and $B(x,hD)$ is a periodic perturbation, $\varepsilon=O(h^\varkappa)$, $\varkappa>0$. Further, we consider generalizations.

Topik & Kata Kunci

Penulis (1)

V

Victor Ivrii

Format Sitasi

Ivrii, V. (2019). Bethe-Sommerfeld conjecture in semiclassical settings. https://arxiv.org/abs/1902.00335

Akses Cepat

Lihat di Sumber
Informasi Jurnal
Tahun Terbit
2019
Bahasa
en
Sumber Database
arXiv
Akses
Open Access ✓