On the spectral properties of the Bloch-Torrey equation in infinite periodically perforated domains

Abstract

We investigate spectral and asymptotic properties of the particular Schrödinger operator (also known as the Bloch-Torrey operator), $-\Delta +igx$, 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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