Gap Control by Singular Schrödinger Operators in a Periodically Structured Metamaterial
DOI:
https://doi.org/10.15407/mag14.03.270Ключові слова:
перiодичний оператор Шредiнгера, $\delta'$-взаємодiя, спектральна лакуна, асимптотика власних значеньАнотація
Ми розглядаємо сiм'ю $\{\mathcal{H}^\varepsilon\}_{\varepsilon >0}$ of $\varepsilon\mathbb{Z}^n$-перiодичних операторiв Шредiнгера з $\delta'$-взаємодiями, якi локалiзованi на сiм'ї замкнених компактних поверхонь; мiнiмальна комiрка перiодичностi мiстить $m\in\mathbb{N}$ таких поверхонь. Показано, що при $\varepsilon\to 0$ i при певному порядку сили взаємодiї $\mathcal{H}^\varepsilon$ має на кiнцевих iнтервалах не бiльше m спектральних лакун. Крiм того, гранична поведiнка перших m лакун повнiстю контролюється за допомогою належного вибору цих поверхонь i сили взаємодiї.
Mathematics Subject Classification: 35P05, 35P20, 35J10, 35B27
Посилання
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