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 [17] for studying such operators. In particular, we discuss the existence of the spectrum of this operator and its asymptotic behavior as $g\to \infty$.