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arXiv · 2008.06737

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

Denis S. Grebenkov·Nicolas Moutal·Bernard Helffer
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Abstract

We investigate spectral and asymptotic properties of the particular Schr\"odinger operator (also known as the Bloch-Torrey operator), $-\Delta + i g x$, 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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Denis S. Grebenkov, Nicolas Moutal, Bernard Helffer. 2020-08-15. On the spectral properties of the Bloch-Torrey equation in infinite periodically perforated domains. https://doi.org/10.4171/ecr/18

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