无限周期穿孔区域上Bloch-Torrey方程的谱性质
On the spectral properties of the Bloch-Torrey equation in infinite periodically perforated domains
摘要：
我们研究了特殊的薛定谔算子（也称为Bloch-Torrey算子）$-Δ+ i g x$在$\mathbb R^d$的无限周期穿孔域中的谱和渐近性质。我们考虑这个算子的Dirichlet实现，并形式化[J. Phys. A：Math. Theor. 53，325201（2020）]用于研究此类算子。特别地，我们讨论了该算子谱的存在性及其作为$g\to \infty$的渐近行为.
英文摘要：
We investigate spectral and asymptotic properties of the particular Schrödinger operator (also known as the Bloch-Torrey operator), $-Δ+ i g x$, in infinite periodically perforated domains of $\mathbb R^d$. We consider Dirichlet realizations of this operator and formalize a numerical approach proposed in [J. Phys. A: Math. Theor. 53, 325201 (2020)] for studying such operators. In particular, we discuss the existence of the spectrum of this operator and its asymptotic behavior as $g\to \infty$.
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